Endgame Workshop: Principles for the Practical Player 1888690534, 9781888690538

Table of contents :
Introduction
Lesson I: Opposition
Lesson 2: Queen
Lesson 3: Queen and rook
Lesson 4: Rook
Lesson 5: Two bishops
Lesson 6: Bishop and knight
Lesson 7: Minor pieces
Lesson 8: Corners
Lesson 9: Queen vs. rook
Lesson 10: The Exchange
Lesson 11: Rook and minor piece vs. rook
Lesson 12: Major piece tandems
Lesson 13: Pawn endings
Lesson 14: More opposition
Lesson 15: Critical squares
Lesson 16: Outside critical square
Lesson 17: Minor pieces and pawns
Lesson 18: Quadrangle of the pawn
Lesson 19: Outflanking
Lesson 20: More complex outflanking
Lesson 21: Corresponding squares
Lesson 22: Outside passed pawn
Lesson 23: Diagonal king moves
Lesson 24: Queen against pawns
Lesson 25: Rook against pawns
Lesson 26: Minor pieces against pawns
Lesson 27: Minor pieces and pawn vs. minor pieces
Lesson 28: More minor pieces and pawns
Lesson 29: Rook tricks
Lesson 30: Various matters
Solutions to Practice Positions
Appendix: Concept index

Citation preview

Introduction 4 Lesson I: Opposition 7 Lesson 2: Queen 18 Lesson 3: Queen and rook 28 Lesson 4: Rook 36 Lesson 5: Two bishops 41 Lesson 6: Bishop and knight 48 Lesson 7: Minor pieces 56 Lesson 8: Corners 63 Lesson 9: Queen vs. rook 67 Lesson 10: The Exchange 75 Lesson 11: Rook and minor piece vs. rook 81 Lesson 12: Major piece tandems 88 Lesson 13: Pawn endings 97 Lesson 14: More opposition 105 Lesson 15: Critical squares 113 Lesson 16: Outside critical square 118 Lesson 17: Minor pieces and pawns 124 Lesson 18: Quadrangle of the pawn 139 Lesson 19: Outflanking 148 Lesson 20: More complex outflanking 153 Lesson 21: Corresponding squares 158

Lesson 22: Outside passed pawn 169 Lesson 23: Diagonal king moves 177 Lesson 24: Queen against pawns 182 Lesson 25: Rook against pawns 187 Lesson 26: Minor pieces against pawns 194 Lesson 27: Minor pieces and pawn vs. minor pieces 203 Lesson 28: More minor pieces and pawns 210 Lesson 29: Rook tricks 218 Lesson 30: Various matters 231 Solutions to Practice Positions 243 Appendix: Concept index 244

I first began teaching chess in 1972. Bobby Fischer had just won the world chess championship and several opportunities arose. I no longer had a job shelving books at the Strand Book Store, so I gave chess teaching a try. From all around New York I was inundated with students and classes. Clueless, I turned to what chess books there were, and there were many. I soon realized that few of these books were written by authors who had given chess lessons. Manuals were often too esoteric, with little thought given to the learning process, or artificially simple, with each book omitting what every other book left out. If there were an unstated educational philosophy it was that all students should learn the same material the same way. Personal differences in knowledge, skill and nature were of small moment. But then, prior to Fischer's meteoric rise, chess teaching as a profession didn't exist - at least not in America. Suddenly, there were countless individuals wanting to learn how to play. To meet their needs a whole class of educators arose. This troupe was quite innovative. While they didn't necessarily add to the theory of the game, they developed all kinds of art and new science for teaching it. I don't think I knew what I was doing in the beginning. But I kept my eyes open and tried to absorb the savvy of my colleagues. Taking what I thought to be their best ideas, adding them to my own practice, and using certain classic texts as instructional backbone, I set out trying to teach the game and make a living. Inspired by the likes of Tarrasch and Capablanca I began concentrating on the endgame. At that point I still accepted their arguments for teaching the endgame first. Essentially, they felt the endgame was more fundamental and easier to understand. "We are considering endgames first because it is the simplest part of the game," wrote Dr. Siegbert Tarrasch in the Game of Chess (1931). And from Irving Chernev's Capablanca c Best Chess Endings (1978), the Cuban great said: "In order to improve your game, you must study the endgame before anything else." Over time I varied my tactics in accord with experience. Naturally I delved into all aspects of the game as respective areas seemed relevant and fitting. But at heart I still believed in those chess warriors, Tarrasch and Capablanca, and carried their colors into battle. From 1972 until 1977 1 averaged fifty teaching periods a week, a schedule few chess educators have ever equaled. Probably about a third of those lessons focused on the endgame. Starting with a body of preconceptions - and a bunch of misconceptions - gradually my endgame course selections adapted to the accumulation of group and face-to-face sessions. Student questions had to be answered and their learning roadblocks had to be overcome. I decided that if I were to help them as players I had to satisfy them as people. So I never dismissed a psychological misgiving and always tried to move past impediments by logic, clarity, and gentle, but persistent, persuasion. Sometimes all of that even worked. Nevertheless, step by step the regimen grew, and after a point I was offering a general endgame

program. Along the way certain examples were dropped, others were added. What remained was cut down to bare bones. I especially tried to reduce complex positions to elementary ones, with fewer pieces on the board, hoping that concepts would then leap from the board. Visual patterns and designs became significant. But words were also critical. I had found that routine ways of expressing some standard chess thoughts were confusing. I'd say one thing and students would hear something else. So the language of presentation had to be simplified and defined. And there was constant repetition, relying more and more on mnemonics and other devices. I called all this, where anything might serve purpose, the endgame workshop method. Starting at a traditional place, usually with the basic or simple mates, I'd integrate examples and concepts as they made an impression. Often that veered discourse from the main path. The diet of ideas was subject to constant change anyway, since student practice always had to be reviewed, reflected and incorporated. It might mean, if logic allowed, jumping from a queen ending to one with just pawns. From that pawn ending the conversation (and I always called lessons "conversations" to emphasize the casual balance between student and teacher) could move back to the opening and how a particular system was likely to generate a certain structure. Endgame lessons could even segue into other fields. If I thought it could help the student understand, we might discuss how and why a student understands. Within reason, there were no limits. This endgame-workshop approach may be inherently unsound (who knows?), but it appeared to score in the roll of student response. And the process became quite humanistic. Paramount was student happiness. Ideals were important, but received satisfaction was more important. Still, I couldn't let it go at that. While I didn't like the concept of standard courses and fixed presentations, without consideration of individual requirements, one reality soon became clear: in order to stay in business, with allowances for human needs, I had to find an endgame treatment that worked on paper. It became clear that something like a curriculum had to be written out, especially since I was constantly being overseen by department heads and other academics, all of whom were uncertain whether chess, or any aspect of it, could be a legitimate college offering. Granted, practically none of them knew anything about the endgame, so I may have gotten away with murder. Five courses in particular forced me to spell out my ideas more concretely. They were given at New York University, the New School for Social Research, the Rockefeller Institute (I recall that two Nobel laureates sat in on the rook-andpawn sessions, though it's possible they had no place else to go), the University of Alabama at Birmingham, and Chess City, where the workshop lasted ten weeks and consisted of about a dozen players, all with a USCF rating between 16002000. The paradigms developed for those five courses, modified by a legion of experience from private lessons and seminars, constitutes the bulk of material in this book. Clearly, this is not an all-inclusive manual. Yet I can say that most of what appears here has been fashioned for real people with real problems about chess problems. True, after finishing my endgame course, it's not likely that any of my former students sensed they had solved the mysteries of the universe. But the vast majority (okay, the ones willing to speak to me afterward) seemed to feel they knew much more about the endgame phase and were confident to play it better. For most of them that was good enough. Whoever you are I'm hoping that may be good enough for you too. I hate writing

introductions. I'm glad this one is over. Bruce Pandolfini New York City February 2009

Getting started As we begin our journey it's expected there be a few definitions, setting clear certain words and expressions needed to push the discussion forward. Much of this may appear incredibly simple and even unnecessary. Yet in didactic works it can be a had idea to take things for granted. I'm reminded of an old episode from The Odd Couple, where Felix responds to Oscar's use of the word "assume." Felix points out that when you "assume" you make an "ass" of "u" and "me." Rather than risking humiliation, toward which in this introductory section I suspect I'm already well on my way, I'm going to assume nothing else and begin at the beginning. A word of advice If you haven't already done so, please familiarize yourself with algebraic chess notation, which is essential to reading this book. To be fair, you could read the book without understanding algebraic notation, but it probably wouldn't make as much sense (I'm guessing). Where can you find an explanation of algebraic notation'? There are thousands of books that explain it. But if you can't find any of them, there's always the Internet. Endgame or ending? First up are two words, endgame and ending. These terms are often flip-flopped to name the same things. Yet while ending and endgame are interchangeable I typically use them in slightly different ways. More often than not "endgame" signifies the final phase itself, after the opening and the middlegame, and "ending" a particular endgame position within the final phase. What is the endgame? Normally, a full chess game of forty moves or more is described as having three phases: the opening, middlegame, and endgame. Since the flow of a chess game doesn't automatically stop, the endgame is not necessarily independent of the earlier two phases. If anything a player's aim should be to make the endgame the logical outcome of the opening and middlegame by selecting a cogent plan and implementing it consistently. Some openings, such as the Exchange Variation of the Ruy Lopez (1. e4 e5 2. NO Nc6 3. Bb5 a6 4. Bxc6), are played with a specific view toward a favorable endgame, especially because of the pawn structure and the possibility of creating a desirable pawn majority. Indeed, activity throughout a chess game is often fueled by the interplay of favorable pawn majorities. You have a pawn majority when, over any given number of files, you have more pawns than your opponent. What's good about a healthy pawn majority is that it has the potential to produce a passed

pawn. A passed pawn is a pawn that has literally gone passed all the enemy pawns able to halt its advance toward possible promotion. That is, no enemy pawn can block it or guard squares in its path. Three phases, one game While it's convenient to think of a chess game as being made up of three separate phases, there are no clear-cut boundaries between the phases. It's customary to think of the three main stages as being connected by almost imperceptible transitions that are difficult to perceive and define precisely. To that end, it's not unreasonable to think of a chess game as an organic whole, each phase closely integrating with the others. Phase by phase by phase Various characteristics tend to mark the three phases and support their distinctive descriptions. The opening is viewed as the building phase. The middlegame is stamped by further development and the realization of correct planning. The endgame is the phase where one can finally exploit the advantages accumulated earlier, in the opening and middlegame. Beyond this theoretically woven relationship, however applicable it might be for a particular case, it's still useful to make additional general statements about endgames and their distinguishing markings. They commonly differ from openings and middlegames in at least some of the following ways. These, of course, are not hard and fast rules, some overlap, and other tendencies could be included for certain types of endings. But this is a good place from where to branch out. Endgame characteristics (for most endings, though not all): 1. They generally have reduced forces on the board. 2. They usually don't have queens, though not necessarily. 3. They lend themselves to exact calculation. 4. They tend to emphasize material advantages. 5. They may impact relative values, especially where pawns go up and minor pieces down. 6. They have their own principles, which don't necessarily apply earlier. 7. They commonly play off tactics that have special resonance in situations of reduced force. 8. They can transform weak pawns, away from the main theater, into dangerous deflecting decoys. 9. They routinely revolve around converting an extra pawn into a win or thwarting that prospect. 10. They often rely on timing, where being first (or being second) or getting somewhere first (or

getting somewhere second) may decide the game. 11. They not infrequently depend on situations where it's desirable not to move. 12. They typically require the active participation of the king. King activity Of the above twelve statements, it's the last with which we are most concerned in the next part of our discussion. Because in the endgame the material on the board is apt to he reduced, and a surprise mating attack is less likely, the king is usually able to play a more active role than in the opening and middlegame. Generally, it should he developed toward the center or some other important area. That way it can support attacks and strengthen fragile spots and zones. Nonetheless, if both White and Black have the same objective, to get the king to the center, or toward a high focus spot, it's probable that at least one of the two players won't succeed. An important question therefore arises as both kings approach each other: How can you determine which king will be more powerful? The answer lies in the special nature of the relationship between the two kings, where neither king can move onto a square the other attacks. That relationship, once it's obvious that each king is definitely affected by the other, is known as the opposition. In endgame situations with only kings on the board, the opposition connotes both a relationship and a measure of distance between the two signature pieces. Note: Throughout this book the words White (white) and Black (black) will be distinguished by the use of capitals and lower case letters. Capitals will be used when White and Black are nouns, designating a player or side, as in "White moved to d4." Lower case letters are used when white and black are colors, as in "the white pawn moved to d4." Thus we could say "Black's king" or "the black king" and mean the same thing, being just as correct in either case. Consider Diagram I. If it's White's turn to play, which king stands better'? A cursory analysis shows that the black king does, because if White plays I. Ke4, Black can choose between I...Ke6, stifling the white king, or I...Kc5, advancing on it. Moreover, if White instead tries 1. Kc4, Black can once again select stances: the defensive I...Kc6, holding the fort, or the aggressive I...Ke5, hoping to breach White's position. Although White goes first, it's Black who decides what's to happen. 1) The kings stand in opposition

In this case, and in analogous ones where White also must move first, it's said that Black has the opposition. Having the opposition is comparable to having the advantage. In the particular case of Diagram 1, Black's opposition is direct. That is, Black has the direct opposition. Oppositional rules Put simply, for straight-line (or true) oppositions, kings stand in opposition if they: 1. occupy squares of the same color, and 2. are separated by an odd number of squares (one, three, or five) along the same rank, file, or diagonal. 2) Distant opposition

In Diagram 2, the kings stand in distant opposition. Whoever doesn't move has the opposition and, of

course, the advantage. In Diagram 3, the kings stand in diagonal opposition. Once again, whoever doesn't move has the opposition and the advantage. In Diagram 4, the kings stand in distant diagonal opposition (a very distant diagonal opposition at that), separated by five squares along the a8-h1 diagonal. Again, whoever doesn't move has the opposition and the advantage. 3) Diagonal opposition

For straightforward oppositions, where the kings already occupy the same rank, file, or diagonal, you have the opposition, which, again, is synonymous with saying you have the advantage, if the above two conditions are fulfilled and it's your opponent's turn to move. In related situations, where the kings occupy the same straight line (either vertically, horizontally, or diagonally) but do not already stand in opposition, whoever moves can take or "seize" a form of the direct or distant opposition. Thus, in Diagram 5, whoever moves takes the opposition. If it's White to move, Kb5-c6 takes a diagonal opposition, as does Kb5-a4. If it's Black to move, Ke8-d7 gives Black the diagonal opposition. 4) Distant diagonal opposition

But the already mentioned kinds of opposition available in Diagram 5 aren't the only possible oppositions to be taken. In addition to the diagonal oppositions cited, White to play can take rectangular oppositions (also known as oblique oppositions) by moving the king to a6 or c4; Black to play can take a rectangular opposition by placing the king on t7. 5) Taking the diagonal opposition

Rectangular opposition The kings don't have to occupy the same straight line to be in opposition. Rectangular opposition is a special case, and must be considered separately. If the kings are not on the same straight line, but are on squares of the same color, then in your mind draw the smallest possible rectangle containing the two kings. If both the long and short sides of the rectangle are odd in number, the kings stand in rectangular opposition, and whichever king doesn't move has the advantage (has the opposition), as in Diagram 6.

6) Rectangular opposition

Stopping forward advance Another way to look at having the opposition is this: If you have the opposition, especially along a straight line (on a rank, tile, or diagonal), your king ultimately can stop your opponent's king from moving along that very line. For example, in Diagram 7, Black has the opposition, which means it's White's turn to move. If the white king moves to d7, advancing along the d-file, Black's king can stop White's further advance on that line by playing to d5. 7) Distant opposition

Or, in Diagram 8, if Black has the opposition, and therefore it's White to move, White's king in the end can be prevented from moving along the fourth rank after 1. Kb4 Kf4 2. Kc4. The white king stops on c4 after 2...Ke4.

In Diagram 9, with White to move, it's already clear that White's king must abandon the fourth rank, it being unable to move to M. 8) Very distant horizontal opposition

A further example is seen in Diagram 10, with the kings standing in diagonal opposition. The white king can't move to d5 and must abandon the a8- hl diagonal, or move backward on it ineffectually, retreating to V. Thus, in all the examined cases, it's as described: the side with the opposition can stop the forward advance of the enemy king along the line of the opposition. This way of looking at the opposition does not apply to cases of rectangular opposition, since, to begin with, the kings are not positioned on the same straight line. But what's clear is that, on a board with just two kings and nothing else, if the kings stand in opposition, the side having the opposition can maintain it permanently, if so desired, across and over the whole board. In that sense the board can be viewed as an oppositional field, with correlated oppositions in play over all sixty-four squares. The oppositional field The oppositional field refers to the interrelation of every possible opposition, taken one to the next, extending across the playing surface. For example, if, on the line of mutual occupation, a player gets a distant opposition with the kings separated by five squares, he or she can convert it, as the opponent's king ap proaches, to a distant opposition of three squares. Thereafter, if the opposing king steps even closer along the line in question, that distant opposition can be converted to a direct opposition. By the same token, if the opposing king steps backward, it should be possible to keep some form of opposition, with several options. 9) White to move

10) Diagonal opposition

If in Diagram 11, for instance, White plays 1. Kg7, Black can maintain the opposition by moving the black king to any of four squares: 11) White to play

(I) c3, converting to a distant diagonal opposition; (2) e5, keeping a diagonal opposition; (3) c5, assuming a rectangular opposition; or (4) e3, taking a different rectangular opposition. In real situations (where other forces are on the hoard and interact), ifyou already have the opposition, you may want to keep it until you've attained certain goals. Once your mission is accomplished it might not be constructive to maintain the opposition any further. Having achieved your aims you can then abandon the opposition to your advantage, and certainly without incurring disadvantage. Accordingly, it's useful to describe oppositions as being meaningful or meaningless. A meaningful opposition is worth having; it can affect the course of the game. A meaningless opposition is not worth having; it has no effect on the outcome of the game. Indeed, it's often possible to have a meaningless opposition and be dead lost. At other times, a meaningless opposition is merely a temporary one, which must be discarded at the beck and call of the player with ultimate control. (Effectively, ultimate control is what a chess game is really about.) If you should have a meaningful opposition, you can keep it to a desirable point, surrendering it when you no longer need it. Clearly the opposition is a kind of negative concept. In most chess situations, and in many other aspects of life, it tends to be desirable to have the move so you can strike first. But when it comes to the opposition, it's preferable to go second in order to exploit what the opponent has done or conceded (the information he or she has released by having made a move). In a world dependent on information and its processing, it's not only good to have a meaningful opposition, it's also good to know you have it. Zugzwang The opposition is therefore a kind of zugzwang. This is a German word and it means something like "compulsion to move." A true zugzwang refers to situations where neither player wants to move, since

moving means losing the game or losing the ability to win (drawing, when otherwise you'd be winning). So a zugzwang is really a mutual zugzwang, or what some theorists refer to as a reciprocal zugzwang, with the concept being illustrated in Diagram 12. 12) Zugzwang

Diagram 12 displays a true zugzwang: neither player wants to move. If Black moves, Black loses, and Black doesn't want to lose; if White moves, White draws, and with an extra pawn, White doesn't want to draw. In ordinary chess parlance, however, zugzwang doesn't have to be mutual. It tends to refer to positions where a particular player doesn't have any good moves, rather than both players not having any good moves. Endgame purists don't particularly like this generalized usage of the word zugzwang (you should see the letters I get). They prefer labeling situations where it's undesirable for just one player to move as being a squeeze. Diagram 13, illustrates a squeeze. There is no mutual zugzwang. Black is at no disadvantage to move, winning with or without the move. White, however, doesn't want to move, and, in fact, is lost whether going first or second. Thus there are four notable kinds of endgame situations: (1) Neither player wants to move (a zugzwang); (2) Only one player doesn't want to move (a squeeze); (3) Both players want to move; (4) Either player can move without significant consequence. 13) White is squeezed

In some cases people misuse the word "zugzwang" to signify a situation where one player is losing, with lots of bad or immaterial moves available, but there isn't an actual zugzwang or squeeze. For example, consider the final position from a game played between Samisch and Nimzowitsch at Copenhagen in 1923 (Diagram 14). Technically, it's not a zugzwang or a squeeze. White has moves that don't immediately worsen the situation; it's just that there aren't many useful ones. But it's a memorable portrayal of White's unhappy circumstances, true zugzwang or not. However, this is no place to zug this or zug that. We're merely setting groundwork for some simple mates and tactics. Yet before we go further, let's raise a rhetorical question and try to answer it. Positions with just kings? Why all this talk about the opposition and use ofthe king, when no other forces are on the hoard and the game is theretore a draw anyway'' With just two kings on the hoard, the game is drawn by insufficient mating material, and that's a rule. Nevertheless, on an otherwise empty chessboard, there are a number of reasons for such kingly exploration. 14) A famous "zugzwang" position after 25...h6! (0-1)

First, with nothing else on the hoard, it's easier to understand the kings as existing in a relationship with each other. Having other units on the board night only serve to complicate the issue. Second, it enables us to understand that the king is actually a strong piece. This is a helpful truism, since most of us are bombarded by bromides warning against king activity in the opening. Naturally, with so much emphasis on defense and safety, it's easy to overlook the king's attacking capabilities, and such neglect could he fatal in the endgame, when king participation is virtually essential. Indeed, for some of the most basic of checkmates, such as that with a lone queen and king against a lone king, one indeed needs the friendly king to guard certain squares and keep the opposing king trapped. Third, the import of the king goes far beyond the basic mates. The main body of endgame theory has to do with converting an extra pawn into a win. The friendly king is typically needed (though, of course, not always) to support and empower that enterprise. To be sure, comprehending the nature of how the kings respond to each other, with no interfering forces, equips us to understand more sophisticated facets of endgame play. Those same aspects are definitely better grasped from a solid base of fundamental principles, built on an understanding of how kings contend in hand-to-hand fighting with the opposing king. To cap our preparatory discussion, let's take a look at the so-called opposition game (Diagram 15), which is a convenient way to introduce a few concepts. The opposition game The opposition game has to do with the fight for certain squares, just as the use of the opposition in real chess-play does. In Diagram 15 you have White. To win from this position you must fulfill a task. That task, as prescribed for this situation apparently arbitrarily (hut actually with hidden purpose), is to occupy either dR or tK with your king. For this example we call these two squares critical squares: if the superior side's king can occupy either of them, the game is won. Note: A fuller explanation of critical squares, as it applies to actual positions, will be put forth later. But to clarify a point for now, the defender doesn't have to occupy either of the critical squares so

designated in Diagram 15. He or she merely has to prevent the attacker from doing so. Why this task? Because it's not dissimilar to basic endgame situations in which a lone king must stop an advancing pawn supported by its king, as we shall learn from subsequent investigation. If in Diagram 15 White goes first, he or she can take the distant opposition with 1. Ke2!. That move signals a critical opposition (in many instances, the middle opposition is the critical one), smack dab between the two goals, d8 and f8. What can Black now do'? It seems Black has three basic choices, though, because of the board's symmetry, the choices really reduce to two options, since (b) and (c) offer opportunities for analogous responses. Black can play (A) I...Ke7; (B) I...Kd7 (or I...Kd8) (C) I...K17 (or I...Kf8) 15) The opposition game

After (A) I...Ke7, a sample line might go 2. Ke3 (converting to a distant but closer opposition) 2...Ke6 3. Ke4 (taking the direct opposition), and now, disregarding retreat to e7, Black has a choice: to play to the d-file, or to the ffile. If Black plays to the d-file, 3...Kd6, White has a turning maneuver (a tactic by which the attacking king uses the opposition to advance meaningfully to a critical square), here onto the f-file and the fifth rank, 4. Kf5. This maneuver aims the white king straight at f8, occupation of which wins the opposition game. If Black plays 3...Kf6 (instead of 3...Kd6), White has a different turning maneuver, 4. Kd5, aiming alternatively at d8. Thus Black has little choice, and might as well play 3...Kd6. After 3...Kd6 4. Kf5, play might conclude 4...Ke7 5. Ke5 (regaining the opposition meaningfully) 5...Kf7 (or 5...Kd7 6. Kf6) 6. Kd6 (a turning maneuver) 6...Ke8 7. Ke6 (retaking the opposition, most meaningfully) 7...Kf8 8. Kd7, and wins next move by occupying d8. Of course, after 8. Kd7, Black could take the opposition, 8...Kf7, but that opposition is meaningless, it

being unable to stop White's king from advancing to d8 and winning the opposition game. Again, if Black tries 3...Kf6, White has 4. Kd5, a turning maneuver leading to similar results going the other way. The opposition and turning maneuvers are thereby employed to gain ground. That is, whenever Black tries to stop the white king from advancing, White first retakes the opposition, poised to continue the advance thereafter, playing off Black's inability to protect both of the critical (winning) squares, d8 and f8. Meanwhile, if after 1. Ke2, Black answers with (b) I...Kd7 (or 1...Kd8), White doesn't have to wait to play a turning maneuver. Instead White can immediately play a turning maneuver to 13, heading for f8, eventually winning in accordance with the above variations. And no better is (c) I...Kf7, when the turning maneuver, 2. Kd3, reveals analogous designs on d8. Turning maneuver In the oppositional dance between the two kings, a turning maneuver allows the attacking king to advance to a critical square. That cedes the opposition temporarily and meaninglessly. If the defender then takes the opposition, he or she will soon have to abandon it anyway, in order to stop the further advance of the attacking king. Practice this Practice this exercise by picking out any two same-color squares on the same rank or tile, separated by a single square. Then place the kings in opposition, with your opponent to move. Or place them not in opposition, with you to move so that you can then take the opposition. Using the opposition as a tool (as one does in actual endgames), and adapting similar variations to the above analysis, try maneuvering to occupy one of the two same-color related squares. It's a good way to prime for what the kings can and can't do. Enough of this theoretically abstracted talk. At this point let's begin to explore a number of positions to show some of the abilities pieces have in conjunction with the friendly king, especially concerning their talents for mate and winning quickly.

Mating without pawns Traditionally, there are four basic mates, checkmates that can be given by the king and one or two supportive pieces (with no pawns present). They are (I) king and queen vs. king; (2) king and rook vs. king; (3) king and two bishops vs. king; and (4) king, bishop and knight vs. king. While not properly categorized as basic mates, several other mates, not requiring the friendly king, but displaying pieces in combination, are also worth knowing. These include mate with (I ) two rooks; (2) queen and rook; and (3) two queens. It's not just about basic mates The basic mates and their relatives are important because they show the powers of the pieces in their purest form. Curiously, most of endgame study has little to do with the basic mates. Instead, the overwhelming bulk of endgame play, as said earlier, is concerned with the promotion of an extra pawn into a queen, or with the thwarting of the attempt to win with an extra pawn. (While endgame theory also naturally looks into equal situations, as well as those with disparities of two pawns or more, many of the thematic positions springboard from the battle over converting a single plus pawn.) Still, even with all the emphasis on promoting an extra pawn, it helps to understand what the pieces can do by themselves, with no pawns present (or only inconsequential ones). It's intriguing that, though knowledge of the basic mates underlies the winning process, the basic mates almost never appear in serious contests. Strong players seldom bother to play out positions a queen or rook down. After all, any experienced opponent good enough to get a rook ahead probably knows how to win from such a superior position by force (by being able to control the outcome and see the moves leading to it). As a rule of thumb, however, newcomers and other inexperienced players should play out all lost positions until they learn how to save and win them. Generally, one is not going to become a good endgame player unless one puts in his or her time, which translates into losing many games. Observation: Losing is a good way to learn how to avoid losing. Forced replies Your move is certainly forced when you have no other legal play. But a move can be considered forced for practical reasons if you have no other reasonable alternative, when no other move could do any better or as well as the move it seems you're compelled to play. In such instances, a move is deemed forced if it's really the only move that makes sense. While the basic mates of king and queen and king and rook are forced wins, most experienced players confronted with the losing side wouldn't bother to play them out. Veterans wouldn't waste their time defending against two lone bishops either, since the technique needed to implement that mate is also quite easy and definitely forced. True, the possibility of the basic mate with two lone bishops doesn't happen that often (whereas opportunities to mate with just a queen or rook do occur frequently). But then it's unusual solely for one player's

bishops to survive all the way through a full game of forty moves or so, while every other unit for both sides has come off the board. If there's a basic mate that strong players do tend to defend toothand-nail, even though it also is a forced loss, it's that of king, bishop and knight against king. Some aspects of it require exact maneuvering, and if the opponent has a shortage of time on the clock, playing it out could result in time forfeiture (thereby drawing) or the superior side going awry and exceeding the fifty-move rule, also drawing. But don't count on it. The fifty-move rule If fifty moves have been played, with no unit being exchanged, and no pawn being moved, a player may claim a draw. The player should announce the intention to claim a draw before playing his or her 50th move. In tournament competition, the claiming player should also be able to back it up by producing an accurate score sheet. Naturally, the inferior side is the one usually seeking such a draw, although there may be an eccentric or two, somewhere on the planet, more concerned with getting a good laugh than gaining a good half-point. Before proceeding, we're going to explain a few more terms and notions to establish underpinning for what follows. The edge When we refer to the edge we mean any of the chessboard's outer rows, including the a-file, the eighth rank, the h-tile, and the first rank. A row Any rank or tile is a row. If we're talking about use of the rook and queen on open files and ranks, it can he handy to refer to lines of power and potential movement as rows, instead of ranks and tiles. Driving the king When friendly chess units force the enemy king toward the edge or to a particular corner, by checking and guarding potential escape squares, we say they are driving the king back. This is a common theme in all four of the basic mates, as well as in many other simple mates. Since, for these core mating patterns, the lone king can't be mated in the center of the board legally, the friendly forces often have to work at driving the lone king from the center toward the edge, and from there, toward one of the corners. Friendly forces When we say friendly forces we mean to indicate the side or perspective from which we're playing out the position. More often than not, this especially, though not exclusively, refers to the side or player having material superiority. Generally, the superior side is also the attacking side. Meanwhile, the other player, the infe rior side, can he looked at as the enemy, the opponent, the defender, or the losing side, whether that player winds up losing or not. To be sure, if we're concerned with trying to draw, the friendly side is then the inferior one. I thought it best to get all this out of the way now,

before we make any more enemies of any kind. Use of descriptive terminology Descriptive notation has become obsolete in today's world, even though some of the classic texts in English have yet to be converted to algebraic notation. While algebraic is the standard, the use of descriptive terms (though not descriptive notation) still has a place. In some cases descriptive terminology actually conveys very useful information. For instance, is it better to refer to "problems of the a- and h-pawns," or "problems of the rook pawns'?" Certainly, the latter expression is more elegant and inclusive. Furthermore, if talking about occupying the seventh rank with a rook, a valuable Nimzowitschian concept, it only promotes confusion to insist on describing the placement by referencing the Cartesian grid of algebraic description. So when a black rook moves from d8 to d2, for example, we describe the rook as occupying the seventh rank, even though, following algebraic notation strictly, it would really he placing the rook on the second rank. For such and similar renderings, obviously the general description takes precedence over the specific. That is, sometimes we may wind up understanding and expressing more and better if we point out the overriding concept than a particular incidence of it. Of course, sometimes it works the other way, too, and the specific, not the general, is the right way to go. Let us hope, throughout our little book, we choose wisely. The cutoff A key weapon in many endings is the idea of the cutoff. An instance of a cutoff would be where a rook or queen is positioned to control a file or rank, preventing the opponent's king from reaching freedom (or aggressively participating). That is, a king cut off by a rook or queen is unable to cross the guarded row of the cutoff and take active part. Cutoffs can occur in various ways. The following position offers an illustration (Diagram 16). White cuts off the black king at the g-file with 1. Rg4!. That forces 1...Ke1, whereupon mate ensues, 2. Rgl mate. 16) The cutoff

Sometimes the cutoff happens along a rank. In Diagram 17, White's rook can indeed cut off black's king along a rank, 1. Rh5!, preventing the king from moving up to support the advance of the spawn. After this cutoff, the winning technique consists in waiting till the pawn reaches its sixth rank, whereupon a rook attack along the rank will win the pawn. 17) Cutoff along the rank

After 1. Rh5!, the game might go: I ...a4 2. Kg7 a3 3. Rh3, and the pawn is lost (if 3...a2, then 4. Ra3 does the trick). For clarification, if Black doesn't try to advance the pawn, White's king eventually maneuvers into position to stultify productive efforts, as after 2...Ka6 3. Rd5 (placing the rook where its cutoff won't interfere with the white king) 3...Kb6 4. Kf6 Ka6 (if 4...Kc6, then 5. Ra5 wins the pawn immediately) 5. Ke5 Kb6 6. Kd4 Ka6 7. Kc3, and the pawn soon falls. To be sure, the queen has the same cutoff power as the rook and more, since it also moves along diagonals. 18) Trapping along the edge

In Diagram 18, White's queen can cut off the black king at the second rank, 1. Qh2!, trapping it along the first rank's edge. Thereafter, White's king moves into position along the third rank, and mate ensues. (Note that throughout the text "cutoff" is used as a noun, and "cut oil" when functioning as a verb.) A possible conclusion is I...Kfl (or I...Kdl 2. Kd3 Kcl 3. Qc2 mate) 2. Ke3 Kel 3. Qe2 mate (as well as 3. Qg I mate and Qh I mate). Options In the case of the queen, you maybe able to choose between a few cutoff possibilities. Consider Diagram 19. Here White has two possible cutoffs: 1. Qa7 and 1. Qg2. On the surface, 1. Qa7 looks excellent, in that it confines Black's king to the eighth rank edge. After I...Kg8 2. Kf6, White mates next move. But a better first-move cutoff is 1. Qg2!, seizing the g-file. That constrains Black to play I...Ke8, which leads to 2. Qg8 mate. 19) A choice of cutoffs

Look for a better move Intuition is a mysterious thing. It often leads us to the right place, however it does that, but certainly not all the time. If it generates what seems to be a good move, there's a tendency to play that move without a lot of confirming thought. The result is that other promising moves may go unexplored. As a good habit one should routinely try to find at least a couple of moves that do the same things, hoping to compare them. Much of chess thinking is just that: comparing moves. The second world champion, Emanuel Lasker (1868-1941), summed it up when he supposedly said " /f you see a good move, look for a better one." I suspect he was onto something. Patterns and repetition Chess is a highly graphic game, where forces often assemble in unforgettable patterns. Certain ideas can sometimes be described in terms of how pieces and pawns line up, or on the tracings of their movements. Throughout this text emphasis will be placed on those patterns, arrangements, and vectored paths that bring out definite motifs, hoping to make them visually more memorable. To that end, some of the themes may be repeated for reinforcement. Repetition, if it doesn't put you to sleep, over time can make the artificial be intuitive. Worse, even though it's terribly unexciting, it usually works. King and queen vs. king There are several ways to bring about this basic checkmate. In all cases, the losing king must be mated by being checked as it occupies an outside row. You can win by: (A) a support mate, where the king protects the queen (Diagram 20); (B) a right triangle mate, where the queen checks along an outside row, so that a right triangle could be traced over the three pieces (Diagram 21); 20) A support mate

(C) a cornered mate, where the losing king is trapped in the corner, obviating the need for the friendly king to oppose it directly (Diagram 22). (D) an outer row mate, where the queen must guard an escape square on the next row in (Diagram 23). Diagram 20 shows an ordinary support mate. The same mate would result if Black's king were on either c5 or c7. In Diagram 21, the three pieces line up in the shape of a right triangle. Other right triangle mates would ensue if the queen were instead on h8, h4, h3, or h2. 21) A right triangle mate

Diagram 22 shows mate to a cornered king. The queen could deliver the same mating check from h3,

h5, h6, h7, or h8. In Diagram 23, White's king is mated along an outer row, with every square in the overall pattern being guarded just once (no overkill). The queen guards g4, as well as all the squares on the h-tile; the black king guards g3 and g2, and the queen doesn't help to guard those two squares. This type of mate, where no square in the pattern is guarded more than once, is called a pure mate. 22) A cornered mate

General approach Getting to these final setups or comparable ones is not hard. There are only a few ideas to play with. The plan is to drive the opposing king to the edge where it can be mated in one of the four initially defined ways. When first learning how to do this it helps to divide the approach into separate stages, though actually the speediest way to mate might require a mixing of stages. For the first stage, the queen drives the enemy king toward the edge. In the second stage, the friendly king is brought into position to support mate. Finally, the mate is given. But by mixing the first two stages, using the queen somewhat, then the king, then the queen, then the king, it's often possible to mate sooner. Of course, we must also factor in the defender's replies. You never know where those might lead. 23) An outer row mate

The queen's method Since it's not uncommon for the uninitiated to proceed by giving queen checks fruitlessly and endlessly, it helps to have a technique to go about actually mating. One way to use the queen more effectively than merely checking with it is to rely on confining cutoffs that drive the enemy king toward an outside row. If a tempo is needed, the friendly king can be moved up, since it needs to be brought into position anyway. In order to confine the enemy king along an edge, the queen should occupy the next row in from that desired edge. The only caution being that the losing king must have at least two squares to play with to avoid being stalemated. Once the enemy king is so confined, but so that it can't be stalemated, the friendly king can then be stationed, eventually to a square on the third row inward from the edge occupied by the defending king. As already indicated, the two stages can he mixed into one overall approach from the beginning. Let's play out a position to see how it's done, keeping in mind that almost any method is better than no method. Knight's distance away The initial placement of the queen could be viewed as creating a cage, where the enclosed formation of controlled lines traps the enemy king inside a smaller, cordoned off area. A typical way to establish such a cage is to place the queen a knight's distance away from the enemy king. To be sure, it's often useful to describe how far away a queen is from the enemy king (or from a certain square) by referring to this term, which is also a measure of distance. A queen is a knight's distance away from the enemy king (or a knights jump away) when, if it were a knight, it would be giving check. In Diagram 24, let's say that Black begins with 1...Qf5, which is not necessarily the best move, but it's a serviceable one for the purpose of this explanation. This move places the queen a knight's distance away from the white king. It also establishes barriers trapping the enemy king within an imagined cage or box, here running from a5 to f5 and from f5 to fl (additionally, though not factored into the cage concept, the queen also takes away squares along the b 145 diagonal). At this point the white

king's available territory is reduced to sixteen total squares. 24) A method

Other confining first moves would be I...Qb5 (reducing available territory to fifteen squares, with the aid of the king); I ...Qf3 (narrowing available space to twenty squares); I...Qe2 (downsizing also to twenty squares); I...Qe8 (offering twentyfour squares). Naturally enough, those first moves work, too. There are various mating sequences after I ...Qf5. One possibility goes: 2. Ke3 Kg3 3. Kd4 Kf3 (or 3...Kf4) 4. Kc4 Ke3 (anticipating white's king going to c3, so that a right triangle check could follow) 5. Kc3 Qc5+ (producing a right triangle check) 6. Kb3 Kd3 7. Kb2 Qb5+ 8. Ka2 (after 8. Kc 1, Black's queen plays a waiting move along the b-file, making sure not to stumble into stalemate by moving to b3, say 8...Qb6, when 9.KdI allows 9...QhI, a right triangle mate) 8...Kc3, and this brings us to the position of Diagram 25. The one-two-three formula In Diagram 25, if the white king on the a-file is said to occupy a "first row," the black queen can be said to occupy a "second row" (here, the b-tile), which is the second row inward from the edge occupied by White's king, while the black king occupies a "third row" (the c-tile), which can be described as the third row inward from the mating edge (the a-file). 25) The one-two-three formula

This type of mating arrangement, where the losing king occupies the edge, the queen occupies the next row inward, and the winning king occupies the next row in after that, is known as the one-two-three formula. Say it a few times and you won't forget it. The position of Diagram 25 might conclude 9. Kal Qb2 mate (a support mate). No better is 9. Ka3, allowing mate by a queen check at b3 (a support mate), a5 or a6 (where both of the latter would be right triangle mates). Watch out for stalemate When applying any approach, one should be careful about being too methodical or automatic. For example, in using the queen as a driving mechanism, torcing the enemy king hack (by constantly moving the queen a knight's distance away), it would be easy to wind up getting too close, allowing stalemate. 26) "The queen is too close

In Diagram 26, if it were Black's move, the game would be drawn by stalemate. If it were White's move, however, mov ing the queen back one square along the g-file (or to g5, g6, g7, or g8), similar to a variation analyzed in Diagram 24, keeps Black's king confined and avoids stalemate. After 1. Qg4! Kh2 2. Kf3 (occupying a corner of the inner box, running from f3-f6-c6-c3) 2...Kh1 3. Qg2 is mate. Invading to avoid stalemate Sometimes avoiding stalemate is not a matter of withdrawing the queen. Rather it may have to do with putting something in the way, such as the invading king, which winds up rendering previously guarded squares suddenly unguarded and therefore available to the troubled king. In Diagram 27 White merrily plays 1. Kb3!, avoiding stalemate (it would be stalemate if White blindly played 1. Ka3??) by obstructing the queen's control of the b-file. After I...Kb1, White has 2. QhI mate. Whatever you do, don't forget about the queen's diagonal power. Who knows: that in itself (the queen's diagonal power) could one day save your life (said for those chess players who favor hyperbole). 27) White mates in two moves

Cutting off at the pass We've already seen that sometimes the queen gets too close and must step back to offer breathing room for the enemy king. On other occasions the enemy king has plenty of breathing room and attempts to flee. Instead of chasing the enemy king, however, time (if measured in moves or tempi) might be saved by shifting the queen ahead, cutting off the escaping king and forcing it back toward the friendly king, as in Diagram 28. 28) Avoid a chase

Rather than chasing Black's king down the board (I. Kf6 Kh4 2. Kf5 Kh3 3. Kf4 Kh2 4. K13 Khl 5. Qg2 mate), it's over faster and sooner after 1. Qg3! (cutting off) I...Kh6 2. Qg6 mate (or 2. Qh4 mate). But this position didn't happen out of nowhere. It follows very logically from Diagram 29, as this becomes that," Diagram 29 becoming Diagram 28. (As a habit of mind, chess players are always trying to figure out how positions arose and where they logically came from, since the process brings with it a wealth of additional information.) 29) White to play and mate in five moves

In Diagram 29, after 1. g7 Kh7 2. Kf7 Kh6 3. g8/Q Kh5, White doesn't chase Black's king but forces it back, 4. Qg3 (Diagram 28), with mate next move.

Redactive instruction Chess players are always trying to look ahead. Chess teachers are often trying to look back. Since the early 1970s, when I introduced the expression in a class given at the New School for Social Research in New York City (1973), I have called the method of teaching students to look backward to a position's earlier stages as reductive instruction, which is merely a form of reverse or inverted reasoning. Do you know how to solve this? Diagram 30 offers a position where the defender has very few possible moves. A prudent way to tackle such a situation at first, after you've ascertained that the position indeed falls into the class of problems where the defender has few possibilities, is not necessarily to look for your next move. Instead it might be more productive to consider where your opponent must move and what the situation will look like after that. Once you see where the opponent has to go, then you might be able to go back to thinking about your own first move, hoping to figure out how to take advantage of it. Applying this approach to the position at hand, White should see that Black has but two moves, Ke8d8 and Ke8-f. Before we analyze those moves, let's introduce two related concepts: candidate moves and mental lists. Candidate moves and mental lists A move worthy of being considered for analysis and possible play is called a candidate move. In Alexander Kotov's famous book Think Like a Grandmaster, he proposes making a mental list of candidate moves, typically consisting of three or four plausible possibilities. Then he suggests arranging the list in a preferred order, with the idea of analyzing each option on the list. By making a mental list, two good things tend to happen. First, the mere act of making a list leads to an initial comparison, which could result in the list's reduction, where moves not up to the quality of the others are winnowed out. So it functions as a filter. Second, in knowing that the list exists, after mulling the first idea and getting nowhere with it, one recognizes that there are still other moves on the list to be considered. Without having made this list at the start of the analysis one could easily become engrossed, forgetting there are other moves to fall back on. So the list of candidate moves can function as both an analytic tool and a handy reminder. Don't try to analyze two moves at once So let's analyze Diagram 30, starting by considering Black's possibilities. Black has only two candidate moves to ponder. In fact, he has only two possible moves to play, clearly a position with limited choices. Black can move the king to d8 or f8. Since we can't analyze two moves at the same time that is, people with normal aptitude can't - let's start with one possibility and come back to the other. Imagine that the black king moves to d8. (Reminder: when referring to the side playing the

move, "Black" is capitalized; when describing a unit by its color, "black" is lower case.) When the king is on d8, the queen could mate by going to b8. (Yes, it could also give mate at that point by occupying d7.) Pushing ahead, imagine that the black king instead had moved to f8. The queen could then mate by going to h8. (Yes, the queen could also mate at that point by going to f7.) 30) White mates in two moves

A natural question emerges. Going back to the original position, can the white queen move to a place that attacks mating squares in both directions'? An obvious idea is to position the queen to hit both b8 and h8 (there being no way to attack d7 and f7 simultaneously). Since, as we will see, many wonderful things happen from the center, especially with regard to the queen, it should be easy to see that 1. Qe5! answers the need. That is, after 1. Qe5, if I ...Kd8, then 2. Qb8 is mate. If instead Black plays I...KfB, then White wins with 2. Qh8 mate. Stay with the position a bit more and you'll possibly find that 1. Qb2 as well as 1. Qh2 accomplish the same task: they both lead to mate on the next move. Symmetrical beauty The answers to the above problem display marvelous symmetry. Symmetry is an aspect of beauty, and the beauty of certain patterns reinforces the concept that chess is an art. That is, many solutions to chess problems offer symmetrically proportioned arrangements and reflect mirrored balance. What works on one side of the board may also work on the other. Indeed, in Diagram 30, the pattern created by the two crossing diagonals b2-h8 and b8-h2 is striking and geometric. It seems to trace a giant "X" crossing the board, with e5 in the very middle of the axis. Queen centralization From the center the queen is a powerhouse. In the opening phase the queen doesn't get to hang out in the center much. Too many enemy units can attack and drive it away. Time is then wasted moving it to safety. But in endgames with fewer units on the board it's often a lot harder to drive the queen from the center. If a queen can establish itself in the middle, or near it, the effect can be devastating.

Moreover, it typically signifies that the enemy queen is going to have a reduced role. Thus we see a leitmotif of queen endings: To hamper the enemy queen, centralize your own. A related, but slightly different position to Diagram 30 is shown in Diagram 31.Once again, White mates in two moves, and once again, Black's king has but two moves. This time White's queen prevents one of the moves from being played at all (to g8), as it finds a station from which to exploit the other place Black's king must go (e8). With 1. Qc4!, White forces 1...Ke8 2. Qc8 mate. 31) White targets g8 and c8

Alternating queen and rook checks Let's shift our focus a bit, from the basic mate of king and queen vs. king, to another elementary mating idea that's easy to grasp and has superb utility. Although not a basic mate, the queen and rook are a wonderful team, and how they operate together is useful to know. The following example provides a case in point. From Diagram 32, White drives the enemy king toward an outside row (either the first rank or the h-file) by alternating queen and rook checks. Here there are two ways to do it in four moves. In the first method (method A) the queen and rook rely on mutual protection. In the second method (method B) the queen merely has to protect the rook. 32) Alternating queen and rook checks

Method A) 1.Qf5+ Ke3 2.Rd3+ Keg 3.Qf3+ Kel 4.Rdl mate. Method B) I.Qe6+ Kf4 2.Rf5+ Kg4 3.Qg6+ Kh4 4.Rh5 mate. 33) White mates in two moves

A bad habit I can't help indulging is recalling positions for tangential reasons. Here, in Diagram 33, the trigger is the material, the queen and rook mating force. One of the original issues of Chess Review, back in the 1930s, offered a version of the following two-move checkmate. White already has crossing cutoffs, the queen along the sixth rank and the rook along the f-file. The key is looking ahead, instead of finding White's move, seeing where the black king has to go, and making sure to cope with that future setup. Well, if it were Black's turn, he or she would have to play 1. Kd5, threatening to escape at c4. So White's move needs to deal with that fleeing possibility. The correct play turns out to be 1. Qa6!, guarding c4, when I...Kd5 is answered by 2. Rf5 mate. Rook after rook

One of the simplest mating forces of all, and the one many players learn first, consists of two rooks, where the friendly king isn't even necessary. In fact, sometimes the friendly king gets in the way, interfering with the actions of its rooks. For the most part, the mate is brought about when one rook establishes a cutoff line and the back rook then checks, so that two consecutive ranks or tiles are controlled as a block - a super cutoff. In the end the enemy king is driven toward an outside row and mated, as in Diagram 34. It starts with the back rook, in Diagram 34, the rook on the fifth rank (on g5). For this example, the starting front rook is the one on the fourth rank (on f4). There follows 1. Rg3+ (driving back the enemy king) I...Kc2 2. Rf2+ (bringing up the new back rook, converting it into a front rook) 2...KdI 3. RgI mate. In the end, the rooks have maintained their double-row cutoff to ensure mate. 34) Rolling action of the rooks

Play the right move, if you can In all situations, you should endeavor to play the best move, ifyou can figure out what it is. Thus in Diagram 35, White can mate in two moves by playing 1. Raa7, bringing up the hack rook to double on the seventh rank. After Black plays the forced reply, I...Kd8, either rook mates by checking along the eighth rank, thereby keeping the tworook (double rank) cutoff intact. 35) White mates in two moves

It's okay to he practical Be correct, but it's also okay to be practical, especially if you're a developing student. Let's say you're very nervous and can't think, whether because of shortage of time on the clock or for some other unsettling reason. For Diagram 35, as many newcomers quickly pick up, you can gain control of the situation by shifting the rooks far away from their target, so that the enemy king can't annoy them. This idea, though not so requisite here, can be quite important in more complex endings, where practical decisions abound. On those grounds, even though it's better to play the correct move, if you can see what it is, good technique renders it acceptable to play a second-rate move that maintains control if you can't determine the correct move. The idea is that, when you're having doubts, it's okay to play it safely, opting for domination and security. Thus, in Diagram 35, if White didn't see 1. Raa7, White could try 1. Rg7 (or 1. Rh7), moving far away from the aggressive enemy king, positioning the rook to function on the kingside. After I...Kb8, to stop mate at a8, the other rook could also shift over to the kingside, 2. Rh6 (or 2. Rg6, if on the first move White had played Rb7-h7 instead). Now safe and poised to continue operations on the other side of the board, the rooks are ready to deliver their tandem mate. As a guideline, it's helpful to think of rooks as being long-range pieces, performing best from a distance. That's when they can attack without fear of being menaced by enemy forces, such as the king, which need proximity to be effective. Remember the maxim: Rooks work best from far away. Mate in the middle Depending on circumstances, you don't necessarily have to force the enemy king to the edge to give a mate with two rooks. That is, if the friendly king is also participating, the middle of the board may serve as well as the edge. Diagram 36 shows how mate can happen in the middle, with the immediate 1. Ra4 being mate. 36) The rooks mate in the middle

Did you castle yet? In Diagram 37, Black's king is trapped in a kingside cage, but mating it in two moves is impossible, unless you find 1. 0-0!. After I...Kh3, there follows 2. Rlf3 mate. How do you know in the diagram that White hasn't castled yet? It's simple: White mustn't have castled since there isn't another way to mate in two moves. Be careful not to mention this to other chess players. Most of them have an aversion to circuitous reasoning. 37) White mates in two moves

Two queens Enough of two rooks, their trials and wonders: it's time to move to another power base, that of two queens. In the process, we'll examine mating possibilities, some avoidances of mate, and a few other tactical motifs that don't necessarily end in mate. On a clear board, no mate is easier than that of two queens working together. A "technique" is hardly needed to bring it about. The main concern is that

one avoid stalemating the opponent out of carelessness. Diagrams 38 and 39 show two convenient mating patterns. 38) A simple two-queen mate

For Diagram 38, the black king could also he on c5, d6, or c7 (it would also he mate if the black king were on a6). Note how the pattern of a three-by-three square (b7-b5-d5-d7-b7) can be drawn over the two queens and black king (this pattern couldn't be drawn with the black king on a6). 39) Another two-queen mate

For Diagram 39, the black king could also be on c5. In both instances, the queens occupy the corners of a side of a 4x4 square box (running from b7-b4- e4-e7-67). here is a problem (Diagram 40) with the same kind of hidden pattern in the offing (as in Diagram 39). White to play can mate in two moves. Every move White has is winning (except for one, 1. Qd6'?7

stalemate), but only one of those winning contingencies leads to mate on the next turn. Mate ensues from 1. Qd5!. Whether Black plays, I...Kc7, or I...Ke7, White promotes to a new queen, 2. d8/Q mate. In both instances, after either move for Black, it's mate by the pattern designated for Diagram 39. 40) White mates in two moves

Working backward The puzzle of Diagram 40 of course becomes easier if we look ahead. Instead of' trying to find White's next move, we have a better chance to solve the problem if we first establish where Black has to go, making certain we're in position to take advantage of it. In other words, this is one of those problems that could be solved opportunely by working backward. Two doesn't always beat one Two queens are an awesome force, but sometimes a lone queen can hold its own against two queens, warding off mate before it can be realized. In Diagrams 41 and 42, we see one queen able to check without stop, in each case the two queens being unable to put an end to the checks. In either case the game is drawn. 41) White has a perpetual

In Diagram 41, the white queen checks at the appropriate point (a5, c3, or el) along the a5-el diagonal - the hypotenuse of the a l -a5-e I -a l triangle). In Diagram 42, the white queen checks at the appropriate point (B, d5, or hl) along the d5-h I portion of a diagonal - the hypotenuse of the d 1-d5-h 1-d l triangle). Geometry or not, both positions are drawn, one queen against two. One proviso 42) White also has a perpetual

In most cases, having an extra queen is decisive. Unless tactics dictate against it, usually it's good to be up two queens. Thereafter checkmate should follow fairly quickly, whether it be a support mate or some other patterned one. But this attraction to extra queens can lead the newcomer down a hazardous path, where, before bringing about mate, the player tries to win all the enemy material, while making as many extra queens as possible. This is not only terribly impractical, it's downright ugly. It's impractical because it takes longer, when one should be winning as efficiently as possible. And by

virtue of extending the game beyond a point, it provides the opponent chances for stalemate and winning or drawing by time forfeit. If the opponent has any material at all, prolonging the game could lead to oversight and actual loss by surprise mate or overturning tactics. But, as I say, it's also hideously unattractive. It implies that one has no appreciation for the game. The combined approach of taking everything and promoting every pawn violates the principle of economy. That plan, if we could so dignify it, defies what serious players invest a lifetime trying to learn: the practical marriage of artful method and precise technique. Constant application of this jejune counter-strategy has even been known to reduce advocates to the level of poltroons. So, whatever you do, don't do it.

King and rook vs. king Back to the basic mates: this time, it's king and rook vs. king. Once again, as with situations of king and queen vs. king, the enemy king must be driven to an edge. But unlike the queen, the rook by itself can't give a support mate since it doesn't guard squares diagonally. 43) A right triangle mate

This means that, for a rook to give a support mate, other units would have to be on the board, either friendly units for help or enemy units for obstruction. The rook must deliver mate by checking along an edge, with the friendly king on the third row inward from that edge to guard potential escape squares. You can win by: (1) a right triangle mate, where the rook checks along the edge, so that a triangle could be traced over the three pieces, with the friendly king guarding all escape squares on the second row in from the mating edge (Diagram 43). 44) A cornered mate

(2) a cornered mate, where a rook checks along the edge, with the friendly king guarding flight squares, as the reduced space in the corner denies the attacked king an opportunity to escape (Diagram 44). Surprise, surprise It's a simple fact that surprising answers tend to be more memorable. Teachers love to give problems with a little twist, hoping to bring about a few smiles. Consider Diagram 45, where it's White to play and mate in three moves. Through the years, I've posed this problem, and similar ones, any number of times. I've gotten many answers, from the mundane to the intriguing. But I seldom get the response I'd like to get. Typically, in attempting to answer the question, students offer a particular line, such as 1. Re6 Kh4 2. Re3 Kh5 3. Rh3 mate. If it's a class of students, one of the students will surely spot that the symmetrical chessboard suggests a comparable answer, 1. Re4 Kh6 2. Re7 Kh5 3. Rh7 mate. Thereafter, other variations may be found that also produce mate in three moves. But the most comprehensive answer, the one I always hope to hear articulated, but never have (unless students have seen or been shown the problem previously), says that any rook move whatsoever leads to the desired mate in three. Try it. I'd be surprised if you found an initial rook move that doesn't work. 45) White mates in three moves

The inner box The chessboard itself is obviously a square. Within that large square are all kinds of other squares. One important quadrangle of squares is the inner box. The defining lines of that inside block contain the squares running from c3-c6-f6-f3- c3. Transactions within that realm abound, and this is often a zone where the kings reign, once it's safe for them to become activated. To be sure, it takes a king placed at a corner of that box, say c3, merely three unfettered moves to reach any of the other three corners of the inner box. Furthermore, though, from c3, there is only one path to reach f6 in three moves, there are four paths for a king to go from c3 either to c6 or 0 in three moves. To be sure, under the right circumstances, it's not necessarily that hard to shift the friendly king from one wing to another, to set up new mating possibilities, as in Diagram 46. It takes three moves for White's king to reach f6, the other end of the inner box and chess galaxy. Meanwhile, the rook maintains a g-file cutoff, keeping the black king trapped along the h-file, an outer row. White therefore gets into position with 1. Kd4 Kh7 2. Ke5 Kh6 3. Kf6. Atter3...Kh7 (Diagram 47), White can force the enemy king to be mated along the h-file or eighth rank. 46) Crossing the inner box

47) White mates in three moves

48) A right triangle mate

Mate along the h-file: 1. Kf7 Kh6 2. Rf5 (a waiting move: White could achieve the same effect by moving the rook to e5, d5, c5, b5, or a5) 2...Kh7 3. Rh5 mate (a right triangle mate, also known as a linear mate, illustrated in Diagram 48). Mate along the eighth rank: (again starting from Diagram 47) 1. Rh5+ Kg8 2. Rh6 (a waiting move: White could also play the rook to h4, h3, h2, or h 1) 2...Kf8 3. Rh8 mate (shown in Diagram 49, another linear mate, again, also called a right triangle mate). The corner of the inner box As already implied, the corners of the inner box are great pivot points for setting up operations in two directions. In Diagram 50, White mates in three moves by first occupying a corner of the inner box, 1. Kf3!. If 1...Kg 1, it's over after 2. Rh8 (cutting off along the h-file) 2...Kfl 3. RhI mate. If instead I...Kh2, then 2. Ral (cutting off along the first rank) 2...Kh3 3. Rh I mate. 49) A right triangle mate

50) The inner box's pivot

Another type of waiting move In Diagram 51, White's king is a knight's distance away from Black's king. If White plays 1. Kc3, opposing Black's king directly, Black, "having the move," moves out of direct line with White's king, and mate does not immediately follow. White would prefer Black's king to move directly into line with White's king, so that White would then have the move while the two kings are lined up. With the move, and the kings so arrayed, White could then give mate. To that end, White plays a waiting move, which doesn't really change much, other than passing the turn to Black. So White begins with 1. Rh2! (White could also play 1. Rf2!, without having to fear the oncoming attack of the opposing king). This transfers the move to Black, without changing anything essential. There follows 1...Kb1 2. Kc3 Kal 3. Kb3 Kbl 4. Rhl mate. 51) White plays a waiting move

The king and rook need each other The rook needs the help of the friendly king more than the queen does, since the enemy king can attack

a rook diagonally. But in Diagram 52, even though White's rook is threatened, it doesn't have to move away. Instead, White's king- let's call the white king the zoo keeper - merely moves up and defends the rook. This keeps the cage door closed, with the enemy king (the trapped animal under watch) ensnared inside. 52) Closing the door of the cage

Anticipation The tandem of king and rook can require precise maneuvering. It's one thing to move the king into position and another to move it into effective position. In the typical mating situation, the two kings oppose each other directly, standing in opposition, and the rook checks along the edge. If the friendly king moves into direct line with the enemy king, it will be the opponent's move, and the enemy king could then be moved out of line, avoiding a mating check. So, as indicated previously, a better idea is to place the friendly king, not in direct line, but in position to receive the enemy king's movement into direct line: that is, a knight's distance away. Eventually, the defending king moves into direct line with the attacking king, and the rook can then do its job: a right triangle check (mate). Thus, in Diagram 53, White's king anticipates Black's king with 1. Ke3!. The black king must then move into line, 1...Kel, and White concludes with 2. Rcl mate. Again note that in playing 1. Ke3, White is positioning the friendly king to be a knight'.v distance away from the black king, waiting for Black's king to oppose White's king directly. 53) White anticipates Black

The king-and-rook mate: a general approach Generally, the two pieces (king and rook) work together, with the rook establishing cutoff cages and the friendly king locking the door when needed. Various motifs come into play to drive back the enemy king. Space-gaining checks can reduce the size of the cage. Meanwhile, the friendly king upholds the rook and important squares. The attacker also anticipates where the defender has to go to save time. Diagram 54 provides an opportunity to see these various ideas in action. Although not the only winning variation, White could confidently go about it this way: 1. Re4 (establishing a cage, a4-e4-el) 1...Kd3 2. KO (locking the door of the cage) 2...Kc3 3. Ke2 (moving a knight's distance away, anticipating where Black's king is going) 3...Kc2 (if 3...Kb3 then 4. Kd2, still anticipating) 4. Rc4+ (a right triangle check, driving back the enemy king) 4...Kb3 5. Kd3 (locking the door of the cage once again) 5...Kb2 6. Rb4+ (or 6. Rc3, reducing the cage, is an option) 6...Ka3 (if 6...Kc1, then 7. Rb8, or some other safe waiting move along the b-file, mates next move) 7. Kc3 (locking the door) 7...Ka2 8. Kc2 (or 8. Ra4+ Kb1 9. Ra5, or some other safe waiting move, 9...Kcl 10. Ral mate) 8...Ka3 9. Rh4 (or some other safe waiting move along the fourth rank) 9...Ka2 10. Ra4 mate. Paraphrasing Weaver Adams via Bobby Fischer, if Black plays differently, Black loses differently. 54) A team effort

Another great team: king and two bishops Mate with king and rook requires a team endeavor, and so does the basic mate with king and two bishops. Not surprisingly, the bishops can form cages too. But whereas the rook needs to be supported by the friendly king, the bishops can confine without kingly support. They can create a Vcage. In Diagram 55, without the aid of their king, the bishops keep the black king trapped, guarding consecutive diagonals on both sides of the hoard. The dark-square bishop lays down a fence going from a7 to d4 to h8, while the light-square bishop provides similarly incarcerating harriers running from a8 to e4 to V. Positioned in the center, united bishops can he a tremendously confining weapon. Beyond the basic mate, the concept of having two friendly bishops against two knights, or against bishop and knight, tends to confer an advantage typically described as having the bishop pair or having two bishops. While such diagonal teams don't automatically give one the upper hand, the two bishops, conceived as a functioning unit, often are a sought after objective, fueling attacking play through all phases of a chess game. 55) A V-formation

Centralizing the pieces Centralization is the process of bringing pieces toward the middle for more options, increased mobility, and greater flexibility. Generally, once the endgame is reached, in addition to centralizing the pieces, the king should also be activated, it being a piece as well. By centralizing it, one hopes to ready it for both attack and support of various units and squares. While all pieces obtain an increase in mobility from the middle, rooks in particular don't have to occupy the center so much to be effective (in fact, for rooks it may even be counterproductive), since they can exert full influence along an open tile from far away, with less danger of being assailed. Nevertheless, as a rule of thumb, one should centralize the pieces, including the king, as soon as the danger of counterattack becomes

reduced. It's usually much less risky to bring the king to the center once the enemy queen has come off the board. Bishops can shine from the center, and it's a great place to establish a V-cage. For the two bishop mate, if one hasn't yet set up a V-cage, the possibility of doing so should still be kept in mind. In Diagram 56, the black king hopes to escape to h6, but 1. Bd4!, takes away that possibility while trapping the enemy king inside a V-cage. 56) White creates a V-cage

57) The Wall

Once the process gets going, the friendly king should take an active part to push it along. A good starting point is to have the king and two bishops line up together, preferably in or near the center. In Diagram 57 we see the wall, which is an arrangement of king and two bishops. Here White can force the black king back by 1. Bd5! (a drive-back tactic). Initially, White is trying to drive Black's king to an outer row, and from there to a corner. Once the

proper setup is achieved, mate is brought about by a series of checks, forcing the king toward its cornered snare. We see the final steps in Diagram 58, a bishop roll-up: 1. Be3+ Kh7 2. Be4+ Kh8 3. Bd4 mate. Waiting moves for the bishop The rook and queen are able to play waiting moves by retreating along the cutoff line. A bishop has the same capability. For example, in Diagram 59, White can shift the tempo by moving the darksquare bishop anywhere along the d8-h4 diagonal, or by moving the light-square bishop anywhere along the c8-h3 diagonal (excluding the vulnerable square c8, since it can he attacked by Black's king, which thereby loses the tempo gained by the waiting move). A sample winning line is 1. Bf5 Kb8 2. Be5+ Ka8 3. Be4 mate. But White has to be careful, for the thoughtless 1. 13e5'?? traps Black too quickly, and it's stalemate. 58) A bishop roll-up

59) White plays a waiting move

Putting it all together Once the enemy king has been driven to the hoard's edge, it must be further driven to a corner, where mate can be delivered. Toward which corner should the enemy king he coerced'? Usually, it should be pushed toward the corner closest to the friendly king. Consider the following position, Diagram 60. Af1er 1. Kd6 Ke8, White prods Black's king along by a process of taking away the last square it occupied. The drive continues 2. Bg7 (taking away 08) 2...Kd8 3. Bf7 (taking away e8) 3...Kc8 4. Kc6. White's king has now reached a corner ofthe inner box. This is better than 4. Bf6, which allows Black's king to escape at b7. After 4. Kc6, there follows 4...Kb8 (or 4...KdS 5. Bf6+ Kc8 6. Be6+ Kb8 7. Kb6 [taking away a7] 7...KaS, and White plays a waiting move, such as 8. BfS, with the game ending 8...KbS 9. Be5+ Ka8 10. Be4 mate) 5. Bd4 (preventing escape at a7 and providing a useful subsequent tempo) 5...Kc8 6. Bf6 (taking away d8) 6...Kb8 7. Kb6 Kc8 (or 7...KaS 8. Be6 Kb8 9. Be5+ Ka8 10. 13d5 mate) 8. Be6+ Kb8 9. Be5+ Ka8 10. Bd5 mate. 60) Driving toward the corner closest to friendly king

Two bishops vs. rook Two bishops working together can be quite a force for good (or evil, depending on perspective), even when facing the counterweight of a rook. In situations where two bishops confront a rook, the possibility of' victory is striven for by first attempting to win the rook, then maneuvering for the final kill with the basic mating forces. In Diagram 61, Black is already in trouble, the rook being pinned. Yet if White piles up on the pinned rook, I. Kh4?, Black can undo the pin (an unpin) with a gain of time, I...Kg7!, threatening the f7- bishop, and that salvages a draw. Now that we know what's in store for White, we see how to fashion the win: 1. Be8!, which represents a kind of anticipation. Black can no longer get out of the pin with a counterthreat, and the rook falls for nothing, without White even having to pile up on it. After gaining the rook, White then wins by the standard two-bishop basic mate. 61) White wins the rook

It doesn't have to be in the corner The losing king doesn't have to be in a corner to be mated. Even the presence of a rook doesn't help much in Diagram 62. Here, White wins the rook with 1. Bg3!, which threatens a murderous check at h4. Black could save the rook momentarily by retreating it, 1...Rf6 (which also averts the dark-square bishop check at h4), but 2. Bh4 (anyway) 2...Ke7 doesn't quite hold, since White has the crisscrossing cutoff, 3. Bc4, and the rook must be abandoned. The crossing power of the bishops in this example is striking. It also helps that, in the initial position, White's bishop at b5 obstructs the b-file, preventing the rook from moving to b2, giving a time-gaining check. 62) Mate or win the rook

Still another great team: king, bishop and knight When it comes to line pieces (pieces that move in straight lines, namely the queen, rook, and bishop), it's easy to grasp how they can work together in pairs, attempting to guard consecutive ranks, files, or diagonals. Yet the bishop-and-knight mate is another matter. Since these two types of minor pieces move in very unlike ways, they tend to have distinct functions within the process, which often enough must be supported by the friendly king. Nor can the method necessarily be broken into convenient parts, as the king-and-queen mate can. In the king-and-queen mate, if so desired, it's possible to use mainly the queen until a certain point is achieved, then the king can be brought in for the finish. In the bishop-and-knight mate, however, all three units must function together as well-oiled parts of a machine. To be sure, it's not a mate that often happens over the board. Why study the bishop-and-knight mate? Since the bishop-and-knight mate (this is more traditional than calling it the knightand-bishop mate) seldom occurs in standard chess-play, students protest. Why bother to study something that seems to have little practical significance'? True, the actual mate doesn't frequently transpire. But how the pieces function etlec- tively has much greater application. Especially worth knowing is how the two minor pieces can interact harmoniously. Indeed, they can cordon off wide areas, preventing the approach of enemy pieces, particularly the opposing king. This is significant, since control of territory is integral to all phases of chess, not just the endgame. So it truly does make sense to learn how bishops and knights synchronize, regardless how frequently the actual bishop-and-knight basic mate comes to pass. Even if you never get to the endgame, and basic mating positions, the gods require that you go through openings merely by playing, and bishop-and-knight teams must match up there as well. But don't all textbooks say the same things? If you examine some of the famous endgame textbooks you'd be surprised how this material is treated.

Typically, a few exemplary variations are offered, some of which are questionable and even wrong. Meanwhile, right or wrong, very few tricks and techniques are offered to help students assimilate the procedure. It's not sufficient to point out that the mate must occur in a corner of the color the bishop moves on. Practically every chess book in the universe says that. Nor is it particularly wonderful to point out there's a maneuver that traces the letter W. Okay, it's a little wonderful, so what? Let's see if we can say just a few of the things that should be said outside of Andromeda. Bear in mind This isn't something to worry over while trying to learn how to do it. But keep in mind that during real game-play, if you're trying to win, there's an overriding harrier that must not be crossed: the fiftymove rule. If no capture or pawn move occurs in fifty moves, the game can be claimed as a draw. Therefore, in learning the technique of mating with king, bishop and knight, stay vigilant to what's happening. Since some of the lengthier bishop-and-knight peregrinations go about thirty moves or more, a mistake or two can cause irreparable delay, with the fiftymove rule rearing. Still, don't at first be so concerned with precision. Instead, while learning seek an overview, keeping the big picture in mind. After you've absorbed some of the essentials, then you can get particular and strive for accuracy in execution. Don't attempt to do it all perfectly before you can do some of it imperfectly. The actual mate To force checkmate the lone king must be driven to a corner of the same color on which your bishop moves. That is, with a light-square bishop, mate can be forced in the a8 or h I corners; with a darksquare bishop, mate can be forced in the a l or h8 corners. This, however, doesn't mean that mate has to occur exactly on a corner square. The defender has some options, with the ability to determine how he or she is going to lose. He or she may prefer getting mated by the knight on squares opposite in color to the bishop, adjacent to the target corner. But we'll see this all in context. For now become conversant with two terms. The term right corner is used for one in which mate can be forced; wrong corner for the other kind. 63) The bishop mates in the corner

64) Black mates on the move

What the mate looks like There are two typical mating patterns. Diagram 63 illustrates the bishop checkmating the lone king, while the friendly knight and king guard escape squares. A comparable mate might occur in the a8 corner. Diagram 64 shows that sometimes one doesn't even need the presence of the friendly king. The king could be replaced, for instance, by a pawn. Thus, Black to move wins with 1...Bf3 mate. A fun variant, also with an extra pawn in place, is offered in Diagram 65. Black to play mates in two moves, starting with 1...Kf3!. This temporarily obstructs the bishop's diagonal, giving White a move, 2. Khl, which is answered by 2...Kf2, discovered mate. The other usual mate is shown in Diagram 46, where it's the knight that gives the mate, the bishop having just driven the lone king from the hI -corner. A similar mate could happen with the knight checking from e2 or h3, and a comparable set of mates might occur across the board, near the a8

corner. (65) A fun mate in two moves

66) The knight mates next to the corner

The driveback It's not that hard to mate once the lone king has been driven to the right corner. We'll see some specific variations shortly. The difficulties surround getting the king into the right corner in the first place. In order to do that it helps to assimilate certain motifs. 67) The driveback

One useful idea is the driveback. This is a lined-up formation of friendly king and bishop against the enemy king, forcing the defending king back a row. For example, Black to move in Diagram 67 must retreat his or her king to the c-file. Now that we know this handy way to force the enemy king back, we can move to the next chapter to see what lies ahead.

Three interrelated nets Rather than looking for precise moves, to implement mate with king, bishop, and knight, it helps to think big picture, hoping to set up three interrelated nets. For lack of imagination we shall refer to these nets as the first, the second, and the third nets, and we see individual cases of them in Diagrams 68-70. Naturally, there must be comparable nets working the other way, toward the other right corner. These mirror-image nets are given in notation under each corresponding diagram. What's the connection? These three nets (and their respective mirrors) are related in that each is a stage in the same confining process: in all three the lone king clearly has no escape. The first net can often be established even without your opponent's realizing it. Once that first area has been cordoned off, you should maneuver your king closer toward the lone king, square by square, tightening the first net into the second net (or its mirror). Finally, by the same gradual maneuvering, you should squeeze the second net into the third (or its mirror). As you practice this you'll sometimes find it useful to waste a move (to play a waiting move) by moving the bishop along the last diagonal it had to control. 68) First net

69) Second net

70) Third net

71) First net

Three corresponding triangles The overriding connection between these three nets can best be seen if we trace over them a certain geometric shape (it's amazing how helpful visual patterns can be). Consider the next three related positions, Diagrams 71-73. Notice that a right triangle appears in all three nets. The first net offers triangle b I-h l -h7 (or h l -g l -g6); the second net has the triangle dl-hl-h5 (or d l g l -g4); and the third net the triangle fl -h l -h3. Notice also that the bishop occupies the hypotenuse (the slanted side opposite the right angle) of each triangle in succession: first the h I -h7 diagonal, then the d I -h5 diagonal, and finally the fl-h3 diagonal. Indeed, the crux of the whole restricting process is to transfer the bishop from the first hypotenuse, to the second, and finally to the third. 72) Second net

Working with the three nets

The rudiments of this system can be traced back to 1780, but it wasn't published as a system until 1923. In 1979, for my ABCs column in Chess Life, I expanded on its didactic aspects so that students could digest it for actual use. 73) Third net

Let's work our way from the first to the third nets to see how the process moves along. Once again, in following the analysis, try to avoid getting lost in particulars to take in the process as a whole. Starting from the first net, the main moves will be offered in boldface type, while other possibilities will be given parenthetically. From Diagram 74, White begins with 1. Bc2 (a driveback, aiming to push Black's king toward h 1) 1...Ke3 (keeping the king near the middle, where mate is impossible) 2. Kcl (better than 2. Kc3, since White's king needs to guard e2, probably from dl) 2...Ke2 3. Bg6 (a waiting move, and Black has to give ground) 3...Ke3 4. Kdl (guarding e2) 4...Kf2 (4...Kf3 5. Kd2 Kf2 6. Bh5, and White soon establishes the second net by shifting his knight to e4 and the bishop to g4 or e2; as a rule of thumb, the bishop is always looking to shift to the next shorter hypotenuse, when and if it can be done satisfactorily) 5. Kd2 Kf3 6. Kd3 (keeping an eye on e3) 6...Kg4 (staying as far as possible from the h 1 corner and preventing the bishop from reaching h5, shifting to the hypotenuse of the second triangle; on 6...Kf2, White has 7. Bh5, tightening the net) 7. Ke3 Kh4 (still guarding h5, preventing the bishop from going there) 8. Kf4 Kh3 (Diagram 75). 74) Proceeding from the first net

75) Moving toward the second hypotenuse

Play continues: 9. Bh5! (mission accomplished: the bishop controls the hypotenuse of the second triangle and has narrowed Black's territory) 9...Kg2 (trying to run away; but on 9...Kh4 10. Bet Kh3 11. Ng5+, or 11...Nc5 and 12...Ne4, establishing the mirror image of the second net) 10. Nc5 (or Ne6-g5) 10...Kf2 11. Ne4+ Kg2 (on other king moves, White replies the same way) 12. Bg4 (arriving at the second net; now White moves the king in, squeezing Black into the third net) 12...Kf1 13. Kf3 (or 13. Ke3) 13...Kel 14. Ke3 KfI 15. Kd2 Kg2 16. Ke2 Kgl, and now we have Diagram 76 (if 16.,..Kh2, then 17. Kf2 Kh 1 18. Bh3 Kh2 19. Ng5 Kh 120. Bg2+ Kh2 21. Nf3 mate). 76) Ready for the third hypotenuse

From Diagram 76, White finishes up with 17. Bh3! (seizing the hypotenuse of the third triangle) 17...Kh2 18. Bfl Kg1 19. Ng5 (preparing to guard h2) 19...KhI (on 19...Kh2 20. K12 Khl 21. Bg2+ Kh2 22. N13 mate) 20. Kf2 (obviously not 20. Nt3 stalemate) 20...Kh2 21. Nf3+ Kh1 22. Bg2 mate (Diagram 77). These variations show some of the niceties of how the three pieces, king, bishop and knight, are able to work harmoniously. 77) Mated in the corner

From the wrong corner The nets are foolproof but, naturally, the side with the lone king aims to avoid them. Moreover, the king is not going to retreat toward the right corner voluntarily, where it can he mated by force, without a tight. Instead, if ground must be ceded, the lone king will head toward the wrong corner. What's therefore needed is a method for driving the king from the wrong corner to the right one. This is done by a definite procedure of steadily controlling square after square along the very edge the king is

trapped on. Consider Diagram 78. In Diagram 78, White has the option of systematically driving the black king toward either a8 or hl. White's king is ideally placed at 116, a working corner of the inner box, a pivot to go in either direction, equidistant between a8 and h 1. By rotating the board in your mind, you can see that if the wrong corner were a8, White's king should start on c6; if it were al, the king should start on c3; and if it were hl, the king should start on D. From the diagrammed position, the first square White must control is h8. This can be done by positioning the knight either on 17 or g6. To drive Black's king toward hl, White should play Ne5-g6; to drive it toward a8, White should play Ne5-t7. Let's look first at driving the king toward a8: I. Nf7+ Kh7 (on I...Kg8, White still plays 2. Be4, taking away h7) 2. Be4+ Kg8 (Diagram 79). Since White wants to guard g8 by putting the bishop on h7, a waiting move must be played, shifting the bishop to some safe place along the b I -h7 diagonal (any square but h7 itself). As a comparison, note that in Diagram 80 White needs to guard g8, with the idea of driving Black's king toward h 1, so the bishop's waiting move should occur along the a2- f7 diagonal. 78) Starting from a wrong corner

Knights don't play that game Note that knights can't play a real waiting move. They can make it be the opponent's turn by playing a move, but in moving thereby change the squares they attack, which in some instances may not matter, but in other cases might. To restate this slightly, knights can't move and keep the same essential position. Every time a knight moves it winds up guarding different squares. A bishop, on the other hand, can move and still guard all the vital squares it did in the previous position. It's one advantage a bishop has over a knight: it can make a true waiting move. 79) White needs to guard g8

Back to our analysis of Diagram 79: there follows 3. Bf5 (for example) 3...Kf8 4. Bh7 Ke8. White must guard f8, the next square along the edge heading toward a8. Since 1`8 is a dark square, White must draw upon the knight. Play continues 5. Ne5 (preventing escape at d7 and repositioning the knight to guard f8 from d7). Black now has a choice. Black can attempt to stay close to the safer corner by playing 5...Kf8 (Diagram 81, the passive defense), or run toward a8 and queenside escape with 5...Kd8 (Diagram 82, the active defense). 80) White needs to guard h7

Let's look at the passive defense: (A) 5...Kf8 (Diagram 81) 6. Nd7+ Ke8 7. Ke6 Kd8 8. Kd6 Ke8 {on 8...Kc8 there follows 9. NO, and if 9...Kd8, then 10. Bg6 Kc8 11. Bh5 (or 11. Bf7) 11 ...Kd8 12. Nb7+ continues the driving process; if instead 9...Kb8 10. Kc6 Kc8 11. Nb7; and if 10...Ka7, then 11. Kc7, and the black king is trapped} 9. Bg6+ (White eats up another square along the edge) 9...Kd8 10. Nc5 (preparing to guard d8 from b7, but not from e6, since that would interfere with the bishop)

10...Ke8 (since White wants to play Nc5-b7, he needs to interpose a waiting move with his bishop) 1 1 . Bf7 (or I I . Bh5, another waiting move) 11...Kd8 (or I I ...Kb8 12. Kc6, and the black king will be trapped, as in an earlier variation) 12. Nb7+ Kc8 13. Kc6 Kb8 14. Kb6 Kc8 (or 14...Kag 15. Nc5 Kb8 16. Be6 Ka8 17. Bd7 Kb8 18. Na61 Ka8 19. Bch mate) 15. Be6+ Kb8 16. Nc5 Ka8 17. Bd7 (a waiting move that mates in two moves). 81) The passive defense

Now let's turn to the active defense: (B) 5...Kd8 (Diagram 82) 6. Ke6 Kc7 (6...Ke8 transposes to the passive line after 7. Nd7, while 6...Kc8 creates possibilities similar to the text) 7. Nd7 Kc6 (on other responses White can play the same eighth move) 8. Bd3! (Black is trapped after all) 8...Kc7 (or 8...Kb7, when White plays 9. Bb5 anyway) 9. Bb5!, placing the bishop on the hypotenuse of the second net, going toward the a8 corner. Some of the classic writers, including Lasker in his famous Manual o/' Chess, recommend the 9. Be4 idea. Thereafter, until the present day, chess writers have copied this idea in obeisance. Obviously it works, but not as nicely as 9. Bb5, trying to create the second net. Play should continue: 9...Kd8 (on any other move White plays Ke6-d6) 10. Nb6 (or 10. Nf6) 10...Kc7 11. NdS+ (and we have Diagram 83, with White having the trappings of the second net). 82) The active defense

A sample conclusion might go: I I...Kd8 12. Kf7 (12. Kd6) 12...Kc8 13. Ke7 Kb7 14. Kd7 Kb8 15. Ba6! (seizing the third hypotenuse) 15...Ka7 16. Bc8 Kb8 17. NO (or 17. Nh4 or 17. Ne7) 17...Ka8 18. Kc7 Ka7 19. Nb5+ Ka8 20. Bh7 mate. 83) Converting to the second net

Let's suppose, starting from Diagram 78, that you'd prefer to drive the lone king toward h 1 instead of a8. Here are sample variations for that possibility: 1. Ng6+ (or 1. Bd5 Kh7 2. Ng6) 1...Kg8 2. Bd5+ Kh7 3. Be6 (a waiting move) 3...Kh6 4. Bg8 Kh5 5. Ne5. And now either (A) 5...Kh6 6. Ng4+ Kh5 7. Kf5 Kh4 8. Kt4 Kh5 9. B17+ Kh4 10. Ne3 Kh3 11. Bg6 Kh4 12. Ng2+ Kh3 13. K13 Kh2 14. Kf2 Kh3 15. BfS+ Kh2 16. NO Kh 1 17. Bg4 Kh2 18. Nfl+ Kh1 19. BD mate; or (B) 5...Kh4 6. Kf5 Kg3 7. Ng4 Kt3 (7...Kg2 8.Bc4) 8. Bc4 Kg3 9. Be2 Kh4 10. Nf6 Kg3 11. Ne4+, and we've arrived at the second net. I recommend that you practice this setup, taking it from here. The W Maneuver

A particularly intriguing possibility is the Mahler WManeuver. Although it's not a main line, and sometimes it's given far more space than it deserves, the W maneuver is worth examining because it shows beautiful interaction among the pieces, while providing a useful mnemonic device. It also, once again, offers an example of how visual patterns can fire our thinking and reduce the game to easier-to-grasp pictures. Consider Diagram 84. In one satisfying line all three white pieces trace W's: the king by moving over the squares e5, d6, c5, and b6: the bishop covering d5, c6, b5, and a6-, the knight traversing f4, e6, d4, and c6. From Diagram 78, let's see: 1. Key Kd8 2. Kd6 (tracing the first half of the king's W) 2...Ke8 3. Bd5 Kd8 4. Bc6 (the first half ofthe bishop's W) 4...Kc8 5. Nf4 Kd8 (on 5...Kb8 6. Kc5; if 6...Kc7 (or 6...Kc8), then 7. Ne6+ transposes into the main line; and if 6...Ka7, then 7. Kb5 Kb8 8. Kb6 Kc8 9. Ne6 Kb8 10. Bd7 Ka8 11. Nc7+ Kb8 12. Na6+ Ka8 13. Bc6 mate) 6. Ne6+ (the first half of the knight's W) 6...Kc8 7. Kc5 Kb8 8. Kb6 (completing the king's W) 8...Ke8 (or 8...Ka8) 9. Bb5 Kb8 10. Ba6 (completing the bishop's W) 10...Ka8 11. Nd4 Kb8 12. Nc6+ (completing the knight's W) 12...Ka8 13. Bbl mate!. 84) Mahler's W maneuver

What is a transposition? In several of the variations above, some of the same results occur from different move orders called transpositions. You transpose moves when you play the same moves in different order. By playing the same moves in another sequence, such as playing the second idea first, you're not only exercising creativity, you might thereby achieve or prevent something you ordinarily wouldn't. Beyond that, there's always a possibility of confusing the opponent, which I hear is not a bad thing to shoot for in chess. Mating from random positions

Most of the time your pieces will not be so conveniently placed as they are in these didactic examples, so you need to know how to prepare your forces for action. Unless the position clearly suggests a more propitious plan, start by moving all three pieces (king, bishop, and knight) toward the center. Specifically, move your king to a central square not the color of your bishop, the bishop to a central square next to your king, and the knight to the side of the king away from the bishop, so that the three pieces form a straight line (more visual patterns), say, Nc4, Kd4, and Be4. This approach is especially helpful when you have no idea what to do. Since a central arrangement can be achieved without much trouble, create random positions and practice trying to centralize the pieces as an exercise. If you can't find a person to be your partner and help you do this, consider using a piece of software, such as Fritz. By grappling with it on your own, with or without assistance, you should get a better feel for how the pieces work together, but hey, no promises.

If you're really having trouble with the bishop-and-knight mate, consider Diagram 85, which has a third minor piece, an extra knight. Your mission, if you should decide to accept it, is not just to win, but to do it in two moves. Think for a minute and see if you can find a way to end White's agony. Black mates starting with 1...Nc3!. White's only move is 2. Kxcl, and Black wins with 2...Be3 mate. Getting to the finale was a little deceptive; but in the end it wound up being just another bishop-andknight mate. 85) Black to play and mate in two moves

Reshevsky's favorite Not to be ignored, the bishop and knight combination, a pair often favored by American great Sammy Reshevsky, can be quite a force. When facing a lone king the team can indeed force mate with precise play. And sometimes, even with the opposing side having an extra minor piece thrown into the mix, such a potent combat squad might still be able to fashion mate. This is especially so when the bishops are of opposite color (when they don't travel on the same color squares). 86) White mates in seven moves

In Diagram 86, White plays 1. Nf3!, confining the enemy king, and there's no way Black can fend off eventual mate. Black is reduced to bishop moves, the black king being in effect stalemated. It's simply a matter of transferring White's king to fl, then following with a bishop check at g2. Black is powerless to stop this idea. A sample conclusion is 1. Nf3! Bc3 2. Kb5 Bb4 (hoping for 3. Kxb4, stalemate) 3. Kc4 Bc3 4. Kd3 Bb4 5. Ke2 Bc3 6. Kfl Bel 7. Bg2 mate. In Diagram 87, it looks as if White has to deal with Black's menacing g-pawn, which is done by 1. Bb6!. But actually White is shaping a bishop-and-knight mate, since after the pawn promotes, White's knight has a mating check on c7. 87) White mates in two moves

88) Black wins the knight or mates

The situation in Diagram 88 has nothing to do with promotion. At stake instead are mate or the possibility of gaining a piece. Black begins the example by moving in with the king, 1...Kfl!, keeping an eye on the white knight. To avoid losing the knight, White must play 2. Nh4, but that permits the surprisingly nasty 2...Nf2 mate. Once again, the bishop-and-knight combo works its magic. Naturally, the bishop-and-knight team seems to work best from relatively up close, especially the knight, but what happens when the friendly king is far away'? Diagram 89 tries to answer that question. Whether or not it does so adequately, it does supply a delightful idea. The problem begins with Black needing to give White a move to avoid stalemate. This Black does with 1...Kb2!, obstructing the bishop's line of assault. White now has several moves with the knight, so let's pick a representative one and see: 2. Ne6 Kb3+ (discovered check) 3. Ng7 Kc3! (avoiding stalemate once again) 4. Ne6 Kc4+ 5. Ng7 Kd4! 6. Ne6+ KdS+ (see, it i.' possible to answer a check with a check) 7. Ng7 Ke5! 8. Ne8 Ke6+ 9. Ng7+ Kf6 10. Ne8+ Kf'7+, with mate next move. The path Black's king took in Diagram 89 has been described as walking a staircase. I wouldn't want you to think that walking staircases is the sole province of kings. 89) Black's king walks the staircase

Queens can do it, too, as is the case in Diagram 90. Without a lot of verbiage, step-by-step Black ascends to mate with I...Qc6! 2. Kb8 Qd6+ 3. Ka8 Qd5! 4. Kh8 Qe5+ 5. Ka8 Qe4! (you get the idea, so we're dropping the exclamation points from here on) 6. Kb8 Qf4+ 7. Ka8 Qf3 8. Kb8 Qg3+ 9. Ka8 Qg2 10. Kb8 Qh2+ 11. Ka8 QhI! (okay, maybe one exclamation point more) 12. Kb8 Qh8 mate. 90) Black walks the staircase to mate in twelve moves

Bishop and knight vs. rook The bishop and knight amalgamation can work nicely against additional forces, too, especially if the defending king has reduced mobility, as in Diagram 91. Here, the rook actually gets in the way, obstructing a flight square, preventing Black's king from escaping to d8. Thus 1. Nd7+!, an alluring double check, leads to mate next move, whether Black's king goes to a8 or c8. In both cases, 2. Nb6 mate does the trick. Mating with two knights

This is not a basic mate because it isn't. Basic mates are those that can he forced. It's not possible to force a mate with king and two knights against a lone king - not without help. In order for king and two knights to frame mate, either the losing side would have to move the king into mate voluntarily, or there would have to be an enemy pawn on the board (or some other enemy unit), so it can move to avoid stalemate. Still, mate, though it can't be forced from ordinary positions, is possible, as Diagram 92 shows. Without explaining how the position came about (like at the movies, let's suspend disbelief), White to play wins with 1. NO mate. 91) White mates in two moves

Why the two-knight mate can't be forced This can be understood by examining what happens once the lone king is first driven to the edge, and then toward one of the corners, where its options are reduced and mate seems more likely. The problem is not one of driving the king toward the corner. Rather it has to do with time, or the lack of it, once the lone king is in the corner. In order to force mate, the attacking side would need an extra move, since one move before mate it's stalemate. 92) Mating with two knights

Consider Diagram 93. With the e2knight guarding c 1, the d I -knight is free to move. The next square along the edge that White must control is bl. This is accomplished by 1. Nc3+. After Black replies 1...Ka1, White needs to maneuver the e2-knight to c2, to give a mating check. Yet if White plays 2. Nd4, Black is stalemated. If only Black had an extra move, say with a harmless pawn. Harmless or not, no such pawn is on the board in Diagram 93, and the position is drawn. 93) One move before mate it's stalemate

Don't necessarily take that last pawn In some cases, with proper maneuvering and circumstances, the king and two knights can let the defender keep an extra pawn, assuming it's not too risky, so that at the critical moment stalemate is avoided. In Diagram 94, for example, White doesn't take the pawn. Because of the extra tempo afforded by the black pawn, White can play for mate: 1. Ndc3+ Kal 2. Nd4 fl/Q 3. Nc2 mate. Knowing the limitations of two knights can suddenly provide unexpected defensive resources. In

Diagram 95, for instance, Black to play is down two minor pieces. Moreover, two of White's three minor pieces are knights. By forcing a trade of knight for White's remaining bishop, 1...Nd3!, the position reduces to a positional draw. The two remaining white knights will not be able to force a win. As we've seen in Diagram 94, two knights don't always have to lead to a drawn position. Add a lone enemy knight for the defender, set up the situation of Diagram 96, give White the move, and watch what happens. After 1. Nc3!, guarding escape squares at dl and e2, White will mate next move, regardless how Black replies. No matter where Black goes with the d3-knight, White's g5-knight mates on f3. 94) Stalemate is avoided

95) Simplifying to a draw

96) White mates in two moves

97) White mates in two moves

Let's help Black out a bit: we'll give Black an extra knight and show that "more" isn't necessarily more. In Diagram 97, White mates in two moves, starting with 1. Kh8!, which turns out to be mainly a tempo shifter. Black is then reduced to moving one of the knights. If the knight at c5 moves, the f4knight mates on e6. If the e7-knight moves (even if it goes to g6, giving check), the f4-knight mates on g6. The advantage of two bishops United bishops, as already seen in previous examples, can guard terrain on both sides of the board and work beautifully in coordination. In many situations, though not all, two bishops generally constitute an endgame advantage over other minor piece combinations (that of bishop and knight or that of two knights). As a reminder, with such a superiority it's said that one has the two bishop advantage or the advantage of the two bishops or the two bishops or the bishop pair.

Although desirable in a majority of typical formations, one shouldn't play to obtain two bishops robotically. Rather, it makes sense to appreciate the nature of the position, and where it's going, before making a commitment on which minor pieces to keep or trade off. The art and science of playing with two bishops could fill up a nice book, so we're not going to get into much of that here. But in keeping with the spirit of this disquisition, let's look at a few more positions showing the bishops to advantage. Even when mate isn't afoot, the ability of these coordinated, long-range monsters to snare enemy pieces is quite impressive. In Diagram 98, the bishops already have clear superiority over the two knights. Stationed at a4 and b4, they radiate Vdominance up and down the board. Indeed, neither knight is safe to move, and if White plays 1. Kb7!, stalemating the enemy king, Black must abandon one of the knights. The remaining knight will soon be won as well. Not too long after that White can garner the black king to boot. 98) The knights are lost

Black doesn't fair much better in Diagram 99. Black's knight is trapped by the g4-bishop, and the black bishop is obstructed by its king. White again wins both, beginning with 1. Be3, a direct attack on the knight. To free the g8-bishop, Black must play 1...KfB, but before taking the knight, White makes sure to put Black back in obstructed trouble with the zwischenzug (in-between move) 2. Bc5+!. There follows 2...Kf7 (once again, obstructing the g8-bishop) 3. Bxgl Kf8 4. Bc5+ Kf7 5. Bb4 (or 5. Ba3 or 5. Bc5, all of which are effective waiting moves), and Black must lose the bishop, too. 99) White wins Black's pieces

But let's give Black a chance. Let's arm Black with two bishops as well, as in Diagram 100. Having two bishops doesn't help, however, as is clear after 1. Bd2+. If I...Ka4, there follows 2. KcS+! Ka3 3. Bcl mate. If instead I ...Ka6, then 2. Bc8+ Ka7 3. Be3+ Ka8 4. Bbl mate. Obviously, two bishops can sometimes be better than two bishops. 100) Two bishops beat two bishops

Analytic practice Throughout the book appear positions for analytic practice. Your task is to solve these problems. The solutions to the practice positions are found on page 243. Practice Position #1

Question: In Practice Position #1, should Black reduce to a draw by l ...Bxa7'? Solution, page 243.

Corner stuff In addition to basic mates (i.e., king and rook vs. king) and other typical mating forces (say, two rooks vs. king), it's also useful to know how certain other forces can best particular ones. For instance, knowing how a queen gets the better of a rook, or how to win when up the Exchange (a rook for a minor piece), as well as understanding the essentials of other common enough clashes, are worth adding to one's knowledge pool. Some useful information pertains to corner battles. Newcomers soon realize that mate with a lone minor piece is impossible. And when a minor piece does deliver mate, it often takes place in a corner, where there's limited flight space. Moreover, in order for a king and single minor piece to give mate , the losing side must have a friendly unit blocking a potential escape square. While the following mating setups rarely happen, they are possible, and at times underlie more complex situations. In Diagrams 101-104, a lone minor piece is able to exploit the corner, and an obstructive enemy unit, to deliver mate. 101) Bishop vs. bishop

103) Knight vs. bishop

102) Bishop vs. knight

104) Knight vs. knight

105) Black plays and wins a bishop

106) White mates in four moves

The stifling corner How often does it happen that a minor piece gets to deliver mate against skeletal forces? Well, it doesn't happen that often, and not usually without help. Diagram 105 shows an alternate solution to a possible final position that might have appeared at the end of the movie Searching for Bobby Fischer. If the final position of the movie didn't end the way it did, it would have ended this way, starting with a setup from a more difficult composition suggested by Grandmaster Pal Benko, with Black playing 1...Ne2. White would then have had poor choices: either the bishop is lost on g3, or White tries 2. Bgl?, allowing 2...Ng3 mate. In the end, the composition was rejected, one day before shooting the scene, because it wasn't thematic to the idea of overusing the queen, which was characteristic of the young champion's play.

When bottled up in a corner, various bad things can happen. Although the position of Diagram 106 starts innocently enough, it winds up illuminating how a bishop, supported by its king, can become a lethal weapon. The example begins with a deflective (driving on/off) sacrifice, 1. g8/Q+!. After 1...Kxg8, White moves in 2. Ke6 Kh8 3. Kf7. Thanks to the presence of the e-pawn, Black has a pawn move. That pawn move avoids stalemate, but it doesn't deter 4. Bg7 mate. (107) White wins the bishop

Sometimes the defender's pieces, in positions that ordinarily are drawn, wind up stumbling into each other and causing problems, and those problems don't have to revolve around mate. In Diagram 107, with the move, White doesn't have mate. But White does have 1. Bg7!, and there's no place for Black to move the king and keep the g8-hishop defended. Even with the move, Black winds up being a move short, since I ...Kg6 2. Kxg8 Kxh6 3. Kf7 will beat Black to the queenside and ultimate victory. Certainly, this position is similar to Diagram 99. 108) Black is lost

Two against one Rarely will one get the opportunity of playing out endgames of two minor pieces vs. one, with nothing else on the board. But it does happen. Trapping and winning the lone opposing piece, or setting up mating possibilities, are conditional on circumstances. Winning chances increase if the inferior side's forces have inadequate scope, gasping for air along an edge or in a corner. 109) White mates in two

In Diagram 108, Black is dead in the water. If it's Black's turn, the knight can't move safely (on I ...Nc8 White has 2. Bxc8, avoiding stalemate). If I...Kh8, then 2. Bd6 I Ka8 3. Kc7 (or some other waiting move with a bishop), and the knight is lost. If it's not Black's move, White simply plays I. Bd6, and the knight is lost once again, with stalemate not entailed. Diagram 109 shows two knights getting the betterofa lone bishop. It's mate next move after 1. Nd5!, when the bishop can't satisfactorily cover both c7 and M. 110) Squeezing Black's knight

Stalemating the enemy king, but not the entire opposing side, is often a valuable tactical weapon. As long as it's not a true stalemate, and the opponent still has some non-king move, the resulting situation may he easier to foresee and manipulate. In Diagram 110, by playing 1. Nf6!, the black king has no move, and the g7-knight must be abandoned to the wolves. If it goes to e6 or f5, the bishop takes it. If it goes to h5, the knight takes it. And if it goes to e8, either the bishop or the knight takes it. If I had a comparable losing setup, I wouldn't be able to take it either. Very often it's not just the minor piece that does the damage. The attacking king may get involved in the action as well. In Diagram I 11, a gentle attack to the black bishop, 1. Kd2!, leaves it no good move. No matter where the bishop goes, White has a discovered check that empowers the knight to capture the bishop on either side of the board, anywhere from the a-file to the h-file! Maybe the knight isn't such a slow moving piece after all. III) Black's bishop is lost

After 1. Kd2:

If I...Bb3, then 2. Nc5+; if I...Ba4, then 2. Nc5+ or 2. Nb6+; if I...Bf3, then 2. Ne5+; and if I...Bh5, then 2. Nf6+.

Queen vs. rook The encounter between queen and rook is not so easy, requiring precise maneuvering and staying attentive. To be sure, it's not uncommon for the side with the queen to press too hard and wind up falling into stalemate or some other unsettling tactic, such as a pin or skewer that drops the queen. No attempt at a full explanation of the process is going to be given here. For that I'm going to recommend that you turn to one of the comprehensive texts (Fine, Dvoretsky, Averbakh, Euwe, etc.). But students, even beginning ones, could gain by an awareness of certain positions and patterns that, as assets, augment their foundational savvy. First up are some pitfalls. In pushing the driving process, aiming to trap the losing king along an edge, it's possible to move in too closely and create an opportunity for a stalemate shot. In Diagrams 112 (1. Rc3+) and 113 (1. Rh3+), White forces an immediate draw. In Diagram 114, it's a little more complicated, though that position is drawn as well. After 1. Ra2+, Black can avoid taking the rook by dropping back, I...Kb4. But White still holds the fort with 2. Rb2+, since 2...Kc3 allows 3. Rh3+, while 2...Ke4 3. Rc2+ Kd4 fails to 4. Rd2, pinning the queen and forcing a draw. 112) White draws

113) White draws

114) White has a perpetual

Perpetual check A perpetual check is a tactic by which one side (usually, the one worried about losing) gives constant check, but cannot force mate. While a standard drawing method, "perpetual check" is not a rule of chess. Rather it falls into another rule category, that of threefold repetition. That's because long before perpetuity is reached the same position will be repeated for a third time. As the player is about to perform the third repetition, he or she announces the intention and claims a draw. The repetitions don't have to occur on consecutive moves, so it can't hurt to have an accurate score sheet. Pundits even recommend it. Watch out for stalemate shots Whenever the queen gets too close, leaving the defending king without an escape hatch, the possibility of jettisoning the rook for stalemate becomes very real. In Diagram 115, Black has no choice. White's rook checks and checks, and Black must be careful not to capture it inopportunely.

115) Another perpetual

An exemplary line us 1. Rb2+ Kc5 2. Rc2+ Kd4 3. Rd2+ Ke4 4. Re2+ Kf4 5. Rf2+ (if 5...Kg4, then 6. Rg2), when Black must settle for a draw. Even though, in capturing the rook (5...Qxf2), the queen moves to a new square, that placement also stalemates. Note that 1. Rc6+'? would be a serious mistake, since Black could escape the checks by I ...Kb7 2. Rb6+ Kc7 (not 2. Rc7+ because of 2...Qxc7, and there's no stalemate) 3. Rb7+ (or 3, Rc6+ Kd7, and now either rook check, 4. Rc7+ or 4. Rd6+, allows Black's queen to capture, ending the possibility of stalemate) 3...Kc8, when a rook check at b8 or c7 is met by a capture with the queen, avoiding stalemate. Diagram 116 shows another set of stalemate possibilities. After 1. Qxf2!, Black can't play I...Qxf2 because of stalemate. But Black can shift the tempo with I...h6!. It doesn't help, however, since 2. Qgl! Qxgl is also stalemate. 116) Two stalemates

Note that Black can't win by I...Ka6, since 2. Qe2+ (or 2. Qfl+) forces the king back; and 2...Ka7 allows the pin to be kept by 3. Qf2 (or if the white queen is on fl, 3. Qgl also works). ('ornered To he cornered is a horrible thing, whether the king is wooden, plastic, or electronic. Black feels the full effect of cornering in our next example (Diagram 117). White's queen does most of, the cornering: I. Qe8+ Kh7 2. Qd7+ Kh8 (best) 3. Qd8+ Kh7 4. Qc7+ Ka6 (4...Ka8 is met by 5. Qc8 mate) 5. Qc6+ Kay 6. Key. and Black is going to lose with minimal fanfare. 117) Black gets cornered

A key position This is a key situation (Diagram 118) in the queen vs. rook position. If it's Black's move, there's trouble (there's trouble for Black if it's White's turn, too). If the black king tries to flee, say I...Ka6, the rook goes just like that, 2. QcX. Several rook moves also fail at once. No good is I ...RhK, because of 2. Qa5 mate. Moving the rook to h6, h5, c7, d7, and e7 all lose it to direct capture. Moving it to b4 runs into 2. Qa5+. while moving it to h2 or g7 meets up with a lurking, centralizing queen check at d4. Thus, the rook has but four places to go without being immediately lost: (A) I...R17.(B) I...Rh7,(C) I...Rb3.and (D) I...RhI. Such tries only delay natters, however, since White's queen can pick off the rook or lurce mate within tour moves. 118) Black to move loses quickly

In all four positions. White starts with a centralizing check, 2. Qd4+. From the center the queen has maximum flexibility and is always working in two directions. It seeks forking points (connection points), which are squares from which a forking check can he given. Since the queen aims to work in at least two directions, the forking check either wins the rook or mates on the other side ofthe hoard. 119) After I...Rf7

Forking points (A) When the rook is on f7 (diagram 119), the main . forking points are e8 (when the black king is on the eighth rank) and a2 (when the black king is on the a-file). 120) After l...Rh7

(B) When the rook is on h7 (diagram 120), the main .forking points are g8 (when the black king is on the eighth rank) and b 1 (when the black king is on b8). (C) When the rook is on b3 (diagram 121), the main forking points are a4 (when the black king is on the a-file) and g8 (when the black king is on the eighth rank). (D) When the rook is on bl (diagram 122), the main forking points are a2 (when the black king is on the a-file) and h7 (when the black king is on a7). From Diagram 119 play continues 2. Qd4+ (a centralizing queen check) 2...Kb8 (on 2...Ka8, there could follow 3. Qal+ Kb8 4. Qb2+, and we're back in the main line) 3. Qb2+ Ka8 (3...Kc8 permits 4. Qh8+, mating next) 4. Qa2+ (the queen works in two directions) 4...Ra7 (to save the rook) 5. Qg8 mate. From Diagram 120 play continues 2. Qd4+ (a centralizing queen check) 2...Kb8 (on 2...Ka6 there's 3. Qb6 mate, 3. Qa4 mate, or 3. Qal mate) 3. Qe5+ Ka8 4. Qal+ Raj (or 4...Kb8 5. Qb 1 +, forking king and rook) 5. Qh8 mate (once again, the queen enjoyed working in two directions). 121) After 1...Rb3

122) After 1...Rbl

From Diagram 121 there follows 2. Qd4+ (a centralizing queen check). I f2...Kb8 (on 2...Ka6 White has 3. Qa4 mate; and if 2...Ka8, then the same 3. Qa4+ succeeds) 3. Qh8+ Ka7 4. Qg7+ Ka8 5. Qg8+, a forking point, etc. From Diagram 122 there follows 2. Qd4+ (a centralizing queen check) 2...Ka8 (on 2...Kb8, the winning line is 3. Qh8+ Ka7 4. Qh7+, forking king and rook) 3. Qh8+ Rb8 4. Qal mate (or 3...Ka7 4. Qh7+, forking king and rook). Once again, the queen thrives in multiple directions. King triangulation

Triangulation as a concept usually applies to king-and-pawn endings. It refers to a maneuver whereby the attacking king changes a correspondence with the enemy king. Instead of taking two moves to get back to where it started, the friendly king takes three moves and thereby traces a triangle pattern in its movement. Meanwhile, the opposing side is reduced to repeating moves, going back and forth with the king. In other words, the triangulating king does a three-step, while the defending king does a twostep, and that breaks the correspondence, shitting the turn. Diagram 123 shows a typical example of'king triangulation. If White plays 1. Kc6, Black has I...Ke8, holding White off. If instead White plays 1. Kf5, trying to invade on g6, Black has I...Kf7, keeping out the white king once again. 123) White to play

But if it were Black's move, White would win easily. If Black played I ...K17, then White follows with 2. Kf5 and gets into g6 on the next move. If Black tries I ...Kc8, there follows 2. Ke6 KI8 3.17 Kg7 4. Ke7 Kh7 5. Kf6 (avoiding 5. 18/Q stalemate, though 5. f8/R does indeed work) 5...Kh8 6. t8/Q+ Kh7 7. Qg7 mate. And I...Kg8 does no better after 2. Ke6 (taking a diagonal opposition with the pawn already on the sixth rank) 2...Kf8 3. P, transposing into the previous winning variation. But it's not Black's move. It's White's. So White triangulates: 1. Ke4! (keeping contact with f5; the same thing could be achieved by first playing 1. Kf4!) 1...Ke8 (or I...Kg8, but not I...Kf7 because of 2. KI'5 and 3. Kg6) 2. Kf4! (if the king had first gone to f4, White would now play 2. Ke4!, with the same ellect) 2...Kf8 (once again, not 2...K17 because of 3. Kf5) 3. Kd5!, and the original position is achieved with Black to move. In triangulating, White's king actually traces a triangle in its three-square movement, which is why it's called triangulation. Chess players are so, so visual. Queen triangulation

In a way, the queen moves like a king -- in any direction. Okay, the queen is more powerful, able to go more than one square at a time. But it moves in all the dimensions traversed by the king, so it should also be able to triangulate. Let's reprise an earlier position. This time, though, it's White to move, and now it's become Diagram 124. 124) White moves and wins

What happens if it's White's turn to play? Since we know that Black to play loses, the winning idea seems to be to make it be Black's move. That is, how can White lose a move to shift turns? It starts with a centralizing check, 1. Qd4+. After 1...Kb8 2. Qh8+ Ka7 3. Qd8, the same position has been achieved with Black to move. White's queen literally traces a triangle (doing a three-step, from d4 to h8 to d8). Note that I...Ka8 doesn't help, since White has 2. Qh8+ Ka7 3. Qd8, inasmuch as 2...Rb8, blocking the check, allows 3. Qal mate (that two-direction thing again). After I ...Ka8, White can even go the other way, 2. Qa I + Kb8 (2...Ra7 is met by 3. Qh8 mate, across the board, in the other direction) 3. Qa5, and that creates a mirror image of the initial position. Double threats Two other positions in the queen vs. rook repertory occur in Diagrams 125-126. In Diagram 125, though not ensnared in the corner, Black quickly runs out of good things to do after 1. Qb5!, threatening mate at b8 and V. If l...Re7+, then 2. Kd6 leaves Black no good move, since 2...Rc7 is crushed by the pinning, 3. Qb6. Other reasonable rook moves, such as 2...Re I end in 3. Qb8 mate. Nor does I ...Rc7 help much, since White still wins with 2. Qb8+ Rc8 3. Qd6+ Ke8 4. Qe7 mate. 125) White wins quickly

In Diagram 126, White will win the rook or mate, starting with 1. Qh8+!. After 1...Ke7, White plays 2. Qh2+, eyeing the forking point at c2. So Black's king must get off the c-tile, say 2...Kb7 (note that 2...Kd8 permits 3. Qb8 mate), and White's queen works its way toward another forking point, the square b3. The rook falls after 3. Qb2+ Ka7 (moving to the c-file allows Qb2-c2+) 4. Qa3+ (or 4. Qa2+), and after Black's king moves to the b-file, the queen hits the forking point at b3, and the rook falls. 126) White wins quickly

127) White to play and draw

One more example, which shows a motif that happens occasionally, before moving on to the next group of problems. In Diagram 127, it's White to move, with White being down a rook for a queen. But all is not lost. After 1. Rc5+!, Black must capture, 1...Qxc5, and that's stalemate. Let's leave this grouping of problems on a lighter note, that being checkmate in two moves, as shown in Diagram 128. True, White has an extra pawn, but after I...Qd5!, it proves to be White's undoing, since White's only move, 2. Kb8, allows 2...Qd8 mate. One shouldn't scoff at becoming familiar with the techniques needed to bring home the win in queen vs. rook endings. since all kinds of situations can reduce to them. For instance, in Diagram 129, we oiler another one of those lighter chess moments. Black is menacing promotion, and White has two ways to cope with it, either 1. Raj or 1. Rel. But after I. Raj, there follows I...Rc8+ 2. Ke7 Rc7+!; and after 1. Rd I, the same idea materializes the other way with I...Rf5+ 2. Ke7 Re5+!. Of course, in both instances, it's assumed that White knows how to win queen vs. rook. 128) Black mates in two moves

(129) White can't save the game

Question: In Practice Position #2, using the staircase method, how can White win Black's rook'? This actually comes from a blindfold speed game played between Vladimir Kramnik and Judith Polgar. If they can do it, you can do it. Solution, page 243. Practice Position #2

We also see this knowledge being important in certain other types of rook endings, again revolving around sacking one's rook to achieve promotion to a queen. In Diagram 130, White is threatening to check Black's king from the flank, but 1...Rh8! stops that and leaves White little choice. Either White has to take the rook and allow Black to queen, producing a typical queen vs. rook ending, or White can try 2. Rdl (both 2. Ra l and 2. Rb 1 lose too), when Black wins outright with 2...Ke2 3. Kc2 Rc8+. As a rule of thumb, you should avoid situations where your rook's safety hinges on defending it with your king. An opposing rook check may upset the balance and wind up winning your rook, either by undermining its protection or driving your king into line for a crushing skewer.

(130) Black to play wins

You win the Exchange (with a capital "E" to distinguish it from merely "exchanging" pieces, which begins with a lower case "e") when you gain a rook for a bishop or a rook for a knight. There's a whole strategy for playing when up the Exchange, which generally consists of using the rook to improve one's situation, gaining space and infiltrating with one's own king, until the position can't be squeezed any further. At that point one's superior mobility should provide tactical chances to win material, such as an extra pawn or two, or it may enable one to fashion a mating attack. If none of that quite happens, the theory of being up the Exchange allows for another possibility. After improving one's position as much as reasonable, the winning line may pivot on giving back the Exchange. In the process, however, the side surrendering back the Exchange gains a pawn or two and simplifies to a controllably decisive endgame position. Thus, in Diagram 131, White's up the Exchange, though the rook is trapped in at bl. But White can simplify the winning task by giving back the Exchange with 1. Rxc I bxc I /Q+ 2. Kxc 1, reducing to a winning pawn ending. The situation might conclude 2... Kb7 3. Kd2 Kc6 4. Ke3 Kd5 5. Kf4, winning by occupying a critical square (this concept will be explained later). Thus we have another rule of thumb: If you have a significant material advantage, be willing to give back some of your material, simplifying your task to gain control. (131) White gives back the Exchange to simplify to a win

Right now we're interested in some of the ways (surely, not all) a king and rook can get the better of a king and bishop or a king and knight. Sometimes it's done by winning the minor piece, sometimes by actually setting up mate. 132) White mates next move

In Diagram 132, it comes down to the latter. No matter who moves, White soon mates, thanks to the deadly pin along the eighth rank, and also because the defending king is in a bad corner. A simple waiting move (or temporizing move - one that shifts the move or tempo to the other player) such as 1. Ra8, and Black's king must separate from the bishop, 1...Kh8, allowing 2. Rxf8 mate. 133) White can't force mate

Compare the position of Diagram 132 to that of Diagram 133. In Diagram 133, White doesn't have a waiting move along the edge (as in Diagram 132), since that produces stalemate. But even if White's rook unpins the bishop, the position of Diagram 133 is still drawn, since no headway can be made with correct defense. The winning idea doesn't have to be dependent on a temporizing rook. Rather it could come down to use of the king. Thus, in Diagram 134a, Black wins White's pinned bishop with the immediate 1...Kf6,

and the white king must move away, abandoning the bishop to its fate. (134a) Black wins the bishop

But the good can go bad Even though Diagram 134b is a draw the defender must be careful. An ill-considered move can lead to big trouble quickly. For instance, from the game Gonda-Paci, played in Budapest in 2001, Black tried I...Bd6?, which quickly lost to 2. Ra7+ (a time-gaining check that disrupts the defense) 2...Kb8 3. Rd7, threatening mate and the bishop. A better first move for Black is I ...Bg3, for example, when 2. Ra7+ Kb8 3. Rg7 is met by the time-gaining 3...Bf2+, and Black holds. 134b) Even the good corner can lose

Here is a standard position that shows a number of winning ideas. In Diagram 135, White starts with

1. Rg2!, and however Black replies, mate or losing the bishop follows. 135) White wins the bishop or mates

136) Forcing a winning setup

1t' 1...Bh4, then 2. Kh5+ wins the bishop. If I ...Bf4, then 2. Kf5+ wins the bishop. If I...Be5, then 2. Re5 Bg7 3. Re8+ Bf8 4. Rag mates. If I...Bc7, then 2. Rc2 skewers the bishop and the square c8, leading to mate. If I...Bb8, then 2. Rc2 threatens an eighth rank fork, winning the bishop. It' I ... Be I, then 2. Reg, threatens the bishop and mate. If I...Bd6, then 2. Rd2 Bel 3. Rc2 (or 3. Ra2) wins the bishop. In Diagram 136, we see White playing to force the previous position. White gets there by 1. Rfl, when l...Bh2 2. Rf2 Bg3 3. Rg2 brings us to Diagram 135.

Occasionally a wayward bishop can even be trapped pretty much in the center of the hoard. In Diagram 137, for example, the bishop has no good place to go after 1...Ke5!. If 2. Bh7, then 2...Rg7 3. Be4 Rg3+ gives a winning fork; if instead 2. 13h3, then similarly 2...Rg3+; and if 2. Bd7, then 2...Rd8, with a triumphant pin. (137) Black wins the bishop

(138) Black traps the bishop

A similar bishop trap occurs in Diagram 138. After 1...Kc6!, the bishop can't move to a5 or a7 because of the forking check at a3; it can't go to g I because of the forking rook check at d 1; and it can't safely go to f2, since the rook checks first at d 1 and then at d2. Some days it doesn't pay to be a bishop. 139) The knight is trapped and won

Rook vs. knight As in the ending of king and rook vs. king and bishop, the defender wants to have good cooperation between king and minor piece. But at least the bishop can move far away from its king with chances of survival. Once the knight is separated from its king, however, it tends to be easily snared by the king and rook. In Diagram 139, White has already trapped the knight along the edge. With 1. Rg4 the knight is won. 140) A visually memorable line-up

As a visual pattern, the line up of the three pieces - knight, rook, and attacking king - is very satisfying and memorable (Diagram 140). 1 don't think I'll ever forget it. In Diagram 141, it takes a few moves of setup, but once again the knight falls along the edge, lining up with its two aggressors: 1. Rfl Nb2 2. Rbl Na4 3. Rb4. Note how in Diagrams 139-141 White's centralized king is prepared to operate in multiple directions.

141) Winning the knight

Another type of knight trap occurs in Diagram 142. Here the rook plays to a central square, 1. Re4, the corner of a quadrant (eI-e4-h4-hI) encasing the knight on a knight-two square (g2). With no safe move, the knight is helpless to the oncoming attack of the white king and rook. There are other ways to trap the knight in Diagram 126, but this one is the most efficient and visually memorable. After 1. Re4, a sample continuation is 1...Kb7 2. Kd3 Kc6 3. Ke2 Kd5 4. Rg4, and the knight is caught. 142) Another knight trap

143) White mates in three moves

The knight can also be lost on a knight-two (or knight-seven) square, even when close to its king, especially when both pieces simply run out of space and seem to stumble over each other. In Diagram 143, White has a mate in three moves: 1. Rh7! (I. Rg7 and 1. Rf7 also work) 1...Kb8 (or I ...Nd8 2. Rh8, as well as I ...Nd6 2. Rh8+ and mate next) 2. Rh8+ Nd8 3. Rxd8 mate. As an already indicated rule of thumb, the defending side should avoid letting the knight get separated from its king. Thus, in Diagram 144, Black can hold the position by 1...Nb8!. White can't force any real progress, since White's king is unable to oppose Black's king directly (thank you knight). In Diagram 145, from the game Neumann-Steinitz, Baden-Baden 1870, with Black threatening mate, White had the saving resource, 1. g8/N+!. After 1...Ke6 2. Nh6 Rh7, Black had an easy draw by 3. Ng8. Instead, Neumann played 3. Ng4?, and with the knight meandering away from its king, it was soon trapped: 3...Rh4? 4. Ne3 Re4 5. NdI Rf4+ 6. Kg7 Rf3 7. Kg6 Ke5 8. Kg5 Kd4 9. Kg4 Rfl 10. Nb2 Rb1 11. Na4 Rb4 (the standard winning line-up). 144) Black to play draws

145) White to play draws

146) Think like an eight-year-old

147) Black can't save the position

It's nice to be eight I was once showing this position to an eight-year-old, and he disagreed with Steinitz's fourth move idea, saying he thought he had a better fourth move. In Diagram 146, instead of playing 3...Rh4?, he found 3...Rh3!. It turns out this wins the knight even sooner. For example, if the white king moves to the g-file, the knight gets pinned, 4...Rg3. On 4. Nf2, Black has the winning fork, 4...Rf3+. Meanwhile, on 4. Ke8, Black has 4...Rh8 mate! Diagram 147 shows what happens if the same underpromoting stratagem is tried with a rook-pawn: it doesn't work. If Black tries I...hI/N+ (since l...h8/Q permits 2. Ral mate), it doesn't quite work out after 2. Kf3, in that 2...KfI is met by 3. Ral mate. Once again, the corner brings along its attendant woes.

Rook and minor piece vs. rook The endgames of king, rook and minor piece vs. king and rook also have some ideas worth adding to one's arsenal. The analysis of the ending with the bishop goes way back. Some of the variations have been attributed to Philidor, the greatest player of the eighteenth century. A simple winning idea is displayed in Diagram 148, where it happens to be White to play and mate in four moves. If the white rook checks on b8, the black rook can block the check. So White interferes with that possible defense by 1. Bc4!. That obstruction not only interferes with Black's rook, it enables the bishop to guard f7, in case the black king tries to make a run for it by I...Keg, when 2. Rb8 is mate. Meanwhile, if I ...Kc8, White has 2. Be6+ (or 2. Ba6+) Kd8 3. Rb8+ Rc8 4. Rxc8 mate. And, if you're hoping to induce your opponent to overstep by delaying matters by sacking the black rook, you still lose quickly after I...Rxc4 2. Rxc4 Keg 3. Rf4 Kd8 4. RI8 mate. 148) White mates in four moves

Diagram 149 shows one of the situations analyzed by Philidor, possibly as early as 1750. White aims to take advantage of Black's weaker side, the one away from Black's rook. A sample winning line begins 1. Raj, threatening mate. Black really only has 1...Rd8+. There could follow 2. Kc6 Kb8 (since the bishop temporarily doesn't guard a8) 3. Ra5 (staying poised) 3...Rh8 (aiming for flank attacks, though 3...Rd7 was possible, in that 4. Kxd7 is stalemate; the try, however, fails to 4. Rb5+ Keg 5. Be6, pinning and winning) 4. Kb6 Rh6+ 5. Bc6 Rxc6+ 6. Kxc6 Kc8 7. Ra8 mate. I49) Working on the weak side

In Diagram 150, White takes advantage of the fact that e8 is temporarily blocked by Black's king. By retreating flexibly, 1. Rf4!, White threatens mate (2. Bc6+), as well as a possible bishop-block or rook-transfer to the queenside. Black could pin the bishop, I...Rd3, preventing the check at c6, but then 2. Rg4 is curtains, since 2...Rt3, hoping to block at 18, loses the rook 3. Bxt3. So after 1. Rf4 Black probably tries I...Kd8, but that meets up with 2. Be4!, and mate soon follows: 2...Ke8 (or 2...Rxe4 3. Rxe4 Kc8 4. Rb4 Kd8 5. Rb8 mate) 3. Bc6+ Kd8 4. Rf8+ Re8 5. Rxe8 mate. (150) Playing for a block

Diagram 151 looks rather like Diagram 150, with the slight difference of Black's king. In Diagram 150 it's on e8. In Diagram 151 it's on d8. The win is merely a matter of causing disruption. White starts with 1. Rd7+, forcing Black to make a commitment to c8 or e8. If I...Kc8, then 2. Raj wins because the bishop prevents 2...Rb3. That leaves Black little choice other than 1...Ke8 2. Rb7 (threatening mate at b8 and giving White's rook some operating room) 2...Kf8 3. Rf7+ Ke8 (3...Kg8 allows the discovery 4. Rt3+) 4. Rf4!, and we're getting at the winning idea of Diagram 148. The

final moves might be (once again) 4...Kd8 5. Be4! Ke8 6. Bc6+ Kd8 7. Rf8+ Re8 8. Rxe8 mate. (151) Playing for disruption

In Diagram 152, the bishop guards dl, dissuading the black rook from checking the white king from that square. Meanwhile, from f3, the bishop is able to shift to several potent places to produce different mates. A winning line here would be 1. Rf4! (threatening 2. Bh5+, as well as 2. Bc6+) 1...Kd8 (clearing e8 for a rook block) 2. Bh5 (by guarding the potential interposition square, White again menaces mate, while still keeping d 1 under observation) 2...Kc8 3. Rb4!, and Black is helpless to answer this cutoff, with the deadly 4. Bg4+ looming. Black will either be forced to lose the rook, 4... Rg 1 5. Bg4+ Rxg4 6. Rxg4; or get mated directly after 4...Rcl 5. Bg4+ Kd8 6. Rb8+ Rc8 7. Rxc8 mate. 152) Super bishop

Diagram 153 shows another jockeying position, where White tries to put the black king and rook out

of synch. White mainly wants to gain time to shift his rook to the f-file, cutting off the f-tile and setting up various possible winning ideas. The final plan begins with 1. Raj, threatening mate and forcing I...Rc1, to block the upcoming back rank check. 153) Gaining the f-file

The white rook now shifts back to kingside, 2. Rf7, but this time the rook has grabbed a key cutoff file. Black is reduced to going hack to block mate threats on the kingside, 2...Rel. Note that 2...Ke8 would fail as it does in an earlier analysis to 3. Rf4 Rdl 4. Rh4 Kt8 5. Rg4. So play continues 3. 130. If 3...Re8, White shifts to the queenside and wins, 4. Raj. Black could try 3...Ke8, hitting the rook, but after 4. Rf4, a menacing bishop check at c6 is coming up. Thus the best attempt to fight ott'defeat after 3. Bf3 is 3...Re3. Play might then continue: 4. Bc6 Rd3+ 5. BdS. A possible conclusion from there is 5...Re3 (5...Ke8 6. Rg7) 6. Rd7+ Ke8 (6...Kc8 7. Raj) 7. Raj Kf8 8. Rf7+ Ke8 9. Rf4 Rd3 10. Ra4 Kf8 11. Rg4, and that's that. Diagram 154 illustrates a position that branches into some of the situations we've been looking at. First White plays to grab the seventh rank, 1. Rf8+ Re8 2. Rf7. Now Black seeks some activity, so he plays 2...Re2. After 3. Rg7 Re] White takes a way d I with 4. B13. There could follow 4...Re3 5. Bc6 Rd3+ 6. Bd5 Re3 7. Rd7+ (creating dislocation) 7...Ke8 8. Rb7 (threatening mate) 8...Kf8 9. Rf7+ Ke8 (9...Kg8 10. Rt3+) 10. Rf4 Kd8 (10...Rd3 1 1. Rb4 Kt-8 12. Rg4) 1 1 . Rb4 Rea (1 I ...Kct 12. Be6+) 12. Bc4 Kc8 (12...KcS 13. Rh8 mate) 13. Be6+ Kd8 14. Rb8+ Rc8 15. Rxc8 mate. 154) Branching into various wins

In Diagrams 155 and 156, we see the win coming about quite surprisingly, not by the threat of mate, but by preventing the defending rook from functioning. In either case, whether the defending rook or king must move, the separation be tween them is increased and a winning skewer results. In Diagram 155, Black has I...Ba2!, whereupon 2. Kdl loses to 2...Rhl+. 155) Obstructing to force separation

In Diagram 156, after 1...Bc2!, White has some choice when it comes to picking a losing move. Whether separation occurs by 2. Kfl or 2. Rai, Black has the nifty skewer check 2...RhI+, which I suspect is sufficient. It doesn't have to be like that In looking for checkmates, we may have to settle at first for less final ways to get ahead, winning material by typical chess tactics. A curious pattern emerges in Diagram 157. Black to play can line up everything with 1...Bb7!, and unless White's a magician, there's no satisfactory counter to that sneaky bishop move.

156) Seventh rank dominance

White has two king moves. However, if 2. Kh2, then 2...Rh6+ will put Black a rook ahead, as does the line 2. Kgl Rc I+. White does have two checks. But if 2. Ra2+, Black blocks the check and simultaneously gives a discovered check from the sneaky bishop, 2...Ra6+, winning White's rook. A similar transaction results from 2. Rg8+, where Black has 2...Rc8+. No matter what White does, Black either mates or winds up at least a rook ahead. Some of the finishes have charming mirrorimage partners. If 2. Rh2, then 2...Rcl mate; if 2. Rgl, then 2...Rh6 mate. Or if 2. Rg3, then 2...Rc 1 + 3. Kh2 Rh I mate; if 2. Rf2, then 2...Rh6+ 3. Kgl RhI mate. 157) Lining up to win

Rook and knight vs. rook There are also worthwhile positions to know in the king, rook and knight vs. king and rook endgame. In Diagram 158, with White's king confined to the edge, Black has an easy two-move mate starting

with 1...Ne3+. If 2. Kai, Black has 2...Rbl mate; and if2. Ka3, Black has 2...Rb3 mate. 158) Black mates in two moves

159) White forces mate

Win in a walk over Emanuel Lasker (White) had a not dissimilar situation in a game against Schiffers, from Nuremberg 1896 (Diagram 159). Lasker won quickly, starting with 1. Re7+, and Black resigned. If I ...Kd8, then 2. Nf7+ Kc8 3. Nd6+ Kd8 (if 3...Kb8, then 4. Rb7 mate), and White has time for the casual 4. Ke6, when Black has no good answer against a subsequent Re7-d7 mate; and if instead I ...KfB, then 2. Ng6+ Kg8 3. Rg7 mate. With mating forces hovering around, you never know how things could suddenly turn out. In Diagram 160,

Black's rook gets in the way of flight, depriving Black's king of a potential escape square. Suddenly, the fifth rank becomes like an edge, and White wins with 1. Rh5 mate. (160) White mates in one move

161) White forces a winning fork

Mate's just one way to win Sometimes it's not a matter of mate, but rather a check that forces the king into a bad place, onto a forkable square. In Diagram 161, White wins with 1. Ra6+. No matter where the black king goes, White has a forking check, reducing to a rook basic mate. If I...Kf5, then 2. Nh4+; if I...Kd7, then 2. Ne5+; or if I...Kf7, then again 2. Ne5+. 162) White prevents a trade and wins

Diagram 162 offers a different kind of winning game. Black is hoping to trade rooks, but White frustrates that end with 1. Nh3!. The only viable response, since Black's king is left without a move, is to shift the rook along the second rank, say 1...Rg2, whereupon the double check ends it, 2. Nf2+ Kg 13. Rh 1 mate. 163) White mates in two moves

The last position was terribly unfair to Black, who was down a knight. Let's make it fair this time, adding a knight to Black's side, and we have Diagram 163. But even with equal forces Black can't hold after 1. Re7!, seizing the seventh rank and positioning for mate next move at V. This standard maneuver, assuming the seventh rank so, has won many a chess game. Black does better in Diagram 164, if we can say that about the situation, since Black has an extra rook and knight. After 1. Rd7!, seizing the seventh rank (taking the Exchange by 1. Nd7+? wouldn't be a stellar idea, since Black is ahead in material anyway), Black doesn't have a way to avoid the impending perpetual check. If I...Nc5, for instance, Black can't stop the perpetual that begins with 2. Nh7+, since 2...Kg8 3. Nf6+ dissuades Black from playing 3...Kh8 because of 4. Rh7 mate.

164) White to play and draw

Practice Position #3

Question: In Practice Position #3, isn't this just an easy draw? Solution, page 243.

Back to queens and such While not traditionally part of the basic or elementary mates, nor should they be, a few other setups are surely worth adding to your set of end-play tactical weaponry. Utilitarian ideas occur in situations of queen vs. queen, queen vs. two rooks, queen vs. two queens, rook vs. rook, and two rooks vs. two rooks. Without exploring these notions too deeply, let's start with situations of queen vs. queen. One concept is simple enough: skewering the enemy queen, either directly or by preliminary checks. In Diagram 165, the black queen is lost after 1. Qc8+, when the black king is forced onto the b-file, say 1...Kb6 (or I ...Kb5, it doesn't matter), and 2. Qb8+ gains the black queen next move. 165) White plays and wins

Downgrading to rooks, we can see a comparable tactic in Diagram 166. Except here, whoever moves first wins the other side's rook with skewering checks. If White goes first, the black rook is lost after 1. Rel+. And if Black goes first, the white rook is won by I ...Rc8+ 2. Kb6 Rb8+. Another premeditated twist is seen in Diagram 167. This kind of tactic often arises after the defending side has just promoted (as is also true in Diagram 165). In Diagram 167, the white king is in check, but after 1. Kg3!, the checks are over, and Black has run out of breathing space. White soon mates. Black could try the desperate, I...Qt3+ (a dying man can try anything), hoping for 2. Qxf3'?'?, which would be stalemate, but 2. Kxf3 puts and end to that hope. 166) Whoever moves wins the other side's rook

167) White plays and wins

168) Black retains the discovery

As we move back to queens, we encounter a curious position in Diagram 168. Black is being checked, and can end the check by moving the king to uncover a queen check, thereby gaining control of the move (answering a check with a check, as in advertising and other misconceiving media). But there's a better idea. By playing 1...Kc3!, Black retains the possibility ofa future discovery, and that indeed speeds up the mating process. For instance: if 2. Qe3+, then 2...Kc2+; if 2. Qc7+, then 2...Kb3+; if 2. Qc I +, then 2...Kb3+; if 2. Ka2, then 2...Qa8+3. KbI Qb7+; or if 2. KbI, then 2...Qh7+. 169) White played 1. Qd5!

Diagram 169 shows the same idea from a real game of Nuemann's played in 1887. White played 1. Qd5!, offering a queen trade, setting up a discovery, but leaving his pawn hanging. Play continued I...Qxb4+ (if I...Qg6+, then 2. Kf4+ Kh2 3. Qe5 Qd3 4. b5 Qdl 5. b6 Khl 6. Qe41 Kh2 7. h7) 2.K11 Qel 3.Qh5+ Kgl 4.Qg4+, and Black resigned. 170) Whoever moves wins

Queens shouldn't have all the fun. Rooks can experience the joy of free play against other rooks too. In Diagram 170 we see that rooks, while not as capable as queens, can also give winning attacks. It all comes down to who moves. If Black goes first it's mate at al. But with White to play, one check, 1. Rh3+, leads to another, I...Kd4 2. Rh4+, and the black rook is lost, as in Diagram 166. 171) White to play wins

172) White has a winning double attack

In Diagram 171 it's White to move, and after 1. Ra4, threatening mate at al, the black rook is lost. If Black tries to escape, I...Kcl, then 2. Ral+ skewers king and rook. As in so many rook endings, the ability to shift wings, from kingside to queenside, just like that, is often a key to winning. A different winning motif is shown in Diagram 172. The black rook has just gone to a4, stopping a serious check along the a-file, but Black loses anyway to 1. Kb3!, when White has a double threat: to capture the rook on a4 and to mate at cI. As they used to say at the Marshall Chess Club (I wasn't the only one to hear this), you can't dance at two weddings at the same time. White has a similar winning idea in Diagram 173. Black is checking White's king, forcing it to move into a winning position, which it does by 1. Ke6!. The f5- rook is then lost because of the mate threat at a8. Rooks are often dropped in these types of positions because of double threats. With the chief threat being mate, the defender may have no choice but to abandon his rook to direct capture or permit a winning skewer in order to stop mate. Such is the case in Diagram 174. After 1...Kc7, White's king must flee, 2. Ka6, and that runs into a skewering check at al I. 173) White wins

174) Black to play wins

You never know when a double threat is in the oiling. In Diagram 175 the position looks terribly even, but White hasn't castled yet, which means it can be done now, 1. 0-0-0+!, and that wins the black rook. 175) White has a winning double attack

Moves like this are often overlooked because one tends to think of castling as being a defensive move, and it gets into our subconscious, affecting our judgments and actions. But obviously castling can also be an attacking move, since a rook is thereby activated. Here, the rook does wind up doing something aggressive: it checks the enemy king. But in the end, the real damage is furnished by the friendly king. By getting to safety the king is going to he able to take something for free. Note that in castling queenside it's okay for the castling rook to pass over a square (here b I ) guarded by the opponent. Another set of ideas, involving essentially equal forces, leading to some memorably worthwhile moments, are offered in some positions of two rooks vs. queen. Sometimes the rooks get the advantage, if both rooks are placed well, and sometimes the queen gets to pick oil one of the rooks, if they are placed poorly. Let's first see some cases of rooks gaining ascendancy. In Diagram 176, Black's rooks are poised to manufacture mate. One rook is confining the white king to an edge; the other rook is ready to deliver a back row mating check. But this is not yet possible because the white queen, centralized, guards hl. The winning idea in such cases typically is to force the queen to stop the mate by capturing on the back row. Then the queen is in a position to be skewered. Accordingly, Black wins by 1...Rhl+! 2. Qxhl Rb1+. 176) Black sacs to get it back

The same idea was possible as a variation from the memorable game FischerTal, Bled 1961 (Diagram 177). Fischer had just played g3-g4. If Tal had captured the pawn, I...Qxg4?, White would have seized the h-file, 2. Rh P, when the only way to deal with the upcoming check at h8 would be 2...Qd4. But White would have done it anyway, 3. Rh8+!, since 3...Qxh8 meets up with the skewer check 4. Rb8+. 177) Black can't take the g-pawn

Diagram 178 shows a variation of this theme. After 1. Ra8+ Ke7 (or I ...Kd7), White is unable to give a skewer check at g7 because the g3-rook is pinned. That whole scene, however, is disrupted by 2. Ra7!, since 2...Qxa7 ends the pin and loses the queen to the skewering check, 3. Rg7+. 178) White sacs to break the pin

In Diagram 179, we see a couple of earlier themes coming together. Starting from a menaced position, Black copes with mate by sacking a rook to lure the queen to a bad square, and then checks to force the king into line for a winning skewer. Black gets the desired result beginning with 1...Ra4!, threatening 2...Rh2-h3 mate. If 2. Qxa4, then 2...Rh3+, and after 3. Kf4 (or to e4 or d4) 3...Rh4+, checks and skewers. And if White turns down the rook offer, opting to guard h3, 2. Qc8, Black plays 2...Rh3+ anyway, since 3. Qxh3 Ra3+ checks and skewers from the other direction. 179) Rooks beat queen

In Diagram 180, the white pieces are suspiciously huddled together in a corner (is there a conspiracy afoot?), with the black rooks dominating a cutoff rank. But White to move could break out with queen checks and a resultant perpetual, if Black allows it. It's Black's move, however, and the counterthreat is squashed with I...Rf7!, impeding the queen's exit strategy (along the a2-g8 diagonal). If the queen now leaves the edge, say moving to g5, the win is realized by either rook checking along the edge (Ra7- a8+ or RI7-f8+). So the queen must stay on the edge, 2. Qe8 (or to any of the other unguarded squares along the eighth rank), and Black wins by 2...Rh7+ 3. Kg8 Rag7+ 4. Kf8 Rh8+ (abandoning

one rook to gain the queen), winding up a rook ahead. 180) Seventh rank dominance

181) White has a forced mate

When the attacking king joins the fray the two rooks can become lethal in a different way. In Diagram 181 White is in check, but answering a check with a check (once again, a standard tactic in Hollywood and on television) leads to a forced mate: 1. Kf7+ Kh7 2. Rh8+! (a deflecting sacrifice) 2...Kxh8 3. Rh6 mate. A not too dissimilar double-rook tactic is displayed in Diagram 182. It begins with a discovery, 1. Kf3+. If I...Kgl, then 2. Rcl is mate. So Black must play 1...Kh3, when the second rook is unveiled with another discovery, 2. Kf4+, and 2...Kh4 3. Rh2 is mate. 182) White forces mate

183) Retreating on the staircase

Diagram 183 shows the power of consecutive lateral threats with the rooks. It relies on one discovery after the other, and the effect is to have the attacking king get out of the way (ultimately) by "walking a staircase." It begins with 1. Rg2+. Obviously, 1...Kh7 fails to 2. Rh I+ and mate next move. So Black has to play 1...KfS. Now begins a process of descending the white king down the board, back toward home base, to find shelter and get out of the way of the rooks so they can function fully: 2. KgS+ Kg7 (2...Ke7 heads into a losing skewer check, either Rel+ or Re2+) 3. Kf4+ Kf6 (moving to the h-file is the cul-de-sac it was earlier) 4. Kg3+ Kg5 5. Kf2+ Kf4 6. Kgl+, and Black's king must move into line for a skewer check, losing the queen. Now that really is an example of advancing backward. But we shouldn't conclude that the queen is helpless. With the right circumstances it can often do a number on the rooks, winning at least one of them. In Diagram 184, for example, the supple queen steals a rook with 1. Qf6+!, when I ...Re6 is exploited by 2. Qd8 mate. So Black must let the f6-rook simply twist in the wind.

184) White wins a rook

And in Diagram 185, the rooks are already stumbling over each other, with the one at b6 pinned. White to play, however, doesn't pile up on the pinned rook immediately by I. Kc5?, since Black can start to untangle the situation with I ...Ka4, and there's no win in sight. Instead White starts with the unexpected 1. Kc4!. Now moving the king fails, I...Ka4 2. QdI+, when both 2...Ka5 and 2...Ka3 end in 3. Qal mate. So Black is reduced to moving the a6- rook, 1...Ra7, when then White can pile on the pin pressure with 2. Kc5!. By taking this extra move to reach the desired square, the white king has engaged in our old friend triangulation (tracing a triangle from d5 to c4 to c5, the latter being actual desired square). After 2...Ra6, defending b6 (2...Rab7 loses to 3. Qa8+), White wins with 3. Qd2+, when 3...Ka4 is shut down by 4. Qa2 mate (a pure mate). One final idea to end this sequence offers a situation of imbalanced material, that is, queen vs. rook and bishop. 185) White has a winning double attack

Naturally we would expect the queen to gain the advantage, but the position of Diagram 186, modified from an idea of Reti, provides another view altogether. After 1...Bb4!, White's queen can do

nothing about the upcoming rook mate at el. 186) Black mates in two moves

So much for queen vs. two rooks, also of interest are various situations of two rooks vs. two rooks. In Diagram 187, simplified from a more complicated original, we have a peculiar situation involving pairs of rooks. Various threats emerge along the seventh and eighth ranks. With 1...Rdd2!, White is left without a good move. Neither black rook can be captured, without a white rook hanging, ending with White getting mated. And if White tries to free one of the rooks, say 2. Ra I, there follows 2...Rh2+ 3. KgI Rdg2+ 4. KfI RhI mate. Nor does moving the white king to begin with help, since 2. KgI Rg2+ 3. Kfl Rd12 is mate (3. Khl falls into the main text, 3...Rh2+ 4. KgI Rdg2+ 5. Kfl RhI mate). White is lost. 187) Black doubles the trouble

Diagram 188 furnishes another winning idea. In the position both sides have threatened rooks: White's

at h5 and Black's at d l . But having the move, White is able to use the time advantage to defend the b5-rook with a threat, 1. Rhb3!. I l 'Black then moves the d I -rook to safety, or defends it with the other rook, White has 2. R3h4, which may not be very sporting, but happens to be mate. 188) Save with a threat

In Diagram 189 White's extra pawn proves to be a problem in that it winds up providing shelter for Black's king to avoid checks. Black starts with the lateral check, 1...Rh8+, forcing a block, 2. Rh6. But rather than trading rooks 189) Black doubles behind the lines

190) White mates in two moves

Black has a nasty doubling behind the lines, a kind of x-ray menace, 2...Rgh7!. If 3. Rxh7 Rxh7+, the b6-rook is left hanging. Meanwhile there simply is nothing to be done to avoid loss of a white rook. It's another case of more being less, since the extra pawn backfires, sheltering Black's king. Finally, just to end on a knightly note (a rookly note doesn't sound right), Diagram 190 offers a mate in two moves. Obviously, the position is an easy win for White whether you find the mate or not. But the winning pattern illustrated after 1. Raga! is symmetrical delight. If Black's king moves, the appropriate white rook mates, as it does if the knight moves instead. Thus 1...Kh4 and 1...Nh6 are both answered by 2. Rh2 mate; while I...Kh6 and I...Nh4 are both answered by 2. Rh8 mate. This is why some people play chess, for patterns, patterns, and more patterns. The rest have their own reasons.

Back to pawn endings The main fight in most endings consists in promoting an extra pawn into a win. Perhaps the most exemplary paradigm of the entire body of endgame theory is the process of winning in the situation of king and pawn vs. king. Much of endgame theory starts there and is built around a few basic ideas. An elemental win is shown in Diagram 191, if it's Black's turn to play. Indeed, the position is one of mutual zugzwang: neither player wants to move. If White moves first it's a draw, and White doesn't want to draw. If Black moves first the position is lost, and only a small percentage of earthlings wants to lose. 191) Zugwang

From Diagram 191, move the pawn back one square and we have Diagram 192. Here it's the opposite: instead of neither player wanting to move, both players want to move. Let's see. If White goes first, the win is achieved by 1. e7, squeezing Black's king off the edge. There follows I ...Kf7 2. Kd7, and the pawn queens. If Black goes first, however, the position is drawn after, I...Kd8, taking the direct opposition, when 2. e7+ (it's a bad sign for the attacker if the pawn advances to the seventh rank with check) 2...Kef 3. Ke6 is stalemate. 192) Both players prefer to move

As a helpful reminder, the side having the extra pawn doesn't want to advance the pawn to the seventh rank with check. To do so leads to a draw. Advancing the pawn without giving check, however, forces the enemy king to move off the outside row, and that's a win. Diagram 193 is more like Diagram 191: once again, neither player wants to move. If White goes first, Black has the opposition, and the game is drawn, I. e7+ (advancing with check to the seventh rank is, once again, a dreadful sign) I ...Ke8 2. Ke6 stalemate (any other move loses the pawn). On the other hand, if Black goes first, White has the opposition, and Black loses, 1...Ke8 2. e7 Kf7 3. Kd7. 193) Nobody wants to move

As a rule of thumb the side having the pawn doesn't want to advance it ahead of its king (unless the defending king is placed so poorly that circumstances justify it). In Diagram 194, from the game Jimenez-Ivkov, Havana, 1962, the black pawn has reached its sixth rank, ahead of its own king. The

tactics do not support it. The defender holds the draw by keeping its king on the same file as the pawn, either one or two squares in front of it. Then, as the attacking king advances, the defending king takes the opposition, and that holds out the barbarians. In the actual game, White played 1. Kc 1, staying on the c-file, and the players agreed to a draw. The final moves might have been 1...Kd3 2. Kdl (taking the direct opposition) 2...c2+ (when giving check is not desirable) 3. KcI Kc3 stalemate, though every other move draws as well. 194) Jimenez-Ivkov, Havana 1962

Four winning positions To introduce this section let's examine four simple winning positions focused around the same center pawn. In all four cases, Diagrams 195-198, it's White's turn to move. White wins in each situation by taking the opposition. In Diagrams 195 and 196 White takes the direct opposition with a king move, 1. Ke6. No matter which way Black's king thereafter goes, White's king turns up the board to its seventh rank, and the pawn then has a secured path toward the promotion square. If, for instance, Black plays I...Kd8, then White wins with 2. Kf7; if Black instead plays I ...Kf8, then White wins by 2. Kd7. 195) White takes the opposition with a king move

196) White takes the opposition with a king move

197) White takes the opposition with a pawn move

In Diagrams 197 and 198 White takes the direct opposition by a pawn move, 1. e6. In Diagram 197 play might continue I...Ke8 2. e7, which forces (squeezes) Black's king off the edge. White then plays 3. Kd7, gaining control of e8, and the pawn will queen with support. In Diagram 198 play would go I...Ke8 2. e7 Kd7 3. Kf7, with a comparable result. The basic position The positions we've just examined may aid us in understanding the next diagram. The situation of Diagram 199 reflects a plain king-and-pawn ending, with White having a single extra pawn. Several questions emerge. Is the position a win? If it is a win, does it matter which side moves first'? It turns out that having the move is crucial. That is, White to play wins, while Black to play draws. In order to proceed, however, it's helpful to introduce a few terms and ideas. 198) White takes the opposition with a pawn move

(199) The basic position

The universe The universe consists of three files: the file the pawn is on, as well as the two adjacent files. Thus, in Diagram 199, the universe is made up of all the squares on the d-, e-, and f-files together. (If instead the pawn weren't on e2, but on d2 (or on any of the other d-file squares), the universe would consist of all the squares on the c-, d-, and e-files.) Generally, once inside the universe, it's not to the advantage of either side's king to move outside the universe. For the purposes of our discussion the rest of the board doesn't have to exist. With White to play the position of Diagram 199 can be won by following certain rules, almost without thinking, though I'm not suggesting here, or any place else, that one handle any aspect of chess without at least a little thought. The real battle depends on getting the white king to its sixth rank, ahead of its pawn, inside the universe. Once the king occupies a square on its sixth rank, within the universe, the pawn can be advanced to its fifth rank, without regard to the opposition (assuming the pawn is not immediately hanging to capture). In order to achieve that winning situation one can play in accordance with a few rules that relate only to play within the universe. To win from Diagram 199: Rule one: Advance your king, aiming to occupy its sixth rank. On any particular move, if you can't do rule one, safely advancing the king toward its sixth rank, go to rule two. Rule two: Take the opposition. This way you can continue the king's safe advance to its sixth rank on the next move. After your king has reached its sixth rank, go to rule three. Rule three: Advance your pawn to its fifth rank. Advice: Save your pawn moves: you may need one to gain the opposition. To be sure, in most endings, its a good idea not to make unnecessary pawn moves, since they may reduce options while incurring weaknesses. Once you get the desired setup, king on its sixth rank, pawn on its fifth rank, then you have to see

where the opposing king is. At that point you should take the opposition. Depending on the enemy king's placement, you will have to see whether you need to make a king or pawn move to comply with the winning procedure previously laid out. Let's turn back to Diagram 199. Following our rules, White to play should go to rule one and advance the king. White can play either 1. Kd2 or 1. Kf2, it doesn't matter: both conform to rule one. Let's say White plays 1. Kd2 (rule one.) Let's further say Black plays 1...Kd8, taking a very distant opposition. White now stays with rule one, 2. Ke3 (yes, 2. Kd3 also satisfies rule one). Black continues with, 2...Ke7, maintaining the distant opposition. White now plays 3. Ke4 (yes, 3. Kf4 and 3. Kd4 both also meet the requirements of rule one, and both also work). Usually the process goes slightly faster by taking the middle road, so that the attacking king eyes both boundary files of the universe (here, the boundary tiles being the d- and f-tiles). Now, Black plays 3...Ke6, keeping the opposition (Diagram 200). White's king can no longer advance inside the universe (it can't yet move from the fourth rank to the fifth rank). Since rule one doesn't work here, White shifts to rule two: taking the opposition. But it can't be done with a king move. Having not wasted pawn moves, however, White is now able to regain the opposition with 4. e3!. Black must then give ground. Whichever way Black responds, the winning process continues by going back to rule one. That is, if Black plays 4...Kd6, White answers 5. Kf5 (advancing the king, in accordance with rule one); if instead Black plays 4...Kf6, White turns up the board the other way, 5. Kd5, again, complying with rule one. In either situation, Black is likely to play 5...Ke7, stopping further advance of White's king. Since rule one doesn't work at that point (the white king being unable to advance inside the universe), White must go to rule two, taking the opposition (here, with a king move), 6. Key (Diagram 201 ). 200) White must go to rule two

No matter how Black replies on this move, White's king advances to the sixth rank on the next move, in compliance with rule one. If 6...Kf7, then 7. Kd6 (if instead 6... Kd7, then 7. Kf6). Thereafter, White moves the pawn to its fourth rank and then its fifth, following rule three (getting the pawn to its fifth rank). An exemplary conclusion (after 7. Kd6) might be: 7...Kf6 8. e4 Kf7 9. e5 Ke8 10. Ke6, and the pawn will queen.

201) Black must give ground

Moving to Diagram 202, it should be noted that White to play shouldn't push ahead with the king, I. Kd7, since I. Kf6 would force the white king hack, and time is wasted. But since White's king already occupies the sixth rank, the correct approach is to move the pawn to the fifth rank, with the immediate 1. e5. 202) Getting the pawn to fifth rank

203) Take the opposition

Another pitfall players tend to fall for occurs in Diagram 203. With 1. e5?, the win is thrown away, and Black draws by taking the opposition, l ...Kt7; when 2. e6+ Ke8 (staying on the pawn's file) 3. Kf6 Kt8 (taking the opposition) 4. e7+ (a bad sign) 4...Ke8 5. Ke6 is stalemate. The correct move is not 1. e5?, but 1. Ke5!, taking the opposition (rule two). Black's king then has to give ground, and White's king has a turning maneuver to the sixth rank (rule one), with an easy win in hand. After getting the king to the sixth rank, White advances the pawn to the fifth rank (rule three), as already indicated. Within the universe, the best opposition for the attacker to possess is the one along the middle file (the critical opposition), since having it allows the king to advance on the next move, as in Diagram 204. 204) The middle opposition is best

205) White needs an extra move

206) White still needs the opposition on the e-file

207) Taking a critical opposition

But in Diagrams 205 and 206, after Black has played I...Ke6, White still has to play 2. Ke4 (whether it's Kd4-e4, as in Diagram 205, or Kf4-e4, as in Diagram 206) before being able to advance the king to the fifth rank. In Diagram 207 White keeps the ball going by taking a critical opposition (along the middle file of the universe), 1. Ke3, reaching the fourth rank on the next move (rule one). Sometimes the superior side has to proceed a little more slowly before getting to the promise land. In Diagram 208 White has to use an initial opposition to obtain a critical one. Thus 1. Kf3! is an interim opposition. After 1...KeS White gets the critical opposition by 2. Ke3, and schooled players can take it from there. 208) "Taking one opposition to get another

209) Start with a diagonal opposition

210) Entering the universe with the opposition

211) Diagonal opposition wins

Diagram 209 illustrates that the proper opposition to springboard from can also be a diagonal one. With 1. Kf3! Key 2. Ke3 (rule two) we're back in familiar territory, White having a critical opposition and a turning maneuver to the fifth rank coming up (rule one). As already stated the side having the pawn doesn't want to advance it ahead of its king unless the defending king is positioned so that resulting tactics work out favorably. Such is the case in Diagram 210. White's pawn is advanced ahead of its king, but the king hasn't yet entered the universe. It does so now, 1. Kf6!, taking the opposition. After 1...Ke8 2. e7 (advancing without check!), Black's king is squeezed off the back row. In Diagram 211, the white king enters the universe, once again taking the opposition. This time, it's the diagonal opposition, which here wins appropriately, 1. Kf6 Ke8 2. e7 Kd7 3. Kf7. 212) Taking the opposition before entering the universe

If the kings are outside the universe to begin with it may be necessary first to take the opposition outside the universe before entering it. Thus, in Diagram 212, White first plays 1. Kg6!, taking a

direct opposition, outside the universe, before walking the king, and the opposition, across to f6, inside the universe. Black can resign after 1...Kf8 2. Kf6 Ke8 3. e7. Note that playing 1. Kf6? draws to I K178 2. e7+ (a bad sign) 2...Keg 3. Ke6.

Whenever the defending king retreats to a corner, or is driven to one, the attacker should be careful not to allow stalemate. In Diagram 213 White must not play 1. c7'?'? (stalemate). Correct is to invade with the king, 1. Kc7; and then 2. Kd7, positioning the king on the outer file of' the universe, ensuring the safe convoying of the pawn. Most of these careless mistakes can be avoided by (what else'?) being more careful. One way to do that is, before playing the intended move, ask a simple question: is it okay for me to play that move'? Then one must take a real look at the upcoming position in one's mind. It's not a profound step, and it's not a surefire route to perfect chess. But that last conscious effort might indeed trigger awareness of a problem while there's still time to avert it. 213) Avoid Stalemate

Even when a king is inside the universe occasionally it can be desirable to move it outside the universe to cope with the presence of other material. In Diagram 214 White wins by 1. Kh6!, when 1...Kg8 loses to 2. Kxg6 Kf8 (or 3...Kh8, hoping for 4. 17 stalemate; but 4. Kt-7 instead brings about the win, similar to Diagram 213) 3. f7; and I...g5 allows 2. t7 g4 3. f8/Q mate (yes, White can promote to a rook too). Note that, if there were no black pawn on g6, White could also win by playing 2. Kf5 Kg8 3. Ke6 (taking the diagonal opposition) 3...Kf8 4. P. 214) First take the opposition

215) Black mates in two moves

Of course, even in these simple endings, there are all kinds of silly ways one can stumble into stalemate. In Diagram 215, the natural tendency for Black would to be to make a new queen, I ...fI/Q?'?, but that's stalemate. Yet, by an act of underpromotion, taking a rook instead, 1...f1/R! (Black could also play l ...Ke2 and then make a queen next move, but why?), stalemate is avoided. Rather it's mate next move, 2. Kh3 Rhl mate. As we've already seen, direct and diagonal oppositions are not the only oppositions. There's also the distant opposition, and it can be quite a weapon in its own right. 216) Whoever moves wins

In Diagram 216 whoever plays first takes a very distant opposition and uses it to force a win. For example, if White goes first, the game could proceed 1. Ke2, taking the very distant opposition. On 1. Kd2?, Black can hold with I...Kd8, stealing the opposition, 2. Ke3 Ke7 3. Ke4 Ke6 4. Kd4 Kd6, and no progress can be made. After 1. Ke2, if I...Kd7, then 2. Kd3 Ke6 3. Ke4 Kd6 4. Kf5 Kd5 5. KxgS Kc4 6. Kf6 Kxb4 7. g5 Ka3 8. g6 b4 9. g7 b3 10. g8/Q, and White is able to prevent Black's bpawn from queening. If it were Black's move at first a similar set of winning variations would apply the other way. That is, after I ...Ke7, taking a very distant opposition, Black would have a forced win in turn. 217) Distant opposition draws

In Diagram 217 the distant opposition is used to hold the draw. White to play has 1. Kgl!, and Black can make no headway. For example, 1...Kf5 2. Kfl! (and not 2. Kf2? Kf4 3. Ke2 Ke4, with a turning maneuver coming up) 2...Ke4 3. Ke2, and White holds. 218) Gligoric-Fischer, Yugoslavia 1959

A not unrelated situation occurred in the game Gligoric-Fischer, Yugoslavia 1959 (Diagram 218). With Black Fischer held it together by 1...Kb8!, when White can't take a distant opposition, since b4 is blocked by White's own pawn. The players therefore agreed to a draw. Diagram 219 depicts an unexpected way to draw using the distant opposition. White draws by 1. Kh1! (but not 1. Kfl?, which loses to I...Kd2 2. Kt2 Kd3, and White must surrender the direct opposition). After I. Kh1, though, Black can make no real progress. For example, if 1...Kd2, then 2. Kh2! (keeping the distant opposition) 2...Kd3 3. Kh3!. Or I...Ke2, then 2. Kg2 Kea 3. Kg3, when 3...e4 4. fxe4 Kxe4 5. Kg4 wins the g-pawn. Nor does the tricky I...g4 go anywhere, since White holds by 2. Kg2, when 2...Ke2 3. fxg4 e4 4. g5 e3 5. g6 Kd2 6. g7 e2 7. g8/Q el/Q is just a plain draw. Note that 2. fxg4'? fails because of 2...e4 3. g5 (or 3. Kg2 e3) 3...e3 4. g6 e2 5. g7 e I /Q+, and White loses. 219) Distant opposition draws

Back to obliqueness

Now and then the oblique or rectangular opposition also can play a determining role. In Diagram 220 we see a position stemming from the insightful analysis of the great Mikhail Botvinnik. It supposedly was based on a variation from an actual game, upon which Botvinnik decided to expand. In it White relies on the opposition to fight tooth-and-nail to occupy a crucial square. In Diagram 219 White's pawn at f3 acted as an obstacle, preventing White from maintaining the opposition in certain variations. In Diagram 220, it's the pawn at a6 that winds up complicating Black's chess life. It all begins with 1. Kf5!, seizing the rectangular opposition. Various things can happen after 1. KfS. Let's examine a few of the contingencies. For one White could win the d5- pawn by force, say I...Kc6 2. Ke6 Kc7 3. KxdS. But after 3...Kd7, taking a meaningful opposition, Black can still draw. For example, 4. Kc5 Kc7 5. d5 Kd7 6. Kb6 (otherwise, there's no direct win by supporting the advance of the d-pawn; best is to use it as a de coy) 6...Kd6 7. Kxa5 (or 7. Kxa6 KxdS 8. Kxa5 Kc5, also drawing) 7...Kxd5 8. Kxa6 Kc6, and that's a draw. White's king can't get off the edge and still bring about a win. 220) Rectangular opposition wins

But there's another way to go, and it does indeed win. White doesn't play to win the d-pawn at first. Rather, White goes for the a-pawns. After winning those, then the win of the d-pawn becomes critical. Moreover, the entire winning process has to do with the opposition and using it eventually to occupy an unexpectedly useful square: a8!. In a way, the key lines demonstrate a dance of death between the two kings. Furthermore, the winning maneuvers occur over a kind of universe; that is, a setup of three ranks (instead of files), including the sixth, seventh, and eighth ranks, with the seventh rank being the middle and key one, where turning maneuvers become important. You have to change your perspective a bit, but you can do it, playing the opposition game at a ninety degree angle. A sample variation begins 1...Kc6 2. Ke6 Kc7 3. Ke7, keeping the opposition instead of winning the dpawn. Now on 3...Kc8, White has a turning maneuver, 4. Kd6!, leading to 4...Kd8 (taking the opposition, but a meaningless one) 5. Kc6 Kc8 6. Kb6 Kb8 7. Kxa6 Ka8 (for instance) 8. Kxa5 Ka7 9. Kb5 Kb7 10. Kc5, winning

the d-pawn and the game. So Black has to try, instead of 3...Kc8, 3...Kc6. Having used the opposition to achieve a winning position, White can abandon it with 4. Kd8! (a turning maneuver). The meaningless opposition Black gets after 4...Kd6 loses to 5. Kc8 Kc6 6. Kb8 Kb6 7. Ka8!, and Black's own extra pawn at a6 prevents the taking of a meaningful opposition. There might follow 7...Kc6 (a meaningless diagonal opposition) 8. Ka7 Kc7 (another meaningless opposition) 9. Kxa6 Kc6 10. Kxa5 Kc7 (still another meaningless diagonal opposition) 11. Kb5 Kb7 (a meaningless direct opposition) 12. Kc5 Ka6 13. KxdS Ka5 14. Ke6 and wins. In the end Black loses because of the extra pawn at a6. The mere presence of this unit prevented the black king from seizing a meaningful opposition and holding. It's another one of those delightful chess absurdities, a case of more being less. Although, to be reasonable about it, if there were no pawn on a6 to begin with in Diagram 220, White could win instead by capturing the d-pawn first with a direct outflanking attack; and then White could follow through, capturing the a5-pawn, simplifying to an easy win. Try it and see for yourself. Shouldering responsibility Not only are there different kinds of opposition, there are different ways to use the opposition. In addition to the obvious uses of the opposition, to force your own king to good squares or to prevent the other side from doing so directly, there are sometimes less obvious methods to achieve the same results, but still involving the opposition. In Diagram 221, White uses the opposition to stop the defender from getting to the pawn. With 1. Kc5!, taking away the square b4, the promotion of the a-pawn is ensured. Being shouldered out by White's king, the black king is reduced to 1...Kb2, when the two-square option, 2. a4, wins easily. 221) Shouldering with the opposition

The same kind of shouldering (as if you were using your shoulder to block participation) can start

much earlier, on the other side of the board. In Diagram 222, White seizes the direct opposition, 1. Kf5!, and maintains the opposition across the oppositional field, until the white king reaches c5, as in the previous example, when the a-pawn is then safe to advance. After 1...Ke3 there would follow 2. Ke5 (maintaining the opposition) and shouldering out Black's king) 2...Kd3 Kd5 3. Kc3 Kc5, and we've arrived at Diagram 221, with a clear win in view. 222) Shouldering across the field

In Diagram 223 White can't push the pawn immediately (I. g4'?) toward promotion since Black's king gets within the square of the pawn. The upshot is, by moving the king to c4, c5, or c6, Black easily catches the pawn. But with 1. Kb3!, White takes the direct opposition and keeps it right across the board, until a critical opposition occurs, with the white king at g3 and the black one at g5. A turning maneuver then follows and White wins in the typical way. A representative variation is 1. Kb3! (shouldering out Black's king) 1...Kc5 2. Kc3 Kd5 3. Kd3 Ke5 4. Ke3 Kf5 5. Kf3 Kg5 6. Kg3, and White has a turning maneuver next move, either to f4 or h4 (depending how Black plays it), and the win is achieved as before, by implementing the rules of thumb already prescribed. 223) Crossing the oppositional field

One thing to worry about in a situation like that of Diagram 223 is the slightly greater complexity of a knight-pawn to the straightforwardness of a bishop-pawn or center-pawn (to be sure, the rook-pawn case is typically worse). With a knightpawn a wrong step could result in unnecessary stalemate. An example of how to do it properly is seen from the game Maroczy-Marshall, Monte Carlo 1903 (Diagram 224), with Black to play. Marshall won after 1...Kg4 2. Kh2 Kf3 3. Kh3 g4+ 4. Kh2 Kf2 (Marshall had to be careful here, since 4...g3+? 5.KhI draws by either 5...g2+ 6. Kgl or 5...Kf2 stalemate) 5. Khl. And now, though it's a win, Black has to do the unusual and go back a rank, 5...Kg3, and, by maneuvering the king to the h-file, Black avoids stalemate, 6. KgI Kh3 7. Khl g3 8.Kg1 g2. With the squeeze on White's king is forced off the home rank and Black wins. 224) Maroczy-Marshall, Monte Carlo 1903

225) Don't take yet

Material is such an alluring element that sometimes the focus is mainly on winning it to the disregard of greater or more immediately relevant issues. Consider Diagram 225. White could play I. Kxe5?, but that loses to I...Kc6 2. Ke4 Kb5 3. Kd3 Kb4 4. Kc2 Kc4, taking the direct opposition and ensuring a turning maneuver to a desired rank on the next move (rule one). But if White temporarily ignores the material in favor of taking the direct opposition, 1. Kd5!, a pawn is captured on the next move under superior circumstances. For instance, if I ...Ke7, White takes the e-pawn, keeping the direct opposition, and later gets back in time to take the c-pawn, 2. Kxe5 Kd7 3. Kd5 Kc7 4. KxcS. If Black instead heads the other way, I ...Kc7, then White first takes the c-pawn, 2. KxcS, keeping the direct opposition and leading to the subsequent gain of the e-pawn, 2...Kd7 3. Kd5 Ke7 4. Kxe5. Nor, after 1. Kd5, does it help much for Black to sac one of the pawns at once, say I ...c4, since 2. Kxc4 Ke6 3. Kd3 Kf5 4. Ke3 is clearly a draw (as is I ...e4 2. Kxe4 Kc6 3. Kd3 Kb5 4. Kc3). A disguised version of Diagram 225 is Diagram 226. White draws by 1. d7! Kc7 2. d8/Q+!, sacrificing the pawn to achieve a meaningful opposition, neutralizing Black's two pawns. After 2...KxdS 3. Kd6, we're in a comparable situation to Diagram 225, with White holding the draw. 226) Sacking to split the pawns with the opposition

Diagram 227 shows a slightly more complicated edition of the same theme. Indeed, whoever moves wins. If White goes first the win is achieved by 1. Kc6 or 1. Kc7) 1...Kc3 (or I...Kc2) 2. Kxb6 Kxb3 3. Kb5!, taking a meaningful opposition that acquires material without losing any. That is, if Black plays 3...Ka3, White takes the a-pawn, 4. KxaS, and after 4...Kb3, keeps the cpawn by 5. Kb5, winning with the spawn. If E31ack instead moves the other way, 3...Kc3, then a similar winning variation occurs in the other direction, 4. KxcS Kb3 5. K65, with White's c-pawn now the one to queen. Note that if White doesn't take the opposition by 3. Kb5!, instead capturing either pawn, Black gets to take a pawn as well and eventually draws, with both sides possibly promoting. For example, 3. Kxc5? Kxa4 4. Kb6Kb45.c5a46.c6a37.c7a28. c8/Q a I /Q. White gets to check first, but can't make anything useful out of it. Nor does 3. KxaS offer more hope after 3...Kxc4 4. Kb6 Kb4 5. a5 c4. Once again, both sides queen, White gets to check first, but it doesn't lead to anything, and the game is drawn. Naturally, with Black having the first move, the same kinds of variations apply to Black, who then wins as White does. A sample line would be , I...Ke3 (or I...Kc2) 2. Kc6 (or 2. Kc7) 2...Kxb3 3. Kxb6 Kb4!, winning similarly to the variations already examined. 227) Delaying capture for the opposition

Forced jettisons Obviously the opposition is often used to force the enemy king to make concessions, and some concessions can be rather amusing, though painful for the side in freefall. In Diagram 228, Black to play takes the diagonal opposition with 1...Kcl!. After 2. Ka2 Keg 3. Ka3 (what else?), Black squeezes White with 3.... Kbl!. White is constrained to lose a pawn by 4. b4. Black can then take with either the a-pawn, 4...axb4+ 5. Kb3 Kal (it's always fun to move to the corner, when it works, though 5...Kcl also wins) 6. Kc2 Ka2; or with the c-pawn, 4...cxb4+ 5. Kb3 KaI (or again 5...Kcl ). 228) Forcing a ditching by taking the opposition

229) Squeezing in the corner

Welcome to Diagram 229. Though it doesn't hinge on the opposition, White does entrap Black's king in the corner, and Black must ditch a pawn to survive. But Black doesn't survive, which is evident after 1. Kf7! h5 (or I ...h6) 2. g6 h4 3. g7+ Kh7 4. g8/Q+ Kh6 5. Qg6 mate. Although the idea is explored in another section of this book as well, here is one more jettison position for your amusement. In Diagram 230, Black conveniently stalemates the white king, but White still has a move, and it leads to a kind of self-imposed mate. The game ends with 1...Kd3 2. b4 axb4 3. a5 b3 4. a6 b2 5. a7 bl/Q mate (or 5...bl/R mate). But this position isn't as critical as certain types of squares discussed in our next section. 230) Forced mate coming up

Critical squares Some previously explored positions are worth bringing up again and again. Not that they're necessarily intriguing, but these repetitions enable certain concepts to be flushed out as they instill fuller perspective. Besides, in trying to comprehend a subject, it can help to break complex ideas down into parts. This may appear somewhat artificial. But over time such reinforcement brings on greater facility as it finds an integrated place for each concept in the overall picture, converting the unnatural to the intuitive. Read on and you'll see it's not as mysterious as it may sound. A case in point is Diagram 231, which we've already examined several times in different contexts. It's an easy win if White goes first. If Black goes first, however, the game is drawn. To understand more about this position, and using it as a launching pad for more intricate positions, we're going to present another concept to broaden the discussion. The conception I'd like to introduce is that of critical squares or key squares. 231) The kings do not stand in opposition (yet)

Diagram 231 is a win with White to play. Diagram 232, after Black has presumably moved the king to e7, taking the very distant opposition, is a draw with White to play. (Note that in Diagram 232 the kings stand in very distant opposition even though there's a white pawn at e2, which does not affect the consideration.) Why should one little king move (Ke8-e7), played so far away from White's side of the board, be of such consequence'.' The answer is that it enables Black to prevent White from occupying any of the critical squares. 232) Black has the opposition

To clarify and expatiate on that answer, let's look at two other positions, Diagrams 233 and 234. Diagram 233 is critical and the outcome depends on which player has the opposition, that is, which player doesn't have to move. If it's Black's turn, which means White has the opposition, Black's king could do no better than moving to squares on the outside files of the e- pawn's universe, to the d-file or the ftile, let's say either to d5 or f5, allowing White's king an advance to f4 or d4 (rule one). In both instances White obtains a winning setup. If it's White's turn, however, the white king can't reach d4 or f4 without eventually advancing the epawn. The result is that the white king isn't able to reach the sixth rank ahead of the pawn, which is required in order to attain a winning game. Accordingly, this position shows a true zugzwang, that is, a mutual one. 233) It depends on who moves

Jump to Diagram 234. Here, it's just the opposite of Diagram 233. In Diagram 233, neither player wants to move. In Diagram 234, both players want to move. In Diagram 234, if Black goes first, there follows I...Ke5, taking the direct opposition and reaching the position of Diagram 233 with White to move, which is a drawn situation. But if White goes first in Diagram 234 the white king can move to e4, d4, or f4, all of which give White a winning game. Generally speaking, with choice, it's better to take the opposition along the middle file of the universe, so that rule one (advancing the king forward) can be applied on the next turn. 234) White to play wins

Thus, from these positions, and the corresponding analysis, two things are clear. With the white pawn on e2: (I) It's a win if the white king can get to any of the three squares (inside the universe) which are two ranks ahead of the passed pawn; namely to d4, e4, or P. (2) It's a draw if Black can stop the white king from getting to any of those three squares. Remember, for these considerations, we're only interested in what happens inside the universe, that is, inside the rectangular block of squares containing three consecutive files, including the d-, e-, and f-files. This rectangle is based on the placement of the superior side's pawn, which occupies the middle file of that very universe. The imagined rectangle therefore runs from dl to d8 to f8 to fI to dl. Every passed pawn has... Every passed pawn has associated with it a system of critical or key squares. (Some authors use the term "critical," others prefer "key." Here we will mainly rely on "critical," but if we vary a bit, rest assured the same notion is implied.) For passed pawns not on the a- or h-files, on an otherwise empty

hoard, the critical squares generally are the three squares two ranks ahead of the pawn, on the files contained within the universe. Thus with a white pawn on e2, as in Diagrams 231-235, the critical squares are d4, e4, and P. What this means is that, if the white king can occupy d4, e4, or t4, the win can be forced, whether or not Black has the opposition. The only exception to this would be if the defending king is so placed that it's already in position to win the pawn directly. To be sure, the concept of critical squares doesn't apply when there are immediate tactics obviating it. Consider Diagram 235. Even if Black has the opposition it doesn't impact the result since the white king already occupies a critical square. White merely advances, 1. e3, regaining the opposition (rule two), and Black must give ground, allowing the white king to move ahead to f5 or d5 (if not e5, if the black king moves hack a rank). In either case the white king will have advanced two ranks ahead of the new placement of the e-pawn. Once the pawn then reaches its third rank, the white king will be occupying a critical square on the fifth rank. This setup conforms to the winning requirement for the superior king, of needing to occupy a square both inside the universe and two ranks ahead of the pawn. 235) White to play

So in Diagram 236, with the passed pawn being on e3, the critical squares are not d4, e4, and t4. The two-rank-ahead formula says the critical squares should be d5, e5, and f5. This means that the white king, in order to force a win, would need to occupy d5, e5, or f5. Moreover, if the e-pawn were not on e3, but on e4, the critical squares would be d6, e6, and f6. With the e-pawn so positioned, in order to force a win, the white king would have to occupy d6, e6, or f6. 236) Neither player wants to move

(237) Neither player wants to move

Once again, a square is critical if, by occupying it with the king, the superior side can force a win. On the other hand, if the superior side's king can't occupy it, or any other suitably comparable square, the win can't be forced. It's as simple as that. Let's further add that the inferior side's king doesn't have to occupy a critical square. It merely has to prevent the superior side's king from occupying one. In Diagram 237 the critical squares are d6, e6, and f6, and neither player wants to move. If White goes first, Black has the opposition, and the white king can't reach d6, e6, or f6 satisfactorily. If Black goes first, however, the white king will be able to reach one of the critical squares. 238) A win no matter who moves

The situation of Diagram 238 shows a limiting case. It turns out, because the edge of the board (the eighth rank) imposes limitations on the black king, the white king doesn't have to get two ranks ahead of the passed pawn. Here, having the king a single rank ahead of the passed pawn (while still inside the universe) is sufficient to ensure the win. Thus once the attacking king reaches the sixth rank, the attacker gets a break, so to speak. The king on the sixth rank actually occupies a critical square for the pawn, whether the pawn is on the fourth or fifth rank (or, for that matter, even if it is on the second or third ranks). Consequently, as said before, once you get your king to the sixth rank, simply advance your pawn to its fifth rank, where the situation is a win regardless who has the op position. Once the king is on the sixth rank, and the pawn is also on the fifth rank, then you can think about the opposition. With White to move in Diagram 238 Black would have a meaningless opposition. After, let's say, 1. Kd6 Kd8 2. e6, White gets a meaningful opposition and a winning position. This suggests that the opposition is merely the tool used to tight for the critical squares. The attacker uses the opposition to help the friendly king occupy a critical square. The defender uses the opposition not to occupy a critical square but to stop the other side's king from doing so. If having the opposition affects the result the opposition is meaningful. If having the opposition doesn't affect the result the opposition is meaningless. Another inference that can he drawn from this analysis is that the concept of critical squares has primacy over the concept of the opposition. The defender can have the opposition and have no control over the result. But if the superior side's king occupies a critical square it doesn't matter who has the opposition. It's no longer a factor. More critical squares Once the attacking king occupies a square on the sixth rank, inside the universe, its clearly a win, whether the pawn is on the second, third, fourth, or fifth rank. With the pawn being on the second rank the critical squares are typically identified as those squares two ranks ahead, within the universe, on the fourth rank. But actually, with the pawn on the second rank (if it's not a rook-pawn), there are

indeed more critical squares. Surely, if the attacking king can reach the fifth or sixth rank inside the universe (or even further ahead), as long as the pawn is safe, that occupation will also lead to a forced win. So, if the passed pawn is on d2, the squares c4, d4, e4, c5, d5, e5, c6, d6, and e6 are surely critical. That is, to reiterate, if the attacking king can occupy any of those squares, and the pawn is not endangered, the win is forced. The reason we designate the fourth rank as the boundary line of critical squares (with the pawn on the second rank) is that we're mainly interested in the limiting case. That's the fourth rank, not the harder-toreach squares beyond. (Anyway, unless already starting at an advanced post, the king couldn't get as far ahead as the sixth rank without having first to pass through the fourth rank.) The reasoning is reminiscent of other analytic situations. For instance, it's usually not necessary to take an analysis beyond the point of clear victory. I f you can see that you're going to promote a pawn to an extra queen, for example, and your opponent has no compensation, there's no need to take the analysis any further than promotion. It would be a waste of time to play out the situation in your mind to the final move of checkmate. But hey, if you're having fun...

The outside critical square We don't need to understand critical square theory to be able to win or draw in Diagrams 231-238. We already have other concepts and methods that work perfectly. This is why older endgame books, such as Basic Chess Endings by Rueben Fine, can talk about these positions without resorting to critical square theory, and by occasionally overemphasizing the concept of the opposition. But as we get into slightly more sophisticated positions, suddenly critical square theory becomes very handy. For example, consider Diagram 239. Let's take a look at a direct variation to get a feel for the position. Black might try I...Kc7, heading for c4 or b4, both of which are critical squares. There could follow 2. Kd2 Kc6 3. Kc2, and White has a distant opposition, with Black being unable to get the king two ranks ahead of the b-pawn (inside the universe, which here consists of the a-, b-, and c-files). But there's an easier way to approach this problem and all similar ones. All you have to do is ask two questions: (1) Where are the critical squares? (2) Can I get to them? In Diagram 239 the critical squares are a4, b4, and d4. If the black king can occupy any of these three squares the win can be forced. Yet moving the black king toward c4 directly doesn't quite work here. It turns out, however, that the black king can get to a6 just as quickly as it can get to c6. By heading toward a6 from the start, the black king can soon occupy a4, also a critical square, and one just as good as the other two (b4 and c4). A sample winning line is I...Kb7! 2. Kd2 Ka6 3. Kc3 Ka5 (heading for the outside critical square, a4) 4. Kb3 (preventing immediate occupation of a4) 4...Kb5! (taking a meaningful opposition), and now White can't prevent the black king from reaching a critical square on the next turn. When you head for the outside critical square (the one furthest away from the enemy king), going behind your passed pawn to do so, it's called the underpass. As a rule of thumb if you have a choice and can indeed do so, and you have little time to calculate, simply head for the outside critical square. 239) The underpass

It's just as good as the other critical squares and often harder to defend. In Diagram 240, White has an elementary win. The critical squares are d6, e6, and f6, so the white king heads for d6, the outside critical square, with another underpass: 1. Ke3 Kg5 2. Kd4 Kf6 3. Kd5 Ke7 4. Ke5. White has a winning turning maneuver coming up. A comparable underpass wins in Diagram 241. The outside critical square is h6 and the white king makes haste toward it. The only complication arises because the passed pawn is a knightpawn, which means that to avoid stalemate possibilities the white king will need to station on the h-file, not the ftile. 240) Heading for d6, the outside critical square

A winning line is 1. Kf2! (heading for h6) 1...Kd7 2. Kg3 Ke6 3. Kh4 Kf6 4. Kh5 Kg7 5. Kg5 (taking a meaningful opposition) 5...Kh7 6. Kf6 Kg8 7. Kg6 Kh8 8. g5 (with the king on the sixth rank, its pawn can be placed on the fifth) 8...Kg8 9. Kh6 (as seen earlier, 9. Kf6 is met by 9...Kh7, when White must go through 10. Kf7 Kh8 11. Kg6 Kg8 12. Kh6, just to be where the king could have been three moves earlier; note that after 9. Kf6 Kh7 10. g6+? will draw to 10... Kh8) 9...Kh8 10. g6 Kg8 11. g7,

and the squeeze is on. 241) Another underpass

Diagram 242 is more of the same. Black to play makes a headlong dash for c4, the outside critical square, not as in Diagram 241, moving behind the passed pawn, but by crossing in front of it: 1...Ke6 2. Kf2 Kd5 3. Ke3 Kc4. By going in front of your pawn to reach the outside critical square you employ a stratagem known as the overpass or the crossover. 242) The crossover: Black heads for c4

Diagram 243 shows an even longer crossover/overpass. White heads directly for f6, the outside critical square: 1. Kc3 Kb7 2. Kd4 Kc6 3. Ke5 Kd7 4. Kf6, mission accomplished. 243) Another crossover

244) Sacking to change critical squares

Sacking to change the critical squares Critical squares certainly apply to situations of king and pawn vs. king, but their application can be much wider than that, with their sudden emergence playing a surprising role. Consider the situation of Diagram 244. If it were Black's turn to play, Black would win by I...Kf4, when 2. Kg2 Kxe4 puts the black king already on a critical square, with a forced win in view. But suppose it's White's turn to play. No matter how White continues the e-pawn is lost. As things stand now, when Black takes the pawn, the black king already will be sitting on a critical square. Since White is going to lose the e-pawn no matter what, maybe there's a better way to lose it. There is. White can sac the e-pawn by 1. e5!. After 1...fxe5, the critical squares have changed. The sacrifice has brought the critical squares one rank closer to the white king. Now the critical squares are d3, e3, and 1`3 (instead of where they were with the black pawn on f6, namely on e4, f4, and g4). Still, even with the critical squares being closer to the white king, White also needs to take the distant opposition, 2. Kgl!. Thus we see how the relationship between critical squares and the oppositional

fight to conquer them can be crucial in many situations. Diagram 245, with White to move, shows another conceptual marriage, where both the underpass, and the tactic of sacking to change the critical squares, come into play. If White were to try a direct attack on Black's a-pawn, 1. Kc3?, Black would offer a sac, I ...a3!, and that would lead to a draw. If White then takes the offered pawn, 2. bxa3, the black king easily gets back toward the a8-corner to draw. If White tries to keep the b-pawn, 2. b4, Black's a-pawn will be lost to the white king, but the critical squares, now on the sixth rank (a6, b6, and c6), are too hard to get to for satisfactory occupation. A sample line would then be 2...Ke5 3. Kb3 Kd5 4. Kxa3 Kc6 5. Ka4 Kb6, with a draw. Nor does moving the b-pawn only one square ahead, 2. 63, help (instead of 2. 64), since that means the white king has to go back behind the b-pawn to try to win the a-pawn, and the loss of time doesn't permit it to work: 2...Ke5 3. Kc2 Kd5 4. Kbl Kc5 5. Ka2 Kb4. White loses the b-pawn and the position is drawn. 245) White to play wins

But there is a winning plan, and that's to start with an underpass to threaten the apawn. Instead of I. Kc3? the right idea is 1. Kbl!, heading behind White's own pawn. If Black relies on king moves the apawn will be lost, with White's king occupying a critical square, I ...Ke5 2. Ka2 Kd5 3. Ka3 (any Black move) 4. Kxa4, occupying the outside critical square. So Black must try to sac the a-pawn, hoping to change the critical squares, moving them a rank closer toward the black side: 1...a3 2. b3! Ke5 3. Ka2 Kd5 4. Kxa3 Kc5 5. Ka4 (threatening to occupy a5, the outside critical square) 5...Kb6 (stopping the occupation ofa5) 6. Kb4!, taking a meaningful opposition and winning, with a turning maneuver coming up. Naturally with a knight-pawn White will have to position the king properly on the a-tile (at a6), once the play goes that far. 246) Sacking to change critical squares

Sometimes one sacrifice is good enough. In Diagram 246, however, White must sacrifice two pawns, changing the critical squares twice, and then White still must rely on a meaningful opposition to hold. The correct line is 1. hxg5+ Kh5 (threatening to win both white pawns) 2. g6! fxg6 (on 2...Kxg6, white's king gets over in time to save the f pawn) 3. P5! gxf5, and now 4. Kgl! Kg5 (a meaningless opposition) 5. Kfl!, and Black's remaining f -pawn obstructs f5, preventing Black from taking a meaningful opposition, so the position is drawn. Every normal passed pawn has a system of critical squares around it, but what of the rook-pawns of the world'? Indeed, they have critical squares, too. Diagram 247 exemplifies the point. White to move would play 1. Kb7, and that guarantees the apawn's promotion. But Black to play has I...Kc8, which prevents the white king from getting to b7, and the a-pawn can't be promoted by force (2. a5 Kb8 is a draw, as is 2. Ka7 Kc7). This suggests that b7 is critical for the a-pawn: if the white king can occupy it, it's a win; if the black king can prevent occupation of b7, however, it's a draw. (The square b8 is also critical, but it's usually easier to reach b7 than b8, and we're more concerned with the limiting case.) 247) The rook pawn has a critical square too (knight-seven)

As a rule of thumb, therefore, the most critical square for a rook-pawn is the knight-seven square on the adjacent file to the rook-pawn in question (the knighteight square, again, is also a critical square). Thus, for a passed white a-pawn, the chief critical square is b7; for a passed black a-pawn, it's b2; for a passed white hpawn, it's g7; and for a passed black h-pawn, it's g2. 248) Fighting for critical squares

249) Panno-Najdorf, Argentina 1968

A further elucidation of the rook-pawn's chief critical square is seen in Diagram 248. Black to move has I ...Kg2 (I ...h3 also wins here, as after 2. Kf3 Kgl 3. Kg3 h2). This occupies a critical square and achieves a winning position. But White to move plays 1. KO!, preventing the black king from getting to g2, and the position is drawn, whether it's by I ...Kg1 2. Kg4 or 2. h3 Kf2, trapping in Black's king. Diagram 249, from the game Panno vs. Najdorf, Argentina 1968, shows a practical example of this critical square fight. Play went 1. Kg5 Kd7 2. Kg6 Ke7 3. Kg7, and Black resigned, with White's king occupying g7, the critical square for the h-pawn.

Diagram 250 offers another practical example. It comes from the game Berger vs. Mason, Breslau 1889. To play, White has an easy draw by pulling his king back toward cI, bee-lining along the cl-h6 diagonal, which would then position it to guard b2, the a-pawn's critical square. The draw is established by 1. Ke3! Kb4 2. Kd2 Kb3 3. Kell. But instead, White played the inexplicable 1. Ke4??, and now Black gets his king to b2 for sure. The game actually finished I ...Kb4 2. Kd3 Kb3 (a meaningful opposition, shouldering out White's king) 3. Kd2 Kb2, and White resigned. 250) Berger-Mason, Breslau 1889

251) Shouldering down the board

A final example in this section also reinforces the idea of shouldering. In Diagram 251, Black to play wins the fight for the b2-critical by 1...Kb6, seizing a meaningful opposition. Black maintains the opposition right down the board until occupying b2 with the king, and the a-pawn is convoyed: 2. Kd5 Kb5 3. Kd4 Kb4 4. Kd3 Kb3 5. Kd2 (heading for c 1 to guard b2, but ... )5 ... Kb2 and wins.

Minor pieces and pawns In most instances of king, minor piece and pawn vs. lone king, having an extra minor piece should be enough to win. Except for certain problem positions, the extra minor piece can always provide key tempi whenever needed. In some cases the extra piece safeguards the pawn until the friendly king's arrival. Thus in Diagram 252 Black simply protects the e-pawn until the black king can be brought into position to assist in the pawn's defense and advance. A sample line might be l...Bd5 2. Kf6 Ke2 3. Ke5 Ke3 4. Kd6 (or 4. Kf6) 4...Kd4 (or 4...Kt4), and the pawn will soon be on its way. So while a lone minor piece is not sufficient to set up checkmate, an extra minor piece, supporting a single passed pawn, is usually enough to win by eventual promotion. There are exceptions, however. Some times the inferior side, even with the presence of such extra material, can't get the minor piece into position to guard the pawn. Moreover, the friendly king might not be able to get into a protective position either. In such instances, when the pawn can't be guarded, the win may be a matter of preventing the defending king from positioning to attack the pawn in the first place, even at the cost of the piece itself. 252) Securing the pawn

In Diagram 253 White to play wins the pawn by 1. Kd6, followed by 2. Kxd7. But Black to play can stop that by sacking the bishop, I...Be5!. After 2. Kxe5 Kc5!, Black's king occupies the outside critical square and the pawn will win. 253) Sacking to occupy a critical square

Diagram 254 doesn't pack the punch of Uranium 235 but it typifies the best way for a knight to guard a threatened pawn: from behind the pawn. Thus 1. Nc2 protects the pawn and the knight can't be captured without allowing the pawn to queen. Note that 1. Nc4?, protecting the pawn from in front of it, allows the black king to take the knight and still be in position to overtake the pawn. After 1. Nc2, however, White merely transfers his king over to the queenside, protects the pawn, thereby releas ing the knight, and the rest, as Capablanca once supposedly said, "is a matter of technique." 254) Knights defend best behind

As a rule of thumb knights defend best from behind. This is especially true in endgames to secure passed pawns, but it's also somewhat true in opening and middlegame tactical situations, where knights are then poised to guard nearby squares while also being able to spring forward toward the enemy position. Diagram 255 seems a hit lopsided. Black is way ahead in material. If we were merely counting points the score is I 1-0, and maybe it was imprudent to promote earlier to a bishop ofthe same color. But the extra material and faulty preceding logic are irrelevant, since neither of Black's bishops can guard

al, the necessary promotion square. Moreover, Black's king has no legal way to force occupation of' b2, the abiding critical square. Thus White's king can hide on a I and h I and Black is powerless to avert a draw. 255) Eleven to nothing draws

The wrong bishop In such situations, under similar promotional circumstances, when the extra bishop is unable to guard the corner square, it's said that the bishop is the wrong bishop, which here is a light-square bishop. The right bishop, which here would be a dark-square bishop (if it were present), is the one that could guard the desired corner square. Moreover, when interior forces are able to prevent superior forces from winning, it's said that the position is a positional draw. Another term that often applies in similar circumstances is that of the fortress, a concept very popular in Russia among strong players and in all those lands where thinking like a strong Russian chess player is encouraged and considered to be a good thing. A fortress is a position where inferior forces can prevent superior ones from invading and winning. We'll see more of the fortress idea in context. The material is greatly reduced in Diagram 256, but here Black's bishop is able to guard the promotion square. There is no positional draw, no fortress, and nothing for White to hope for (ofa chess nature) after I...Be3 (I ...a2+ also clearly wins) 2. Kal Bd2 3. Kbl a2+ 4. Kal Bc3 mate. 256) The right bishop wins

257) Wrong bishop can win too

In Diagram 257, Black to play wins by a simple cutoff. That is, with the move, Black can play I...Bd3!, preventing White's king from heading toward the queenside corner. After 2. Kd2 Black has 2...Kb2 (Black could also save the bishop by moving it safely along the bl-h7 diagonal). With the king occupying a critical square (b2), winning should soon follow. White to play, however, draws by 1. Kb 1, and Black is unable to drive the king from the corner. A slightly more complex version of the idea is seen in Diagram 258. White can set up a wall, preventing Black's king from getting to the corner altogether. It begins with 1. Be6!. On l ...Kf8 White has 2. h6, and it's over, since the black king must then move away from the kingside action. So Black must play 1...Ke7, which is answered by 2. h6. Now Black doesn't have time to take the bishop. After 2...K16, threatening 3...Kg6, White has 3. BfS, barring the black king from crossing over with a diagonal cutoff. Black must then try 3...Kf7, hoping to get to g8, but 4. Bh7! cuts the king off at the pass. Likely final moves could be 4...Kf6 5. Kf4 Kf7 6. Kf5 (or 6. Kg5) 6...Kf8 7. Kg6 (or 7. Kf6),

and White's king occupies the critical g7-square next move. 258) Wrong bishop cutoff

259) Shouldering for the wrong bishop

In Diagram 259, it's not the bishop that so much affects the cutoff: it's the black king. With 1...Ke5! Black's king shoulders out White's king, and the a-pawn proves unstoppable. Note the immediate I...a4 would he a blunder, even though 2. Kb4 Bb5 (or 2...Bc2) secures the pawn. White plays 3. Ka3, and the white king is guaranteed getting back to the corner for a positional draw. 260) Knight and rook-pawn on seventh rank draws

Bishops are hardly the only minor pieces to experience difficulties with rook-pawns. Knights can have their own troubles. White to play in Diagram 260 can draw by direct attack, 1. Kg3!, which forces the pawn to the seventh rank, 1...a2. Thereafter, the position is drawn, and the draw can be understood conceptually. White simply locates the king at g2, and moves it back and forth between h I and g2. The knight cannot reposition without hanging the pawn. So Black must first defend the pawn with the king, placing it at g3 or H. But as soon as Black does that it's stalemate. No need to analyze any further. This type of setup, where less holds out more, is known as a fortress. Nor does it help Black if the knight is on f3 instead of g4. The same limitations apply. In order to move the knight, the pawn must be guarded by the black king, and that leads to stalemate, as in Diagram 261. Once again, the fortress concept predominates. 261) Knight on bishop-six is no better

262) Knight and rook-pawn on sixth rank win

But a rook-pawn on the sixth rank defended by a knight is a horse of another idea. That's a win, as in Diagram 262. After 1. Nc5 (knights defend better from behind), play might go 1...Ka7 2. Kb4 Kb6 3. Ka4 Ka7 4. Kb5 (note there's no stalemate here, and the knight is free to move) 4...Kb8 5. Kb6 Ka8 6. Ne6 (positioning the knight to guard the promotion square by moving it to c7) 6...Kb8 7. a7+ Kc8 (7...Ka8 allows 8. Nc7 mate) 8. a8/Q+. Many of us can take it from here. 263) Knights defends best from behind

Diagram 263 offers White a choice. There are three ways to protect the pawn. On 1. a7? Kb7, it's a positional draw. On I. Nb8? Ka7, and the pawn will fall if the knight moves. That leaves 1. Nb4!, which just happens to be decisive. Defending from behind the pawn, the knight cannot be captured without allowing the pawn to advance. The white king meanwhile crosses over to b5 or a5, frees the knight, and it's a simple win from there. 264) More achieves less

The only situation where the attacker can get away with stalemating the defending king is when the inferior side has some other material present. Its movement can provide the extra time needed to fashion checkmate. In Diagram 264, for example, White can play 1. Kg6, allowing 1...f2 because of 2. Nf7 mate. 265) Underpromotion to a knight is compelling

Rook-pawns give all kinds of opportunities for stalemate. In Diagram 265 Black must promote the pawn in order to avoid losing it. But making either a queen or rook gives stalemate, and promoting to a bishop of the same color is risibly ineffective. Fortunately, Black has I...h1/N+!, and the resulting situation of bishop and knight is a win in any country in the world. Some positions are nice to file away, especially if you're in time pressure and have to switch to automatic. Obviously Black's win is not too difficult in Diagram 266, but it's good to know how to save time and win as quickly as possible, say in five moves: 1...Nc2+ 2. KbI a2+ 3. Kcl al/Q+4. Kd2 Qel+(or4...Qe5 5. Kd l [or 5. Kd3 Qe3 mate] 5...Qe 1 mate) 5. Kd3 Qe3 mate. It's not hard to

imagine, from an earlier discussion, the idea of a triangulating queen, here sketching its geometry from al to el to e5. Draw it in your mind and see. Back to bishops: add a defending pawn, and even add the right bishop, which happens to guard the targeted corner, and you might still produce no more than a draw. In Diagram 267, the game is drawn positionally after 1. Kfl. This prevents Black's king from occupying the h3- pawn's eventual critical square, g2 (it will become critical once Black gains the white pawn), and no progress can thereafter be made. 266) Mate in five moves

267) Even the good bishop can draw

Take the same circumstances of Diagram 267, create the ludicrous situation of adding another bishop of the same color, and the attacker can indeed win, as shown in Diagram 268. With 1. Bc5!, Black's king is forced to the corner, 1...Kh8, permitting 2. Kf7 discovered mate. I know what you're saying: having two bishops of the same color almost never happens, and surely can't have any real significance for legitimate positions. But consider Diagram 269, which is a

famous endgame composition. It's White to play, and something must be done about the threatened b7pawn. If it doesn't advance Black wins it and the position is drawn, devolving into the situation of Diagram 267. But promoting to either a queen or rook gives stalemate. So naturally White analytically tries 1. b8/N+, but this doesn't accomplish much: I...Kb7 2. NO Kc8 (fork city) 3. Nf6 Kxd8 4. Nxh7 Ke7 5. Ng5 K116, and Black will soon force the h-pawn to advance to F. That produces a positional draw (Black's a-pawn will be gobbled up and is therefore inconsequential to the result). This leaves the absurd notion of promoting to a bishop, 1. h8/B!, generating a second bishop of the same color (that is, both bishops travel on squares of the same color). But this turns out to be a win, for White can construct a position similar to Diagram 268, where, in order to prevent White's king from getting to the critical g7-square, Black would have to walk into discovered mate. It's a tough world. 268) White mates in two moves

269) Promoting to a bishop wins

270) Sacking for tempo

Sometimes the situation depends on which player moves, sometimes it doesn't. In Diagram 270, which emanates from a position I had in an exhibition given at Baruch College in 1974, having the move is critical. Black to play draws with I ...Kf8, and there's no way for White to make any progress. But White to play can stop Black from getting to the desired corner with 1. Nc6 Kf8 2. Ne7! (no getting to the corner now) 2...Ke8 3. Ng6!, a time-gaining sac that wins per force. If the knight were captured, 3...hxg6, then the h-pawn would queen. And if Black instead moves the king toward the queenside, 3...Kdt, then the white king invades, 4. Kt7, and that's that. Practice Position #4

Question: In Practice Position #4, how does White mate in two moves? Hint: Close your eyes and think. Solution, page 243. In Diagram 270 Black to play draws by getting the king back to the corner. In Diagram 271, however, even being on a good defensive post doesn't help the white king, which is done in by doubled pawns.

After I...Ng3!, White's king is stalemated, and there's no choice: the knight must be captured, 2. hxg3, when 2...hxg3 wins easily (if 3. Khl, then 3...g2 + 4. Kgl h2+ 5. Kxh2 Kt2 6. Kh3 gl/Q 7. Kh4 Qg6 8. Kh3 Qh5 mate (or 8...Qg3 mate). Who said doubled isolated rook-pawns have no value'? 271) Sacking to get healthy pawns

The isolated pawn Time for another digression, here on isolated and doubled pawns. An isolated pawn stands by itself. No friendly pawns occupy adjacent files to it. If menaced it must be guarded by a piece or moved to safety, which may not be so safe a thing to do. Indeed, as an isolated pawn advances, it could become more vulnerable. It gets closer to opposing forces and further away from support troops. Of course the isolated pawn must be distinguished from a passed pawn, which also may be isolated (have no friendly pawn capable of supporting it from an adjacent tile). A passed pawn's movement can't be hindered by enemy pawns. But an isolated pawn's advance is always, at some point, going to be held back by an opposing pawn. Either its movement will be obstructed or prevented. A chief problem for an isolated pawn is the square in front of it. That square often can be occupied desirably by an enemy piece, such as a knight or, in the endgame, the king. Generally, if you have an isolated pawn, you should try to (1) take advantage of the open lines; (2) guard against crippling blockades; (3) exchange the isolated pawn for a good enemy pawn; and (4) avoid piece trades that result in lifeless endgames, with no counterplay. If you are playing against an isolated pawn, try to (1) prevent its advance; (2) control, occupy, and use the square in front of it; (3) attack it, especially if it's already restrained (you can run, but you can't hide); and (4) exchange pieces to accentuate its weakness and reduce counterplay. Doubled Pawns Two friendly pawns occupying the same file are doubled pawns. They come about because of captures. Doubled pawns have several potential drawbacks. For one, they can no longer support each

other, whereas previously, before their creation, they had the potential for mutual protection. Moreover, since the two pawns of a doubled pawn complex obstruct each other, they tend to advance more slowly, the back pawn's movement retarded by the front one. But they are not automatically targets. It depends on how easily they can be attacked. The worst kinds of doubled pawns are isolated ones, where neither of the two can be protected by any pawn whatsoever. Such a weakness (an isolated doubled pawn complex) is more easily blockaded by an opposing piece, inasmuch as no adjacent pawn can drive away the enemy blockader. But even connected doubled pawns can be held back by a single enemy pawn, if in advancing the complex weaker isolated pawns would result. To be sure, accepting doubled pawns can have its advantages, too, particularly when you can exploit the open lines likely to ensue. Also, sometimes the doubling process allows a pawn to influence key squares, making those places inaccessible to the other side's pieces. If you have doubled pawns, generally you should try to (1) avoid moving them unless you must or can make a good exchange; (2) activate your pieces along the open lines, especially your rooks; and (3) steer clear of exchanges that reduce your piece-play. If you are playing against a doubled pawn complex, you should try to (1) restrain their movement; (2) avoid exchanges repairing your opponent's structure; (3) attack the doubled pawn complex and exploit the squares impaired by that formation; (4) neutralize counterplay by intelligent piece exchanges; and (5) mobilize your own pawn majority, if you have one, hoping to create a dangerous passed pawn. It's easy to view isolated and doubled pawns as plagues, and novices generally try to avoid them at all costs. But clearly pawn problems can be offset by compensating advantages in time, space, and dynamics. With the exception of being mated, nothing is automatically bad, especially if it can't be exploited by your opponent. Certainly, most chess players come to realize that there are up and downs to most chess concepts, and that a fuller understanding of them can only emerge from judgment in context. Back to the march of chess positions. Diagram 272 reflects another situation in a seemingly endless queue of either/ or positions, where having the move matters. The position seems absurd, on the surface, since White is up a knight and pawn. And if White moves, indeed the win is straightforward. The immediate 1. Nd5 forces the black king to move away. White's king then escapes from the corner and the pawn queens. But if it's Black's turn to move the position is drawn by I...Kc7. From that point on Black can close eyes and mindlessly move the king back and forth between c7 and c8. White's knight is powerless to gain a tempo and shift the move. 272) It depends who moves

Knights tend to do things in two's, going from light to dark to light. A knight can't play a waiting move since every time it moves it attacks entirely new squares from those it observed on the previous move. Compare the situation of having a knight at e3 (Diagram 272) with that of having a bishop on e3. With the knight on e3 the result depends on which player moves. But with a bishop on e3, instead ofa knight, White plays the bishop to f4, and Black's king must move away. And if the bishop were already on f4, as in Diagram 273, and it were White's turn, the bishop simply moves along the b8-h2 diagonal (to any square but c7). The waiting move forces the black king to withdraw, abandoning defense of V. The white king then extricates itself from the corner. 273) An easy win

This shows another one of those ways a bishop has it over a knight. It can play a true waiting move (one along the key line it already occupies); a knight can't (it doesn't move on lines, nor can it move and still guard the same squares it did on the prior turn). There are often several ways to explain the

same endings. Players don't necessarily need to know all the possible options. But by becoming acquainted with alternatives, players learn to appreciate nuances more, and accordingly arm themselves for situations requiring fine discrimination. Take the case of Diagram 274. If White were to play intuitively here, the natural move would be 1. Kcl'?, taking the opposition and temporarily locking in the black king. But this loses to I ...Nf6 (or any other knight move whatsoever) 2. Kc2 Nd5 3. KcI Nb4 (or 3...Ne3), and Black's king will get out of its cornered trap. 274) A color rule

Yet there's no need to go in for intricacy and actually having to calculate variations. One can play automatically and still do the right thing by falling back on a color rule. That is, the inferior side's king can hold the draw by moving to the same color occupied by the knight. So 1. Kc2! establishes a forced draw by employing a mindless color rule. If the white king were already on c2, and it were White's turn, Black would have a win, since after 1. Kcl the knight could move to the same color square then occupied by the white king. The rule works that way too. Still, how much practical application does this color rule have? Surely, there are no other instances where it might come into play. 275) Color rule still applies

276) Still thinking color

Actually, there's Diagram 275. Black to play has a simple win, I ...Nb2+, and the pawn will queen. But if it's White's turn there's a way to prevent the bishop from being blocked out, and that's by sacrificing it with 1. Bal !. Black then has two ways to go. The bishop can be taken or the knight can first check on b2. In either case, whether Black goes for I...Kxa1 2. Kc2!, or for I...Nb2+ 2. Kd2 Kxal 3. Kc I!, the white king constructs a positional draw by moving the king to the same color square occupied by the knight. To be sure, everything matters, except if it doesn't. Change the situation a bit, creating the setup of Diagram 276, and suddenly White to play wins with 1. Nb7! (moving the knight to the same color square as that occupied by the black king). It's not check, though that's okay. After I...Kc6 2. Kxa8 Kc7 Black hopes for a fortress. But White then has 3. Nd6 (or any knight move, for that matter), which puts the knight on the same color square as that occupied by the black king and wins. Naturally, if it were Black's move from the start, Black would draw with I...Kd8, occupying a square the same color as that occupied by the knight, arriving at a comparable situation to that of Diagram 276 (after White

plays 1. Bat!). Practice Position #5

Question: In Practice Position #5, how can White to play insure a draw? Solution, page 243. Why should rook-pawns get all the attention? As we have seen, knight-pawns may pose problems, too. In Diagram 277 White to play draws with 1. KO!, and there's no way for Black to upset the positional draw. For instance, there could follow I...Kd5 2. Kg2 Ke4 3. Kh I Ke3 (note that 3...Kt3 is stalemate, with White secure in the fortress) 4. Kg2 Keg 5. Khl Bgl (it's a try) 6. Kxgl Kf3 7. Kfl g2+ (a bad sign, advancing the pawn to the seventh rank with check) 8. Kgl, and the game will be officially drawn in one move, either by stalemate or capturing the pawn. 277) A positional draw

A variation on Diagram 277 is Diagram 278. Black to move wins with I...Bb3, blocking the b-pawn.

Black's king will then maneuver over to the queenside, and the win follows directly. A sample variation is I ...Bb3 2. Kd2 (taking a distant opposition) 2...Kh3 (maneuvering within a make-shift universe of the first through third ranks, eventually to steal back the opposition) 3. Ke I Kg3 (taking the diagonal opposition) 4. Keg Kg2 (the dance of demise continues) 5. Ke3 Kfl 6. Kd2 Kf2 7. Kc I Ke 18. Kb I Kd2 9. Kal Bc2. 278) It matters who moves

With the stalemate avoided, Black has several ways to bring about the win. One way is to maneuver, setting up a partial stalemate, forcing the b-pawn to move disadvantageously. Another idea is to reposition the bishop on the d5-g8 diagonal, playing for a discovery, when the white king is vulnerably placed on a2. But White to play draws by converting into a comparable setup to Diagram 278 with 1. b4!. Either Black must take the b-pawn en passant, with a positional draw ensuing, or maneuver the bishop to e4, hoping to catch the speeding b-pawn, which hangs the c-pawn in the process. That produces a draw, there being insufficient mating material. Make sure to avoid stalemate The situation of Diagram 279 is uncomplicated and leads easily to a win. For example, play could go 1. Kc7 KI8 2. Be4 (avoiding 2. Kd7 stalemate) 2...Ke8 3. E3d5 (aiming at a future target, the f7pawn) 3...KIX 4. Kd7 Kg8 5. Ke7 and the t7-pawn falls. 279) An easy win

280) A positional draw

The situations of Diagrams 280 and 281 are draws, with the defender's position being fortress-like. Whether the bishop travels on light or dark squares is of no consequence. White must watch out for stalemate in each position, and even in Diagram 282, where the bishop could be sacked for the gpawn, reducing to a king-and-pawn vs. king ending would still draw. But give White a knight, replacing the bishop, and the win is elementary. In Diagram 282, White artificially stalemates Black's king with 1. Nf6!. But Black still has a move, I...gxf6. While White wins with 2. Kxf6, taking a diagonal opposition with the pawn on the sixth rank (there would follow 2...Kg8 3. g7 Kh7 4. Kf7 Kh6 5. g8/Q Kh5 6. Qg3 Kh6 7. Qg6 mate or 7. Qh4 mate), a faster win ensues, not by taking back on f6, but instead by playing 2. Kf7, when 2...f5 3. g7+ Kh7 4. g8/Q+ Kh6 5. Qg6 is mate. From the basic setup of Diagram 282, the winning breakthrough must occur when the black king is on h8, and not g8. So if the king is on g8 to start with, White must first play a waiting move. Although the knight by itselfcan't play a meaningful waiting move, White's king can. If the king is on e7, it could

move to e8; ifit's on e8 already, it could move to C. So in Diagram 283, White first plays 1. Ke8!, and then after I...Kh8, l rces a win by 2. Nf6, as in Diagram 283. 281) Another positional draw

282) White sacs to get a passed pawn

283) First a word from our sponsor

284) White sets up a fortress

A few fortresses A little digression here would never hurt anything but the page count. I thought it might be fun to look at a few more surprising fortresses, where less holds off more, even though the material setup may not equate precisely to what's happened earlier in this section. In Diagram 284, for instance, White looks in had shape, with Black's h-pawn breathing down h I's neck. But White holds with 1. Bb7+ Key 2. Bxf3! Nxf3 3. Kg2, and the fortress stands. In Diagram 285, not only is White's queen menaced, but so is mate at h2. If White plays I. QgI, Black wins with 2...Qh4+ (QED). It looks hopeless, but there's a fortress to be set up: 1. Qxf4+! Qxf4 2. Ne4, and there's no way for Black's king to advance meaningfully toward White's, with White guarding all the available squares of approach that matter. Try it and see. 285) White sets up a fortress and holds

286) White has a draw in hand

Finally, we offer one more position, an illogically strange one, but one with a fortress lurking. In Diagram 286 White is behind by a large amount, but that won't matter after 1. Ba4+!. Since l...Kc4 2. Bb3+ gets Black nowhere, Black takes the bishop, 1...Kxa4. But after 2. b3+ Kb5 3. c4+ Kc6 4. d5+ Kc7 5. e6, there's no way for Black's rooks and bishop to penetrate White's light-squared fortress. The game is drawn.

Square of the pawn Passed pawns are a key area of interest in any ending, if not especially in endings with just kings and pawns on the hoard. With kings wandering about, players typically have to decide how far away they can allow their king to drift or be from a menacing passed pawn. In Diagram 287, for example, White to play can indeed catch the b-pawn, 1. Ke2 (or 1. Kel) I ...b3 2. Kd3 (2. Kd2 or 2. Kd 1, if that's possible, also work) 2...b2 3. Kc2. Black to play promotes by force, I ...h3 2. Ke2 b2, and the pawn queens next move. For most newcomers these determinations are made by calculating particular moves in their heads. But more experienced players do it quite differently. Rather than working out several moves of "I go here, and he goes there," the veteran grappler merely has to look, resorting to a visual ploy. Those in the know seek the square of the pawn, also known as the quadrangle of the pawn. This mental trick consists in first imagining a straight line drawn from (and including) the square the pawn occupies to (and including) the square of promotion. That line constitutes the side of a quadrangle. By envisaging three other lines to complete the quadrangle, you can establish the quadrangle of the pawn. 287) Square of the pawn

In Diagram 288 the square of the pawn runs from b4 to b I to e I to e4 to b4. With the move, if the king in question can enter the square of the pawn, inclusive of the squares enclosed in its boundaries lines, the pawn can be caught. I f the king can't enter the square of the pawn, the pawn can't be caught. So there's no need to calculate. All one has to do is look. A step in the envisioning process can be eliminated by picturing the diagonal of the square of the pawn (going from b4 to el in Diagram 287). Cut across the quadrangle to reach the promotion rank (the first rank at el ). Then see if the king can move into the outer boundary file (the e-file), even to its corner square (el here).

288) The two-square advance wins

There are exceptions, one of which is shown in Diagram 288. In the diagram, the square of the pawn ostensibly runs from h7 to h 1 to b 1 to b7 to F. Thus the white king is already inside the square of the pawn. But Black's h-pawn has not moved, so it still has the two-square option. Accordingly, the thrust 1...h5! fashions a new square of the pawn, this time running from h5 to h 1 to d l to d5 to h5, and there's no way for the white king to enter that square on the move. The pawn therefore can't be caught. The inference to be drawn from this is that when a pawn occupies its original rank, one must look upon it as actually being on its third rank when trying to envision the square of the pawn. Similarly, in Diagram 289, Black's having the move doesn't save the game. The black king can superficially enter the square of the pawn by 1...Kg4, but it's not really inside the square yet since the square must be factored from the pawn being on a3 (it therefore runs from a3 to a8 to f8 to 0 to a3). Thus, White plays 2. a4, and the pawn can't be caught. 289) Two-square advance wins

Questions concerning doubled pawns Some curious questions arise in situations of king and two pawns vs. king when the pawns are doubled. In Diagram 290 we see a zugzwang situation, where neither player wants to move. If Black has the move, the front pawn (on e4) is lost and the position is drawn. If White must play, however, it's an easy win: 1. Ke2 Kd4 2. Kd2 e3+ 3. Ke2 Ke4 4. Kel Kd3 (or 4...Kf3. it doesn't matter) 5. Kd 1 e2+ (5...e4 also works here) 6. Kel e4 (so the doubled pawn functions as a move shifter) 7. Kf2 Kd2, and the front e-pawn promotes. 290) Zugzwang

As we've seen in other instances, doubled rook-pawns, in some cases even helped out by an ineffective bishop (the wrong bishop), can't lead to a forced win. In other situations, doubled knightpawns can pose intriguing troubles, since there are increased chances for stalemate. Diagram 291 shows a typical setup. Here, both players want to move. If Black goes first there follows 1...Kf4 2. Kf2 g3+ 3. Kg2 Kg4 4. KgI Kf3 5. Kfl g2+ 6. Kg1 g4 7. Kh2 gl/Q+, when Black's king is already sitting on a critical square for the g4-pawn. If initially it's White's turn, the position is drawn, the immediate 1. Kg3 gaining the g4-pawn. 291) Both players want to move

In Diagram 292 we see some of the fancy steps needed to win such a position. To begin with, the position contains certain landmines. To get to a winning zugzwang setup, making sure it's the other player's turn, one has to pirouette carefully. After I...Kf6, we see the problem. White doesn't want to play 2. Kg3, since Black then has 2...Kf5. Meanwhile, with the black king already at f6, if it were Black's turn to move in that situation, Black wouldn't want to play Kf6-f5 because White would then draw with Kg2-g3. So the barriers are set out: Black's king doesn't want to go to f5 before White's king has gone to g3; White's king doesn't want to go to g3 before Black's king has gone to f5. 292) Dancing around corresponding squares

Accordingly, the dance revolves around those two squares, f5 and g3, which are also known as corresponding squares (squares for White and Black of mutual zugzwang that neither player's king wants to land on first). When it comes to corresponding squares each king wants to occupy a critical square second, after the other king has committed itself and is set up for exploitation. Clearly, the relationship between the two kings is an oppositional one, where going second entails advantage. In Diagram 292 White to play attacks the g4-pawn and wins it, 1. Kg3, achieving a drawn position. But

Black to play wins, a sample variation being: I ...Kf6 2. Kf2 (2. Kg3 Kf5) 2...Ke5! (dancing around, but keeping f5 in sight) 3. Kg3 Kf5 (Black has occupied his corresponding square second, and therefore has controlling advantage) 4. Kg2 Kf4 5. Kf2 g3+ 6. Kg2 Kg4 7. KgI Kh3 8. Khl g2+ 9. Kgl g4 10. Kf2 Kh2 and wins. Underpromotion It's time for a little humor. In Diagram 293, Black has a number of moves that win, but it's nice to mate in three, which is accomplished by l...gl/R! (note that l...gl/Q is stalemate) 2. Kh2 Rg4!, and mate next move (Rg4-h4). 293) White mates in three moves

294) Sacking to avoid stalemate

Another version of the sacking-to-achieve-clearance theme is shown in Diagram 294. Black to move can't play l ...Kf3?'? because of stalemate; nor can Black try 1...g4+?, since after 2. Kg2 the position

is drawn, the front g-pawn being lost. Clearly, from the diagram, the g3-pawn is in the way. Since it takes up valuable space, why not simply get rid of it? So that's what Black does. After I...g2! 2. Kxg2 Kg4! Black has a turning maneuver next move and wins easily. Take the position of Diagram 294 back one move and we have Diagram 295. The same kind of win follows from 1. Kf5 Kh6 2. g7!. In odd cases the doubled pawns can function as a barrier, cutting off the enemy king. Even so, the friendly king may still have to step around the land mines with the usual caution. 295) Less is more

296) Creating a barrier

Thus, in Diagram 296, White begins with 1. b4!, seizing c5 and insuring the integrity of the doubled pawn complex. An illustrative variation would then continue 1...Kd6 2. Ke2 Kc7 3. Kd3 Kb7 (but not

3...Kb6? because of 4. Kc4, getting to b6's corresponding square, c4, second!) 4. Kd4! Kb6 5. Kc4 Kb7 6. Kc5 Kc7 7. b6+ Kb7 8. Kb5 Kb8 9. Ka6 Ka8 10. b7+ Kb8 11. b5 (1-0). 297) Converting to the doubled pawn draw

The doubled-pawn troubles can occur surprisingly. In Diagram 297, White can survive with clarity, and without any further hassle, simply by playing 1. g4+!, when 1...hxg4 2. Kg3 is an elementary draw, the white king having occupied the g3-corresponding square (corresponding to that of f5) second. If it were Black's turn at the start, Black would try I. g4+, and play continues. Connected pawns 298) Simple pawn mate

Connected pawns, with the two pawns being on adjacent files, have the ability to defend each other.

They constitute a win if the attacker has the move, so there's no stalemate. Diagram 298, shows how in some cases it's even possible to mate without having to queen, as with I...a2 mate. A slightly thorny connected pawn situation occurs in Diagram 299. It's a win, all right, but to make progress White must sac the a-pawn, which gets in the way and generates certain stalemate opportunities. After 1. 1. a8/Q+! Kxa8 2. Kc6 Kb8 3. b7 we've reached a standard winning knightpawn position. The final moves might be 4...Ka7 4. Kc7 Ka6 5. b8/Q Ka5 6. Qb3 Ka6 7. Qa4 mate (or 7. Qb6 mate). 299) Ditch the culprit

Diagram 299 provides an opportunity to make a delightful comparison with Diagram 300, which has already been analyzed earlier, but seen again helps bring out the concept of the relativity of value. In most situations a bishop is worth a little more than three pawns. In Diagram 300, with a pawn on a7 instead of the bishop, the position is an uncomplicated win. Diagram 300, with a bishop on a7, however, is only a draw. Clearly, in this comparison, the relative values have changed, with a pawn on a7 being more valuable than a bishop on a7. Go figure. 300) Relative values can change

There are other ways that one can be up two pawns, too, such as the case of having split pawns. Curiously, while connected pawns can protect each other when assailed by the enemy king, split pawns a file apart also have the potential to safeguard themselves. They do so by being lined up on the same rank, such that, if the enemy king attacks one of them, the other split pawn advances, which protects the back split pawn. The back split pawn can't be taken by the enemy king without allowing the front split pawn to queen. In Diagram 301, accordingly, Black achieves a winning setup with 1...c4!. If 2. Ka3, then 2...c3 defends the a4-pawn. And if instead 2. Kc3, then 2...a3 defends the c4pawn. Since White's king can do very little, Black's king eventually gets over to the queenside and escorts home one of the pawns. 301) Splitting the pawns wins

302) Whoever moves wins

In Diagram 302 whoever moves wins - just the opposite of zugzwang. If White goes first the pawns fall, 1. Kf2 h3 2. Kxf3 h2 3. Kg2, and the remaining split pawns win. If Black goes first, however, 1...h3 splits the pawns and creates a mutual zugzwang, with neither player wanting to move as in Diagram 303. Since the sides correspond in their setup, looking at the situation from one perspective can enable the analyst to find a comparable solution going the other way. 303) Neither player wants to move

In Diagram 303, White to play loses. If 1. Kt2 then I ...h2. If 1. Kh2 then I ...f2. Similarly, Black to play loses. If I ...Ka7 then 2. c7. If I...Kc7 then 2. a7. Without a doubt, split pawns can defend themselves (though not necessarily anything else). Diagram 304 affords an opportunity to understand how to deal with an advancing pawn mass. It also shows how split pawns can sometimes outduel a block of three connected pawns. Actually, whoever moves wins. If Black goes first there follows l ...a3, when 2. Kb l is met by 2...c3, splitting the pawns and reducing White to 3. M. Black squelches that with 3...Kg8, and White has no good move. But if

White goes first there's 1. h6, threatening 2. P. So Black must reply 2...Kg8, arriving at Diagram 305. 304) Whoever moves wins

Treating Diagram 305 as a new position, White wins with 1. Kb V. Now, no matter which black pawn moves, White copes by moving the king directly to the square in front of the pawn that's just advanced. Thus, if I ...a3, the pawns are stopped by 2. Ka2! c3 3. Kb3. If instead, l...c3, then 2. Kc2! a2 3. Kb3 again stops the pawns. And if 1...b3, then 2. Kb2 brings the advancing to a halt. Black must then move his king. If the king goes to the f-file (to f7 or f8), then h6-h7 wins; if the king goes to the hfile (to h7 or h8), then f6-f7 wins. Chess is a tough game. Occasionally, just when you think it's safe to go back in the water, and the split pawns are winning easily, a shark rears its ugly head. 305) Stopping three connected pawns

306) Black to move draws

In Diagram 306, Black can avoid going down for the third time with I...Kg7!. No matter how White responds the position is only a draw. If 2. Ke6, then 2...Kf8!, when both 3. Kf6 and 3. h6 are stalemate. Some days you just can't win. Split pawns, of course, aren't always separated by one file. Sometimes they're separated by more than one file, though even then special relationships may pertain. In Diagram 307 White to move can win by ignoring the threat to f4 and simply bringing up the king, 1. Kb2! Kxf4 2. Kc3 Ke5 3. Kb4 Kd6 4. Kb5 Kc7 5. Kc5!. Next move the king advances to a critical square, with a winning position. But from the same starting situation Black to play can take the t4-pawn and get the king back in time to prevent eventual occupation of critical squares (here, b6, c6, or d6). 307) It matters who moves

Take a similar situation, but shift the white king to the other end of the playing surface, and White to move wins a little differently, by using the b-pawn as a decoy. That gains time for the white king to get into position to occupy a critical square. White wins in Diagram 308 with 1. b5!, which results in

1...Kd6 2. Kg2 Kc5 3. K13 KxbS 4. Kf4 Kc5 5. Kf5 (or 5. Ke5) 5...Kd6 6. Kf6, and a winning setup has been achieved. Naturally, if Black were to go first in the same diagram, the position would be drawn after taking the e-pawn. 308) White to play wins

Diagram 309 offers an exception. Here, even with the move, Black can't win. After 1...d4 2. Kb3 a4+ (2...Kb7 3. Kc4 Kc6 4. Kxd4 Kb5 5. Kc3) 3. Kxa4, the position is drawn since White's king can soon move back to catch the d-pawn. 309) It's a draw

310) The shifting quadrangle

Here is a new rule of thumb. In endings of king and two split pawns vs. king, if the pawns are positioned on the same rank, the line connecting them forms the side of a big square or quadrangle, which changes as the two pawns advance and therefore is known as the shifting square of the pawns or shifting quadrangle of the pawns. Ifthis square extends to the promotion rank or beyond the pawns can win without the aid of the friendly king. The main constraint on this concept is if the other side has the move and can capture one of the pawns immediately. This handy visual generality is particularly convenient for Diagram 310, with the passed pawns split by three files. To reiterate, if the shifting square of the pawns reaches the promotion rank, or extends beyond it, the pawns can win even without the help oftheir own king, if they have the move. In Diagram 310, the square in question runs from b5 to bl to fl to 1`5 to 65. With the move Black wins by 1...f4! 2. Kc3 f3 3. Kd3 b4 (among other moves). 311) Black to play wins White to play draws

A further example is Diagram 311. The shifting square here extends to the promotion rank, running from b6-bl-gl- g6-b6. With the move Black wins easily, I...g5, and one of the pawns will queen for sure. White to play can hold as after I. Kxb6 Kb2 2. Kc5 Kc3 3. Kd5 Kd3 4. Ke5 Ke3 5. Kf6.

Let's shift our focus, moving from positions with one side having two extra pawns, to those where each side has a single pawn. Some wonderfully useful ideas are to be found in certain endings of fixed pawns, where enemy and friendly pawns block each other. In some of those situations king management can be critical. Typically, one of the two kings is better placed than its counterpart and can maneuver around the other king to gain advantage. The result has to do with placement, having the move, and/or both. An example of a type of fixed pawn nightmare is shown in the next position, which has been looked at earlier in another context. But just to remind us, in Diagram 312, neither player wants to move. How a player might stumble into one of these choreographic situations is shown in Diagram 313, where it's White to play. If it were Black to play the white e-pawn would be lost. But with the move, remarkably, White has a win, with play proceeding 1. Kb7 Kg6. Note that I...Ke7 loses the e-pawn to 2. Kc7 Ke8 3. Kd6 Kf7 4. Kd7 Kf8 5. Kxe6, and the white king is already sitting on a square that appears to be critical. Play might continue 2. Kc6 Kf5 3. Kd6!. That's zugzwang: neither player wants to move. Unfortunately for Black, Black has to move and the e6-pawn falls. This motif, where one player is able to outdance the other to win the other side's fixed pawn (or pawns) is known as outflanking. 312) Zugzwang

313) Black gets outflanked

Let's analyze the situation of Diagram 313 a bit more. Just from a structural point of view, with the pawns on the very squares they occupy in this example, and the black king on 1`7, White's king can win the e6-pawn by force if it could occupy b6, c6, or d6. When the white king is on d6, it's easy to see that the e6-pawn must fall, no matter who moves. Even if it's White's turn, with the white king on d6, it can shift the tempo to Black by moving the king to d7; if the king starts instead on d7, which still enables the king to assail the e6-pawn, the white king could then shift the tempo by moving to A. So the attacker always has two squares from which to attack the enemy fixed pawn (here, d6 or d7). The defender, however, is limited. I f the black king is on f7, it can't move to f6 to keep the e6-pawn guarded, since f6 is guarded by white's e5-pawn. Thus we see a definite advantage in these outflanking situations: the attacking king will always have the ability to shift the tempo. Since in Diagram 314 king occupation of b6, c6, or d6 guarantees being able to force the win of the e6-pawn, and therefore the game, it's fair to say that b6, c6, and d6 in Diagram 3 14 represent some form of critical squares, herein called critical outflanking squares. It turns out that there are actually six critical outflanking squares for White in Diagram 3 13, though three of them are not practically involved. White could also win the e6-pawn if the white king could occupy either f6, g6, or h6, though in the particular example they're on the other side of the playing field. Naturally, the black king has its own set of critical outflanking squares. Under the right circumstances, if the black king could get to h5, g5, f5, d5, c5, or b5, in a timely and suitable way, beating White to the punch, Black in turn could force a win. Thus we can make a more generalized statement. In fixed pawn situations, where one enemy pawn faces off against one friendly pawn, a friendly king's critical outflanking squares are on the same rank as the enemy pawn. If the attacking king can occupy any of the three squares immediately to the left of the pawn, or any of the three squares to the contiguous right of it, the enemy pawn can be won by force. Many outflanking situations are disguised. In Nimzowitch's famous treatise My System the great expounder of strategic chess ideas otters the following position (Diagram 314). In probing this position it's important to realize that the bishop at a8 prevents the a-pawn from moving. This type of obstruction is called a blockade. The bishop is a fairly good blockader. It

obstructs the pawn and also is able to prevent the white king from breaking the blockade, since b7 is guarded by the blockader. The rook, on the other hand, is a poor blockader. It can sit in front of a pawn, but it can't prevent the opposing king from breaking the blockade, since it doesn't guard against diagonal approaches. Thus we have a solution: sacking the Exchange (the white rook for the bishop) to transform a good blockader into a had one. There follows 1. Rb8+ RB 2. Rxa8! Rxa8 3. Kb7 RB 4. a8/ Q Rxa8 5. Kxa8 K17 and we're back at Diagram 313, with White having an outflanking win. 314) Camouflaged outflanking

In Diagram 315, we don't have a position where neither player wants to move. Rather, both players want to move, since whoever moves can force the other player into that hideous zugzwang (known in some endgame texts as the trebuchet). White to play wins with 1. Kd7 (not 1. Kd6? because of I...Kf5, placing White in the trebuchet) 1...Kf5 (what else?) 2. Kd6, and Black is up the creek. 315) Whoever moves wins

It's amazing how far away one's king can be and still force an outflanking. In Diagram 316, the white

king is significantly away from the battle zone. But White to play has a forced win. To determine this, all one has to do is figure out where the critical outflanking squares are. It turns out they are d6, e6, and f6. (The square h6 is also a critical outflanking square, but there's no way white's king can get there with any logic behind it.) 316) Distant outflanking

Of particular interest for White is the critical outflanking square furthest away from the defender. Here, it's d6. All White has to do is keep the focus on getting the friendly king to d6. A variation that does this is 1. Kb3 Kg7 2. Kc4 Kf7 3. Kd5 (threatening to occupy the outside critical square, d6) 3...Ke7 4. Key! (seizing the opposition) 4...Kf7 5. Kd6!. White's king occupies the outside critical square and the g6-pawn soon falls. The finish might be 5...Kf8 (taking a meaningless diagonal opposition) 6. Ke6 Kg7 7. Ke7 Kg8 8. Kf6 Kh7 (in outflanking situations, the attacking king always has two places from which to attack the target pawn, here f6 and f7) 9. Kf7 Kh8 10. Kxg6 (it's a win, but it's also a knight-pawn, so the attacking king must go to the h-file) 10...Kg8 11. Kh6 Kh8 12. g6 Kg8 13. g7, and Black is squeezed out (1-0). Outflanking isn't an automatic animal. Although, once the kings are situated in an outflanking situation, the dominant king can always win the enemy pawn, gaining the pawn doesn't definitely lead to the win of the game. The determining factor is the rank the pawn sits on when it's captured. If the pawn is captured on the attacker's sixth rank, and it's not a rook-pawn, it's a win, since the capturing king winds up sitting on a true critical square. If the pawn is captured on the attacker's fifth rank, and it's not a rookpawn, then it's not an automatic win, since the capturing king doesn't yet sit on a true critical square. To draw at that point the defender's king takes the opposition and prevents the attacker's king from advancing to a critical square. 317) Draw

In Diagram 317, for example, it's an advantage to have the move. If White moves first White can win Black's epawn by force. If Black moves first Black can win the white e-pawn by force. But whether White moves first and captures Black's pawn, or Black moves first and captures White's, it's not a win, since after the pawn is captured the defending king can take a meaningful opposition and draw. 318) White has outflanked but Black holds

In Diagram 317, if White plays first, the position might go 1. Kc4 Kd6 2. Kb5 (occupying the outside critical outflanking square in order to win the e5-pawn) 2...Ke6 3. Kc5 (or 3. Kc6) 3...Ke7 4. Kd5 Kf6 5. Kd6 Kf7 6. Kxe5 Ke7 (Diagram 293), taking a meaningful opposition and drawing (Diagram 318). If it's Black to play in Diagram 317, there's a mirror image continuation, I. Kc5 2. Kd3 Kb4 (occupying the outside critical outflanking square) 3. Ke3 Kc4 4. Ke2 Kd4 5. Kf3 Kd3 6. Kf2 Kxe4 7. Ke2, taking a meaningful opposition and drawing (Diagram 319).

319) Black has outflanked but White holds

A not unrelated setup materializes in Diagram 320. White hopes for I ...Rxe3+, with a draw. But Black has a surprise, 1...Kf4!, and since white must trade rooks, 2. Rxe4+ Kxe4, Black winds up with the opposition and wins. So with outflanking it indeed matters on which rank the pawn gets captured. In Diagram 321, for example, Black to play could try the immediate 1...Kf3?, and if White continues 2. Kh2?, the advance 2...g4 ensures a favorable outflanking situation. But if Black plays the illconsidered I ...Kt3?, White has the eye-opening counter 2. g4!. The pawn is still lost, but now it's lost on a better rank. So after 2...Kxg4 White has 3. Kg2, taking a meaningful opposition and drawing. Being aware of these considerations would lead Black to start with the correct move, I ...g4!, fixing the white g-pawn on g3, after which the black king still gets to a winning square next move (d3 or e3). And if it's White's turn to start, the simple 1. g4! loses the pawn, but most favorably indeed, with the position then being drawn, since Black's king will be unable to occupy a critical square. 320) Black wins

321) Preventing a favorable outflanking

In Diagram 322, it's a draw with White to move, but White must step carefully. The blunderous 1. Kd2?? permits I ... Kxd4, and the black king gets to a critical square next move (c3, d3, or e3). But by withdrawing to the home rank, 1. Kd I (or 1. Ke I), White waits for Black to capture on d4, and then the white king takes a meaningful opposition, which keeps the draw in hand. A sample continuation is 2... Kd3 3. Ke I Ke3 4. Kd 1 Kxd4 5. Kd2. 322) Outflanked but draws

Diagram 323 offers a first look at situations of two connected pawns vs. one, where there are no immediate passed pawns, and outflanking can play a role. This manual is not a textbook, so we have no intention of analyzing all the related pawn structures in depth. But this particular outflanking formation is worth adding to one's armory, making sure to become familiar with a trap to avoid. White to play wins with 1. Kd5 (hut not I. f6+'?; not because of' I ...gxf6'? 2. Kf5 Keg 3. Ke6; but because of I...KIN! 2. Kc6 KgS 3. Ke7 gxf6! 4. Kxf6 KfX, taking a meaningful opposition and drawing) 1...KfX (or I...Kf6 2. Ke4 Ke7 3. Key; while I...Kd7 loses directly to 2. 17i) 2. Kd6 Ke8 3. Ke6 Kf8 4. Kd7 Kg8 5. Ke7 Kh8. Now White can't continue to move inward with the king, but the breakthrough, 6. f6, just plain wins. If 6...gxf6, then 2. Kf7, it's not stalemate and White soon mates. And if Black instead answers 6. f6 with 6...Kg8, White has 7. t7+ and mate next move, since White's king controls the promotion square. 323) Maneuvering in

324) Ditches pawn to outflank

I was once at the Marshall Chess Club (where else would I be'?) and saw two players struggling with the position of Diagram 324. After a variation such as 1. Ke6 Kc7 2. Ke7 Kcf 3. Kd6 Kdg, the players agreed to a draw. But rather than trying to hop around with oppositional moves, all White had to do was get rid of the c-pawn, 1. c7!. Once the pawn's taken, I...Kxc7, White's king moves to e6, a critical outflanking square, and outflanks meaningfully. It's the old case of less being more. Although some positions may be a technical win, why go through exacting maneuvering when you can convert to a simpler win'? In Diagram 325 White is materially ahead by the Exchange, but making further progress is not immediately in the picture. By giving back the Exchange, however, White can simplify the winning task, reducing to a clearly winning outflanking setup. With 1. Rxc6 bxc6 2. Kd6, Black will get outflanked, 2...Kb7 3. Kd7 Kb8 4. Kxc6, with White's king already occupying a critical outflanking square. 325) Simplifying to an easier win

326) Converting to an outflanking win

The same kind of resolution is available in diagram 326. White is up a queen for a rook, but rather than trying to win by working out labyrinthine variations, White can immediately transmute baser metal to gold with 1. Qxd6+! cxd6 2. Kf6, occupying a critical outflanking square. Diagram 327 is little trickier, but the results are much the same. While White's knight has no way to get out of the corner safely, it can be sacked to create a favorable outflanking setup: 1. Ng6+! fxg6 2. Ke6 (or 2. Kd6). Note that turning down the offer of the knight, I ...Kg7, fails to 2. Nf4 (or 2. Nh4) 2...f6 3. g6. Playing off this previous situation is diagram 328. White can't take the knight since that's stalemate. Instead White has the unbelievable 1. Ra8+!. If 1...Kxa8 then 2. Kxc7 Ka7 3. Kc6 will outflank; and if 1...Nxa8 then 2. Kc8! leaves 2...Nc7, when 3. Kxc7 also outflanks. Note that after I.Ra8+!, if I ...Kb7, then 2. Ra7+. 327) Sacking to outflank

328) White wins

329) White has a protected passed pawn

330) Just a draw

Let's reconsider a previous examined position, now shown in Diagram 329. As we've already seen, White to play wins. To be sure, it's a win for White even if Black goes first. Move the pawns in Diagram 329 a file up (Diagram 330) and the position is drawn, with White not being able to make any progress, since stalemate hangs over the proceedings. Move everything in Diagram 329 to the left by one file, and the position is still drawn, also because of a stalemate possibility. For example, in Diagram 331, it's clearly a draw after 1. Kc6 Kc8 2. b7+ Kb8 (Diagram 332). 331) Position is drawn

332) A draw no matter who moves

From Diagram 332 it's a draw no matter who moves. If it's Black's turn, Kb8-a7 begs White to stalemate by Kc6-c7.

333) White has two ways to win

Move everything in Diagram 329 a file to the right and White has several ways to triumph, winning with action on the right or the left. In Diagram 333 White can win by sacking the d-pawn and then occupying f6, to outflank meaningfully. Or White can blindside, maneuvering the king around to the other side of the pawn complex, and then sacking the dpawn to get into the critical squares a6 or b6. An example of the blindside method is the line 1. Kd4 Kc8 2. Kc4 Kb7 3. Kb4 Kb8 4. Ka5 Kb7, and now 5. d7! Kc7 6. d8/Q+ Kxd8 7. Kb6, with White outflanking meaningfully. 334) White wins by getting the king to d5

Moving everything in Diagram 329 back a rank to reach the position of Diagram 334, which leads to an easy in for White no matter who moves. White simply has to maneuver the king to d5. That enables the c-pawn to advance with protection, and White will wind up winning the black b-pawn. Thus, with

Black to play, a winning variation would be 1...Kc6 2. Ke5 Kc7 (taking a meaningless diagonal opposition) 3. Kd5 Kd7 (another meaningless opposition) 4. c6+ Kc7 5. Kc5. 335) White wins by getting the king to c5

But move everything in Diagram 334 one file to the left and it gets a little trickier (Diagram 335). The chief pitfall is shown in Diagram 336, which could arise from 335 if Black goes first by I...Kc7 2. Kc5 (correct is 2. Kd5) 2...Kb7 3. b6. If it were White's turn in Diagram 336 White would win by Kc5-b5. But Black to move can draw by I...Ka6!, when 2. Kc6 is stalemate. It's evident that the advance of the bpawn (a knight-pawn) must be made in a timely way, since possible stalemate glooms ahead. From Diagram 337, when the black king is at c7, it has to be done with check. If b5-b6 is played when the black king is at b7, however, the stalemate stratagem comes into effect. 336) Black to play draws White to play wins

It turns out that the standard rules of opposition are altered in Diagram 338, with the oppositional field affected by the pawn placements. So the guidelines of being on the same straight line and occupying squares of the same color don't apply: there's distortion in the oppositional field. Thus, in Diagram 337, White shouldn't play for the direct opposition with I. Kc5 (this is the equivalent of a meaningless opposition). Instead White should play for the distorted field opposition, here called a knight's move opposition, by 1. Kd5!. After 1...Kb6 (I ...Kb7, a meaningless opposition, is answered by 2. Kc5 Kc7 3. b6+) 2. Kd6 Kb7 3. Kc5! Kc7 4. b6+ Kb7 5. Kb5. An even more complicated instance of the pawn setup in question is seen in Diagram 338. 337) Knight's move opposition

In Diagram 338, White steps back a file with 1. Kd6!!. There follows 1...Kf7 2. Kd7 KB (note that Black doesn't have full use of the maneuvering space, since f6 is guarded by the g5-pawn) 3. Ke6 Kg7 4. Kf5! (a knight's move opposition) 4...Kf7 (a meaningless opposition) 5. g6+ Kg7 6. Kg5 and wins. Diagram 339 (and Diagram 338), while relying upon knights move opposition, and rippling distortions in the oppositional field, also allows us to reintroduce another concept: that of corresponding squares. 338) White's king eyes f5 when Black's king is on g7

Corresponding squares Two squares, one for White and one for Black, are said to correspond when neither side wants to place their king on such a square first. By occupying a corresponding square second a player is taking an opposition based on a distortion in the oppositional field caused by pawn placements, so that the standard oppositional rules don't apply. Sometimes a number of squares are involved, with one side having several squares that correspond to a particular enemy square. Some positions have a network of corresponding squares extending over the entire hoard, even at faraway places, which makes maneuvering very difficult to figure out properly. For the most part corresponding square theory applies to fixed or restricted pawn structures, resistant to change, where king maneuvering occurs within the complex of essentially inflexible barriers and obstructions. Corresponding square theory is also referred to as coordinate square theory, and the famous artist Marcel Duchamp, a master chess player, once co-authored an entire book on the subject, with extant copies now running ten thousand dollars and more (must be a pretty good book). In a way, corresponding squares are like landmines. Be the first to step on one with your king and watch your chances blow up. For the superior side it may mean throwing away the win, and in some cases, even losing; for the inferior side it always means losing. We cannot treat this subject thoroughly, but it's a good idea to know a few things, for their practical value and to expand awareness of the game's theory. Let's think about this in the perspective of the previous problem. In Diagram 338 the square f5 for White corresponds with the square g7 for Black. That is, White wants the white king to move to f5 when the black king is already on g7; and Black prefers moving the black king to g7 when the white king already is on f5. 339) Fighting for squares

A more complicated version of corresponding square theory is seen in Diagram 339. If it were White's turn, White would win immediately 1. Ke2 (or even 1. K12). No matter how Black replies, White gets the king to e3, safely advances d3-d4, and subsequently wins Black's c3pawn. But Black to play can hold the fort. Here, a network of squares correspond: el corresponds with 13; dl with e3; and, critically, on the blindside, a2 with b4. In the position, with White's king occupying a square (el) that corresponds to f3, Black can play to el's corresponding square, 1...Kf3!. There might follow 2. Kdl Ke3 (with e3 corresponding to di )3. Kel Kd4 (with d4 corresponding to c I ) 4. Kbl Kc5 5. Ka2 (threatening to occupy b3, a critical outflanking square) 5...Kb4 (occupying a2's corresponding square just in time), and Black holds. Note that a mistake would have been for Black to start with I...Ke3'? (which takes a meaningless, and losing, opposition). After 2. Kd 1, menacing a blindside attack, Black must play 2...Kd4, and the correspondence is broken with 3. Ke2!. Black's c3-pawn will be gobbled shortly. Adding to our discussion oftwo pawns vs. one are those situations where each side has a pawn immobilized by an opposing pawn, with the superior side's extra pawn being passed and separated from its partner by one file, as in Diagram 340. The example also allows us to reintroduce triangulation so that we can talk about it in the context of corresponding squares. 340) Triangulation

In Diagram 340, certain squares correspond: for example, e6 to e8, e5 to B, and f5 to IT Neither player wants to move when the kings are on those squares. White to play wins by breaking the correspondence, transferring the turn to Black, relying on a triangulating movement with the king (taking three moves to do what the king could in two moves). The winning continuation, as seen earlier, but here with further elucidation, is 1. Ke4! (or I. Kf4) 1...Ke8 (since White can't yet play Ke6) 2. Kf4! (or 2. Ke4, if the king is coning from 14) 2...KfX 3. Ke5!, and Black must make a losing concession. A practical example of a triangulating idea occurs in Diagram 341. If White plays I. KfO, Black has

I...Kt8, occupying f6's corresponding square; if White tries I. Kc5, hoping to get into d6, Black has I...Kc7, occupying e5's corresponding square. But White wins by breaking the correspondence, starting I. Kf4! (or I. Ke4!) I...Kfli 2. Ke4! (or, if already on e4, 2. Kf4!) 2...Ke8 3. Kf5, and we have the original position with Black to move. White will promote the c6-pawn, or Black's pawns will soon fall. 341) Triangulation from the Ruy Lopez

As a habit of mind it's a good idea when first encountering a setup to imagine how the position arose. This is particularly helpful for giving a player practice at identifying pawn structures within certain opening systems. Superficially it's possible to see in Diagram 342 how Black's pawn structure could have arisen from the Exchange Variation of the Ruy Lopez (I. e4 e5 2. Nf3 Nc6 3. Bb5 a6 4. Bxc6 dxc6). True, a lot has happened since those opening moves, but a further convincing feature is White's passed e-pawn. Indeed, in some lines of the Lopez Exchange Variation a pawn imbalance occurs such that White gains a pawn majority on the kingside, resulting in a passed e-pawn. Specifically, from the opening moves, the line 5. d4 exd4 6. Qxd4 Qxd4 7. Nxd4 produces this type of setup immediately, not that Black doesn't get any compensation. Remove all the pieces except for the kings (Diagram 342) and we see how White's healthy kingside pawn majority is capable of producing a passed e-pawn. That is, White's three queenside pawns can hold back Black's four, while Black's three kingside pawns cannot stop White's four. Because of the healthy majority White has the capability of producing a passed epawn, as if White were a pawn ahead. 342) From the Ruy Lopez

343) From the Caro-Kann Defense

A similar type of majority (four vs. three) can be obtained from the Caro-Kann Defense after the moves 1. e4 c6 2. d4 d5 3. Nc3 dxe4 4. Nxe4 Nf6 5. Nxf6+ exf6 (Diagram 343). Once again remove all the pieces except for the kings and we can imagine how White's three kingside pawns can stop Black's four, but Black's three queenside pawns cannot cope with White's four. Because of the healthy majority, which empowers White to produce a passed d-pawn, it's as if White's up an extra pawn. In this way we can understand at least one way to think in the approach of starting a game. We can play with the plan of heading for a favorable endgame. For those players who feel particularly adept in the endgame, this may not be a bad strategy, keeping an eye on obtaining a propitious ending right in the opening. Even so, one must still recognize that before the endgame "the gods have placed the middlegame," as one chess pundit memorably put it. 344) Trading down works

Let's look at another practical matter requiring some decision-making. Even with pieces on the board it can be prudent to take into account resultant pawn endings and the concept of triangulation, as in Diagram 344. As a rule of thumb you should trade pieces (but not necessarily pawns) when ahead by a pawn. So in Diagram 344, with White to move, White must decide whether or not to exchange pieces by checking at e5. It turns out to be a good decision: 1. Ne5+! Nxe5 2. Kxe5 Ke7 3. Kd5 Kd7 4. e5 Ke7 5. e6 Ke8. Here White has two ways to win: by triangulation, 6. Kd4 Kd8 7. Ke4 Keg 8. Kd5; or by discarding the e-pawn to outflank, 6. e7 Kxe7 7. Ke5 Kt7 8. Kd6, occupying the outside critical square of the immobilized g6-pawn. 345) White wins directly

Again, this is not an exhaustive textbook. But it does contain many useful practical ideas that amateur players can exploit to win and save games. Sometimes analysis is simply too difficult, and ordinary

players can easily wind up getting lost in a maze of variations. If there are helpful principles and rules of thumbs, certainly these should be considered and used to support whatever analysis one can work through. Let's see if there are any signposts that can be garnered from the next set of positions. 346) Having an option wins

Consider Diagram 345. White has two pawns, an a-pawn and a b-pawn, and they are offset by a single black a-pawn. Key is that White has a choice: the spawn can be moved one or two squares. Having this option can be crucial. Here White wins directly with 1. a4 Kb8 2. a5 Ka8 3. b6 axb6 (or 3...Kb8 4. b7!, and not 4. bxa7+??, drawing) 4. axb6 Kb8 5. b7. Compare Diagram 345 to Diagram 346, with Black's king moved over one square toward the kingside. It would be incorrect to play 1. a4? because of 1...Ka8 2. a5 Kb8 3. b6 axb6 4. axb6 Ka8!, taking a meaningful opposition and drawing. But by moving the a-pawn one square instead of two, playing a2-a3 instead of a2-a4, White keeps an extra tempo and that preserves a meaningful opposition in the end. The winning moves would be 1. a3! Ka8 2. a4 Kb8 3. a5 Ka8 4. b6 axb6 5. axb6 Kb8 6. b7, squeezing Black's king off the eighth rank and winning. As an exercise students should get into the habit of trying to find rules, even personalized ones. If anything, they will help the student remember things better, if not actually understand them more thoroughly. Playing detective here, examining Diagrams 345 and 346, we can see that White won in each case by moving the a-pawn to a square of the same color occupied by the black king. When the black king was on a8, a light square, White placed the rook-pawn on a4, also a light square. When the king was on b8, a dark square, White moved the pawn to a3, also a dark square. So we have a new color rule. In such situations the win is achieved by moving the rook-pawn to the same color square occupied by the opposing king. 347) White wins with a two-square advance

Let's see what happens if we vary the situation, making the advanced pawn be a rook-pawn on the fifth rank (Diagram 347). If White tries 1. b3'?, moving just one square, White throws away the win, 1...Kb8 2. b4 Ka8 3. b5 Kh8 4. h6 axb6 5. axb6 Ka8, taking a meaningful opposition and drawing. But with 1. b4!, White keeps the proper tempo and wins directly, 1...Kb8 2. b5 Ka8 3. b6 axb6 4. axb6 Kb8 5. V, and the squeeze is on. 348) One-square advance wins

But in Diagram 348 it's just the opposite. White wins with a one-square move, and to a square opposite in color from that occupied by the black king: 1. b3! Ka8 2. b4 Kb8 3. b5 Ka8 4. b6 axb6 5. axb6 Kb8 6. V. Let's play detective again. In Diagrams 347 and 348, White wins by moving the b-pawn to an opposite color square from the one occupied by the enemy king. That is, White plays to b4, a dark square, when the king is on a8, a light square; and White plays to b3, a light square, when the black king is on h8, a dark square. So extending our color rule thinking, we see that the win is achieved in

these situations by moving the knight-pawn to the opposite color square occupied by the enemy king. I remember a maxim my chess teacher used to say to me, concerning these types of positions. It's silly, but it works. "The rook-pawn's the same, the knight-pawn's a different game." An acquaintance of mine, a fairly strong IM, tried everything he could to find fault with this "silly-gism." In the end, he couldn't, and he had to admit that it was easier for him to remember the rhyme than to recall or work out specific lines, which naturally he could also do. From these last four examples, however, an important concept does come out that has more general application for endgame play. Very often, when mobilizing a pawn mass on one side of the board, players will routinely advance all their pawns. This is often a mistake. Unless the situation requires it, or a clear favorable line can be found that goes against the generalization, one shouldn't automatically move up all the pawns indiscriminately. Rather, it's usually more prudent to keep hack at least a single pawn, say a rook-pawn, so that at the critical moment one has the option of moving a pawn two squares or one. Such an option can he vital, whether it means getting a meaningful opposition, avoiding stalemate, or shifting tempo so the friendly king can occupy a critical square. So, as a rule of thumb: If the situation is unclear, hold back at least one pawn to preserve its two-square option. 349) Stalemating to force commitment

In Diagram 349, for example, with the h7-pawn still unmoved, Black has a simple winning idea: to "stalemate" White's king (it's not a real stalemate), forcing White to commit to an informationreleasing, definite pawn move of one or two squares. After that committal pawn move Black will be able to figure out how to move the h7-pawn, whether to move it one or two squares, in order to keep a winning tempo. After 1...Kf3!, if White plays, 2. h4 (moving two squares), Black can win with 2...h6 3. h5 Ke3 (or 3...Kg3); and if White instead goes one square, 2. h3, Black moves the h7-pawn two squares, 2...h5, when 3. h4 Ke3 gets to the same winning place. Sometimes life comes down to knowing which pawn to move, assuming at least either of two pawns can be moved. 350) First, a tempo

In Diagram 350 we encounter a useful tactical situation. Advancing the knightpawn, I ...b3'?, jettisons the win, an uncomplicated draw resulting from 2. Kc3. But by first moving the rook-pawn, I...a3!, Black gains a worthwhile tempo, since the square c3 remains guarded and therefore inaccessible to White's king, while 2. Kd3 doesn't really bring the white king any closer. Black finishes with 2...b3!, and will promote at al shortly. This runs counter to Capablanca'.s rule, which will be explained shortly, but, in tactical situations, rules often are overridden by specific moves. 351) White wins

Let's look at some other types of pawn majorities, such as the case of three vs. two on one side. Diagram 351 shows a pivotal situation, where all three white pawns have reached the fifth rank. White to play has the immediate 1. g6, when I ...hxg6 2. hxg6 produces the position of an earlier diagram, here with Black to move instead of White. If 2...Ke8, there follows 3. Ke6 Kf8 4. Kd7 Kg8 5. Ke7 Kh8 6. f6 gxf6 7. K17 (best) and soon mates. If instead 2...Kf8, White makes headway with 3. Kd6 Ke8 4. Ke6, and wins as in the earlier variation. Note that after 1. g6, countering with I ...h6 doesn't really help. White still wins with 2. Kd5 Kf6 3. Ke4 Ke7 (on 4...Kg5 White has 5. Ke5 KxhS 6. Ke6 Kg5 7. f6! Kxg6 8. f7) 4. Ke5 Kf8 5. Kd6 Ke8 6. Ke6 Kf8 7. Kd7 Kg8 8. Ke7 Kh8 9. f6.

352) A basic three vs. two advantage

This brings us to Diagram 352, which provides a typical instance of a kingside pawn majority, White having a superiority of three vs. two, with none of the pawns having moved. As a reminder, you have a pawn majority if over any consecutive grouping of tiles you have more pawns than your opponent does. Typically, majorities are broken down by reference to the kingside or queenside, but there are other ways to describe majorities as well, such as a central pawn majority. How should White proceed from Diagram 352? Certainly, moving the king toward the center should he considered, since in most king-and-pawn endings activating the king is quite important. Having an activated king usually means being able to support the advance of your pawns more efficaciously, while reducing the enemy king's counterplay. So 1. Kfl is not unreasonable. But let's say we're committed to getting the pawns going. In situations where one side has a pawn majority, generally the pawn to advance first should he the unopposed pawn, the one with no enemy pawn in front of it on the same tile. This pawn is known as the candidate passed pawn. Here it's the fpawn. It's not passed yet, but it has the greatest prospect of becoming a passed pawn. Since it was ('apablanca who popularized the expression of this in his hook Chess Fundamentals (though he was not the first to describe the process, he's become identified with the concept because of the charm of his presentation), the idea of advancing the unopposed pawn first is popularly known as ('apahlanca'.s rule. Accordingly, Following Capablanca's rule from Diagram 352, White should begin with 1. M. A reasonable variation after t2-f4 might go: 1...Kf7 2. Kf2 Kf6 3. Kf3 (3. g4 is also playable) 3...Ke6. 353) White considers two options

As a defensive principle, one should be careful about making pawn advances. Too move one's pawns too quickly or incautiously - to advance them without being certain of being able to bring about desirable exchanges, or of being able to cope with the consequences can lead to disaster. Indeed, one risks creating weaknesses and overextending the position, and such things can entail that the opponent produces a favorable passed pawn sooner or with less trouble. Thus, instead of 3...Ke6, Black could try a few advances, beginning with 3...h5. But after 4. Ke4 Ke6 5. f5+ Kf6 6. Kf4 g5+ 7. fxg6 Kxg6 8. h4, Black will soon be outflanked, since, whenever it's needed, White has an extra tempo (thanks to the unmoved g-pawn). So after 3...Ke6, play could reasonably go 4. Ke4Kf65.g4Ke66.f5+Kf67. Kf4 Kf7 8. g5 Ke7 9. Key Kf7 (Diagram 353). Let's say White here con siders either of two moves, (A) 10. f6 or (B) 10. Kd6. 354) White does the opposite

These are hardly White's only moves, but certainly both are worthy of analysis. On (A) 10. f6, there are various possibilities, such as I0...gxf6 11. gxf6 Kf8 12. Ke6 Ke8 13. f7+ Kf8 14. Kf6!, stalemating the black king and forcing a commitment, to which White will do the opposite (Diagram

355). If 14...h5, then 15. h3; if 14...h6, then 15. h4). These circumstances are comparable to those of Diagram 349. But after 10. f6 Black could also try 10...g6. Play might then go 11. Kd6 Kf8 12. Ke6 Ke8 13. 1`7 Kf8 14. Kf6! (Diagram 355), causing a pseudo king stalemate (though not an actual stalemate) and forcing Black into a hurtful concession. 355) Forced jettison

Black must now move the h-pawn, 14...h5 (or 14...h6, it doesn't matter), which results in 15. gxh6 g5 16. h7 g4 17. h8/Q mate. Certainly, there are other moves for both sides, but we're just trying to examine some representative variations to get a sense for playing the position with understanding and control. This brings us back to possibility (B) 10. Kd6. What should you do if after trying to calculate some of the above variations you're still uncertain? In such cases, when the analysis isn't clear to you, and it still seems possible to improve the position further before making a committal move, that's what you should do. That is, when in doubt, continue to enhance prospects for favorable action until you're no longer in doubt. Russians again are the first to remind us of this endgame principle: The principle of not hurrying. That is, if before making a final breakthrough you can develop the situation so that the results of the breakthrough are smoother, safer, more definite, or more rewarding, where the gains of waiting clearly outweigh the gains of acting, one should hold back a bit before putting the final stages into motion. As a piece of advice, it would be: Don't hurry. Naturally, there's another side to this question. Some people become so fearful of making a final breakthrough that they delay it endlessly, and suddenly it becomes too late. Thus, the counter-piece of advice would be: Don't prepare endlessly; or, as my teacher used to say to me, don't prepare to do what you can do at once. If, therefore, the consequences of 10. f6 are in doubt in your own mind, there's surely nothing wrong with playing 10. Kd6, maneuvering your king further down the board, aiming to control more of the path ahead of the potential passed pawn. A possible conclusion might then be 10...Ke8 11. Ke6 Kf8 12. f6 gxf6 13. gxf6 Ke8 14. f7+ Kf8 15. Kf6, and White wins by exercising the proper one-square or twosquare option of the h-pawn. Conflicting principles

What should you do when principles conflict'? First of all they may not actually conflict, but only seem to on the surface, or the conditions to which they apply may be slightly different and one doesn't detect those differences. But no matter, whenever there seems to be a contradiction, there's a surefire remedy to the problem: You should think - that is, analyze and calculate specific variations - instead of following bromides and blind advice. Artificial stalemate as a technique As a technique the idea of stalemating the enemy king (as long as it's not really stalemate) can be applied to a range of endings. This is especially so whenever there's a healthy pawn majority (none of the pawns are doubled and the majority has the ability to advance naturally). Often a cog in the process is retaining the ability to exercise a two-square option, thanks to a key pawn having not yet advanced. Once again, this gets back to the idea of not making unnecessary pawn moves, a principle that's clearly true in the opening, the middlegame, and the endgame. The same method for winning with a pawn majority of three vs. two can sometimes be adopted to win in endings with majorities of four vs. three, particularly if it's just a matter of having to factor in a healthy extra pawn for each side. In Diagram 356 an a-pawn has been added for White and an f-pawn for Black, but the winning technique is more of the same: White (I) creates a passed pawn (2) escorts it up the board with the king (3) saves at least one twosquare option and (4) forces the player to commit to definite, and therefore, exploitable pawn moves by stalemating the king. A sample variation is 1. e4 (showing Capablanca's rule, by advancing the unopposed pawn first) 1...f6 2. f4 Kf7 3. Kf2 Ke6 4. Kea Kd6 5. Kd4 Ke6 6. e5 fxe5+ 7.fxe5 (now White has a passed pawn) 7...Ke7 8. Kd5 Kd7 9. e6+ Ke7 10. Key Ke8 11. Kd6 Kd8 12. e7+ Ke8 13. Ke6 (stalemating the opposing king and forcing concessions) 13...h5 14. h4 g6 15. g3 g5 16. hxg5 h4 17. g6 h3 18. g7 h2 19. g8/Q mate. 356) A similar method

Diagram 357 offers a hit more of the same. White has added a d-pawn and Black an a-pawn, but the

process doesn't vary much: 1. KfI Kf8 2. Ke2 Ke7 3. Kd3 Kd6 4. e4 f5 5. f3 Kc6 6. Kc4 Kd6 7. d5 fxe4 8. fxe4 exd5+ (8...Ke5 9. Kc5) 9. exd5 Kd7 10. Kc5 Kc7 11. d6+ Kd7 12. Kd5 Kd8 13. Ke6 Ke8 14. d7+ Kd8 15. Kd6 g6 16. Ke6 (or 16. g3 h6 17. h3 h5 18. h4; on 17...g5 there could follow 18. g4 h5 19. gxh5 g4 20. h6 g3 21. h7 g2 22, h8/Q mate). 357) More madness to the method

Decoying In situations where both sides have passed pawns one side may have the advantage of a passed pawn that can he used as a deflective sacrifice, a decoy that lures away the enemy king. Generally, the decoying pawn is the one furthest away from the main battleground. In Diagram 358 Black to move relies on the h-pawn to break through. The win is achieved after 1...b4+ 2. Kxb4 Kxd4, and the black king gets to the kingside first. Having an extra pawn doesn't always lead to promoting that particular pawn. Rather it may mean having to use the extra pawn as a decoy to lure away the opposing king. The friendly king can then make inroads in the sector of the board that's been abandoned. Such is the case in Diagram 359. 358) Black wins with the outside passed pawn

The white e-pawn can't be promoted by force. But White can use it to gain time to win the h-pawn. With an extra tempo White's king can then get to a critical square (g7), and that will win. The winning way begins with 1. e6+ Ke7 2. Ke5 (a mistake would be to play 2. Kg6 at once, since 2...Kxe6 3. Kxh6 K17 prevents the white king from getting to g7, and the game is drawn) 2...Ke8 3. Kf6 (now it takes two moves for Black to win the e-pawn, and that costly tempo gives White the win) 3...Kf8 4. Kg6 Ke7 5. Kxh6 Kxe6 5. Kg7. 359) The decoy

The decoy concept also applies in Diagram 360. But once again the win is achieved by gaining an appropriate amount of time. It would be a mistake to forge ahead, trying to use the c-pawn as an immediate decoy, since 1. c4 Kt7 2. c5 (2. Kg2 or 2. Kt2 still win) 2...Ke6 3. K12 Kd5 4. Kg3 Kxc5 5. Kh4 (White will win the h-pawn, but Black will hold by getting the king to fR or 17, guarding the g7 critical square) 5...Kd6 6. Kh5 Ke7 7. Kh6 Kt8 (or 7...K17) 8. Kxh7 K17 with a draw. The correct strategy is to make as much headway as possible, im proving the position of the white king. If White is momentarily stopped, then the c-pawn can be pushed to begin diverting the black king. Accordingly, White can move toward the win with 1. Kg2 Kg7 2. Kg3 Kg6 3. Kg4 Kf6 4. Kh5 Kg7 5. Kg5 Kf7 6. Kh6 Kg8. Having placed the king where White wants, on top of the hpawn, the c-pawn can be offered as bait: 7. c4 (actually, even more time can be gained by 7. h4 Kh8 8. h5, but there's no need to be piggish) 7...Kf7 8. Kxh7. The win is then elementary. A version of the decoy idea is that of the outside passed pawn. This can refer to instances where both sides can produce passed pawns, but one side has the advantage in that it's passed pawn is further away from the main theater. This means the defending king will have to expend time to cope with it, thereby being lured away from the area of intense battle, which becomes vulnerable to the other king. In ordinary chess parlance, however, most players use the term to apply to any passed pawn, or potential passed pawn, that can be used as a decoy. Thus, the e5-pawn in Diagram 359 can be described as an outside passed pawn loosely, though it is not technically such, since it is an extra pawn. In Diagram 360, the white c2-pawn can also be so described. 360) Delaying the decoy

361) Maximize the position first

If the potential decoy has not achieved passed pawn status yet, progress should still be made with the king before mobilizing the bait, unless the tactics can be seen to justify other action. Thus, in Diagram 361, the correct strategy is to improve the white king's position. Once no further immediate progress is possible, then it's time for decoy action. As a rule of thumb the process of creating and using a decoy works best when the attacking king is first able to get as close as possible to a target pawn. Then it can be captured as soon as the enemy king tries to cope with the decoy. White can try a procedure similar to the one employed in the previous example: 1. Kg2 Kg7 2. Kg3 Kg6 3. Kg4 Kf6 4. Kh5 Kg7 5. Kg5 K17 6. Kh6 Kg8 7. h4 Kh8 8. h5 Kg8. Now it's time to get the queenside pawns going. How to do it'? By applying Capablanca's rule, advancing the candidate passed pawn first. Thus we have 9. b4 Kh8 (9...K17 loses the h-pawn at once) 10. b5 (or 10. c4) 10...Kg8 11. c4, and White will soon produce a winning decoy. Breakthrough combinations

We've seen generally that the side doing the mobilizing should begin by advancing the unopposed pawn first, in observance of Capablanca's rule. When a pawn majority doesn't exist, in some cases it may be possible to manufacture a passed pawn by tactical operations involving one or more sacrifices. A defining breakthrough combination involving sacrifice is offered in Diagram 362. White begins with 1. b6!. Black has two ways to take the b-pawn. If I...axb6, then a further sacrifice, 2. c6!, essentially forces, 2...bxc6, and 3. a6 wins. If instead I...cxb6, then 2. a6! bxa6 3. c6 queens. But it's a tactical situation, and a matter of who moves. If Black goes first, the stopper I...b6! prevents breakthrough sacs and the position is drawn, even though Black winds up winning a pawn: say 2. axb6 axb6 3. cxb6 cxb6 4. KgI Kg3 (a meaningless opposition) 5. KfI Kf3 6. Kel Ke3 7. Kd 1 Kd3 8. Kc 1 Kc3 9. Kb I Kb3 10. Kal Kb4 I I. Kb2 KxbS 12. Kb3, with a meaningful opposition and a draw. 362) Breakthrough combination

Another not infrequently occurring ending stems from some variations of the Caro-Kann Defense, and consequently is known as the Caro-Kann ending (Diagram 363). It typically arises when a white knight is captured on e5 and taken back by White's d-pawn. Here White has two ways to enforce a breakthrough: by advancing the f -pawn or the g-pawn. After 1. f5 Kb4 2. g5!, Black is in trouble. If 2...hxg5, then 3. f6 wins. If instead 2...exf5, then 3. g6 wins. And if Black continues back with the king, 2...Kc5 3. f6 ensures sneaking a pawn through. 363) Caro-Kann ending

Another simple breakthrough problem is offered in Diagram 364. The breakthrough is achieved with 1. h4!. No matter how Black replies, White will soon have a dangerous g-pawn. If I ...gxh4, then 2. g5+ Kh7 3. Kf7 h3 4. g6+ Kh6 5. g7 h2 6. g8/Q hl/Q 6. Qg6 mate; if 1...hxg4, then 2. hxg5+ Kh7 3. Kf7 g3 4. g6+ Kh6 5. g7, and White queens first. 364) White breaks through

365) Morphy's problem

Clearances and obstructions Breakthroughs aren't always dependent merely on pawns. Pieces can play their role, too. By offering a piece at the right moment, when the other side has small choice other than to take it, the way may be cleared for a pawn to plunge ahead successfully. In Diagram 365, for example, we have Morphy's problem, so named because it supposedly is the only extant problem composed by Paul Morphy. White mates in two moves, beginning with 1. Rh6!. This obstructs the h-pawn and leaves Black essentially two choices: to move the bishop or to take the rook. If the bishop moves, it's mate at h7; if the rook is captured, the g-pawn advances and gives mate. Thanks, Paul. 366) Black mates in four moves

367) White mates in two moves

A not unrelated idea is shown in Diagram 366. Black to play actually has a mate in tour moves, beginning with the sacrificial lure and breakthrough sac, 1...Rh3+!. This forces White's pawn to take, 2. gxh3, which clears the g-tile for 2...g3+ 3. Khl g2+ Kh2 4. gl/Q mate. An even more elementary version of the same idea is shown in Diagram 367. With 1. Ra3+!, White clears 63 and offers Black has no choice but to take the rook, I...bxa3, which also happens to obstruct a3. Those with their eyes open will undoubtedly find 2. h3 mate. In Diagram 368, White obstructs the gpawn with 1. Rg2!. This reduces Black to a single move, I...Rh2, and with h2 now obstructed, White has the piquant 2. Rgl mate. 368) White mates in two moves

One more position in this line is offered in Diagram 369, which is a position adapted from an actual game. White has an extra pawn, and both rooks are hanging, but Black goes first and plays I...Rb2!. Retaining attacking ideas along the rank and file. If White saves the rook by moving along the fourth

rank, Black's rook wins with a back rank check. And if White instead retreats the rook, 2. Rg l , the square next to the king (gl) is now blocked, allowing 2...Rh2 mate. Nice tactics, if you have the black pieces. 369) Black to play and win

Diagram 370 is a position I advise most students to play out and practice, whether it's done against a willing partner or a more obliging piece of software. Learning the ins and outs of this situation helps students understand how to grapple with advancing pawn masses, while embroiling the practitioner in other elements, from pawn races to zugzwang. We're not going to submit this position to the wringer, or consider it in minute detail. Without getting into a thorough analysis, let's look at a straightforward variation or two to get a sense of what we're talking about. The position was thoroughly analyzed by the 19thcentury Hungarian master J6zsef Szcn, and accordingly it's often identified as being the Szen po.citioii or Szen game. When students hear of this, not knowing how to spell Szen, they naturally think what's really being said is Zen position or Zen game. It makes even more sense to them when they start getting lost in the situation's mysteries. White could start with a quick burst of the a-pawn, White's outside passed pawn. But after 1. a4 Black stays within the pawn's promotion quadrangle by I...Ke7. Continuing in that precipitous manner could endanger the pawn, 2. a5 Kd7 3. a6 Kc6. To safeguard the pawn, White then has to play 4. b4 Kb6 5. b5. Now it's Black's turn: 5...h5 6. Kd2 h4 7. Ke3 Ka7 (Black has other moves, too, but this one allows us to usher in an idea, for the purpose of this explanation) 8. Kf4 f5!. I give this an exclamation point, not because it's a scintillating move, but because it illustrates an important concept: the idea of defending the advanced outside pawn of the majority by moving up the inside pawn (for Black, the inside pawn would be the f-pawn). This splitting of the pawns, which for Black means relying on the fand h-pawns, tends to be better than defending the most advanced pawn directly by automatically advancing the pawn next to it (that is, by advancing the one on an adjacent file), which for White means defending the a-pawn with the b-pawn. Both approaches can secure an advanced pawn. But by relying on split pawn advances, rather than connected pawn advances, one thereby retains the option of having the middle pawn serve as a tempo shifter, if and when a tempo

may be needed. 370) The zen game

If play continues 9. c4 Kb6 10. c5+ Ka7 11. c6 Kb6, the white pawns have come to a halt. White's king must cope with the mobilized pawn mass on its own. After 12. Kg2, Black has 12...f4!, splitting the pawns, such that 13. Kh3 0 and 13. Kf3 h3 keep them going. Now if the white king moves to the hfile, Black pushes the f-pawn; if the white king moves to the f-file, Black moves the hpawn. So let's look at 14. Kg 1. To that, Black plays 14...g4, and we have Diagram 371. 371) Nobody wants to move

This is zugzwang: nobody wants to move. Black to move cannot move the king. If the king moves to a7, the c-pawn queens; if the king moves to c7, the apawn queens. So it comes down to moving one of the black pawns. It turns out, the pawns can be stopped by placing the white king on the square directly in front of the pawn which moves. Thus, if f4- 13, White stops the mass by playing Kgl-f2; if

instead h4-h3, then Kgl-h2 will bring down the pawns; and if g4g3, then Kg I -g2 immediately stops the pawns. Meanwhile, if it's White's turn to play, losing concessions must also follow. If the king moves to the f-tile, the h-pawn advances; if the king moves to the h-tile instead, then the f-pawn advances; and if the king plays to g2, then g4-g3 will soon win. Work it out for yourself and see. The two chief ideas to retain from this exercise are: (I) to split the pawns for defense, saving the middle pawn for tempo; and (2) to fight for the three-pawn vs. king structure of Diagram 372, with it being the other player's turn. 372) The player to move wins

373) The player to move wins

Diagram 372 shows a situation in which both players want to move. If Black goes first, the retreating

I ...Kg8!, waits for White to commit to a pawn advance. Black's king will answer that pawn advance by moving in front of it. If at first it's White's turn, however, White advances the pawn in front of the black king, 1. g6!, and that ensures a winning setup. 374) The h-pawn will queen

There are various tactical positions and endgame puzzles that take off from these ideas. In Diagram 373, for instance, the queenside is frozen, so it devolves on the kingside. White to play wins with I. Kg2!, stopping the f-and h-pawns; while I ...g4 is met by 2. Kg l !, waiting for Black to advance a pawn that could then be blocked by White's king. Meanwhile, Black to play has I...g4, and the zugzwang turns against White. To close this section is Diagram 374. It offers a tactical motif that plays off the idea of marking off territory. Black to play wins with I...Bf4!, and the white king must allow the h-pawn to queen.

Diagonal king moves A key element in playing the endgame well is knowledge, especially knowing the various ways to utilize the king. We want to deploy the king effectively, and we want to activate it quickly. Time is crucial, and appreciating how a king can cross from one end of the board to the other, with minimal loss of time, can be the chief determinant in a positive result. Consider Diagram 375, with White to play. It takes four moves for the white king to attack the h7pawn. In the real world the shortest distance between two points is a straight line (actually, it's a geodesic). Yet if 1. Kd7 Kf3 2. Ke7 Ke4 3. Kf7 Kd5 4. Kg7 Ke6 5. Kxh7, Black holds the position with 6...K17. The winning notion is a little different. White still approaches the pawn, but in a way that at the same time thwarts the black king: 1. Kd6! Kf3 2. Ke5! Ke3 (or 2...Kg4 3. Kf6 Kh5 4. Kg7) 3. Kf6 Ke4 4. Kg7 Kf5 5. Kxh7 Kf6 6. Kg8 and wins. By moving diagonally White's king still proceeded toward the h-pawn in a straight line, but combined that movement with an up-the-board movement that also hindered the approach of Black's king. 375) White wins

Some of the most surprising and powerful solutions to endgame dilemmas are based on the diagonal power of the king. A famous problem's analysis is attributed to Richard Reti and illustrates the concept of the diagonal march, where a king moves along a diagonal to accomplish aims in two directions. 376) Reti's diagonal march

The trouble in Diagram 376 is twofold. If White's king tries to catch the a-pawn directly, 1. Ka7, Black advances the pawn and soon queens. If White instead tries to defend the f -pawn, on the surface it seems that Black's king gets there first and wins the pawn. So White can't necessarily accomplish either aim directly. But by combining ideas with a diago nal movement, White can oversee both possibilities, opting for the course that Black allows. Thus White draws with 1. Kb7 a5 (or the apawn will be caught) 2. Kc6! a4 3. Kd5!, still menacing the a-pawn. But 3...a3 could then be met by 4. Ke6, and both sides will queen. Although Black queens first, 4...a2 5. f7 al/Q 6. f8/Q, White's queen can't be won by force and the game is drawn. But let's not be ecstatic yet. Sometimes the position may look hopeful and the draw isn't there. 377) Reti's idea doesn't work

In Diagram 377, White's king is better placed than Black's king is in Diagram 376. By not being on a3, the king is not in a position to he queen-checked after promotion at cl. Thus White to move wins perforce with 1. h5 Kf3 2. KbI! (2. h6? fails to 2...Ke2). If 2...Ke2 or 2...Ke3, then 3. Kc2 stops Black and the h-pawn queens.

378) Reti's idea against three pawns

When Reti's idea works the outcome can seem magical. In Diagram 378 White's king is facing off against three connected pawns. If the g7-pawn (the back pawn) is captured, one might think the for hpawn (the front pawns) can't be safely captured. But the old expression "you can't take the back pawn and still catch the front pawn" falters against the enchantment of Reti's diagonal march. White draws after 1. Kxg7! f5 (or I...h5, which doesn't affect the result) 2. Kf6 f4 3. Ke7! f2 4. c7, and both sides will queen, with Black's remaining h-pawn being irrelevant, if not indefensible. 379) White to play loses

Note how crucial king placement can be in Diagram 379. If White tries to draw with I. c7, Black wins with I...fl/Q, since 2. c8/Q loses to 2...Qh3+, a winning skewer. (White wouldn't he able to save the game by playing 2. Kd7, since 2...Qf5+ 3. Kd8 Kb7 stops the cpawn for good.) But if Black's king were on a6 to start with, instead of being on a7, queening on c8 would also be check, and White would have time to avoid a losing skewer.

380) White saves the game by faking

In Diagram 380 it's clear that White's king is outside the h-pawn's square. A tempo must be gained if the pawn is to be stopped. White begins with 1. Kb4 (or I. c6 could also be played), and Black continues with I...h5. Then comes the diversion, 2. c6! (if White had started with I. c6, then 2. Kb4 would be played). Either White will save the c-pawn and queen, or lose the c-pawn but overtake Black's h-pawn. Play might now continue 2...Kb6 (or 2...h4 3. Kc5 h3 4. Kd6 h2 5. c7) 3. Kc4 h4 (if 3...Kxc6, then 4. Kd4 or 4. Kd3 gets back in time) 4. Kd5! h3 5. Kd6 h2 6. c7 hl/Q 7. c8/Q. Thus White saves the game by faking one thing to be able to do another. 381) Faking promo to get back

With a diagonal king maneuver, White also relies on the possibility of doing one thing to bring about the implementation of another in Diagram 381. Unable to catch the a-pawn directly, White begins by manufacturing threats, 1. Kg5! a5 2. Kf6! (threatening 3. Kg7) 2...Kf8 3. Ke5!, and the a-pawn will be caught, with the game being drawn.

382) The feint

Sometimes, to save a game, it's not just a matter of threatening something else: the king may actually have to move away from the real target before getting back to catch it. In Diagram 382, White can't catch the f-pawn directly. It's too fast. Nor can White guarantee the apawn's defense. But by faking toward the a-pawn, pretending to make it a threat (a tactic called the feint), White gains time needed to come back and nullify the f-pawn. Thus 1. Kc7! f5 2. Kb6! Kxa4 (otherwise, 3. a5) 3. Kc5 and the f-pawn will be caught. 383) Moving away to get closer

A similar save is seen in Diagram 383. To catch the b-pawn, White moves the king the other way, toward the g-pawn: 1. Ke7! b5 2. g4! Kf4 3. Kf6!, and however Black plays, it's only a draw. In many of these problems there is a critical diagonal of retreat that Ieads to the promotion square. If that diagonal becomes blocked, it won't matter even if the defending king gets inside the quadrangle of

the pawn. In Diagram 384 the critical diagonal of retreat is a2-g8. Black's king is already on that diagonal, but the e6-pawn gets in the way, and the g-pawn can queen without interference: 1. g4 Kc4 2. g5 Kd5 3. g6 and wins. 384) The critical diagonal of retreat is blocked

If the critical diagonal of retreat isn't blocked to start with, perhaps it can be dammed up by an obstructive sacrifice. In Diagram 385, the immediate 1. e5! wins, since 1...dxe5 2. h4 ensures the hpawn's eventual promotion. Nor does 2...e4 3. h5 e3 4. Kdl pose a problem (though, if White falls asleep, 4. h6?? loses to 4...e2). On occasion, it's not a matter of blocking one diagonal of retreat. Rather it may come down to blocking several. In Diagram 386 White is able to win with 1. f6! (blocking the d8-h4 diagonal) I...gxf6 2. Kxg2! (but not 2. a4? bxa3 3. bxa3 Kg3! 4. a4 h5 5. a5 h4 6. a6 h3 7. a7 h2 mate!) 2...Kg4 3. a4 bxa3 4. bxa3 Kf5 5. a4 Ke5, and now, 6. d6! (closing the b8-h2 diagonal) 6...cxd6 7. c6! (closing the a8-h I diagonal) 7...dxc6 8. a5!, and the a-pawn can't be stopped. 385) Sacking to block the diagonal

386) Sacking to obstruct three diagonals of retreat

387) ('hanging the critical diagonal of retreat

This motif is seen to advantage in a famous ending between Emanuel Lasker and Siegbert Tarrasch (Diagram 387). If Lasker had tried to get his king back in time directly, 1. Kf6 c4 2. bxc4 bxc4 3. Ke5, he would have lost out to the obstructive sacrifice, 3...c3! 4. bxc3 a4. But by a timely shift with a threat, 1. Kg6!, Lasker changes the critical diagonal of retreat (from al-h8 to hl-h7) and his king gets hack in time. In the actual game Tarrasch had to fight for a draw. Finally, as we come to the end of this section, 1 offer you the fifty-fifty problem. It's so-called because, in Diagram 388, White to play has but two moves, one of which draws and one of which loses. Take your pick. If we play instinctively, moving the white king closer to the pawn complex, we lose: 1. Kc87 Kc6 2. Kb8 (2. Kd8 doesn't help) 2...Kd5 3. Kc7 Ke4 4. Kd6 Kf3 5. Ke5 Kg2 6. Kf4 Kxh2 7. Kf3 KgI and wins. But this is one of those strange cases where the counterintuitive comes into play. By moving further away from the complex, 1. Ka8!, the king is really moving closer to it. Thus I...Kc6 2. Ka7! Kd5 3. Kb6 Ke4 4. Kc5 Kf3 5. Kd4 Kg2 6. Kea Kxh2 7. Kf2!, and the position is drawn. In truth, by moving the king to a8 initially, White wasn't moving away from the complex; rather, White was seeking the critical diagonal of retreat. By moving to a8, the white king is actually closer to this worn hole (the a7-gl diagonal) than it would be at c8. If one thinks about it, there's no fifty-fifty about it. 388) The fifty-fifty problem

Pieces in combat with a dangerous pawn We now come to a section having to do with how each type of piece confronts a dangerous advanced enemy pawn. Many endgames are the outcomes of pawn races. Apawn race is just that, an attempt to queen before the other side does. In pawn races where both sides actually queen, the hope is to be in position to exploit the situation afterward. One result of a pawn race might be that a particular side queens sufficiently ahead of the other. Then, the new queen must cope with the enemy pawn, trying to stop it from promoting. In other cases, a queen might have to stop an enemy pawn without a pawn race having taken place at all. Diagram 389 shows a typical situation of a queen trying to stop a center pawn, already on its seventh rank, and supported by its king. There is a definite technique to win such an ending, even when the friendly king is far away. By giving a precise series of checks and threats, the queen can force the defending king in front of its own pawn, so that the pawn can't immediately promote. This gives the friendly king one move to get a little closer. The process is then repeated, checks and threats, once again forcing the opposing king to obstruct its pawn. And once again the friendly king has another free tempo to approach even closer. Eventually, enough time and moves are gained so that the friendly king can join the queen, either winning the pawn, and/or mating shortly thereafter. In Diagram 389 the process begins with a check, 1. Qe4+. After I...Kf2, White has 2. Qd3!, which is getting on top of the pawn. Black defends the pawn, 2...Kel, but 3. Qe3+ then forces the black king in front of the pawn, 3...Kd1, so that for one move the pawn isn't able to advance. White uses that tempo to bring the king closer, 4. Kb5. The process then starts over. After 4...Kc2 White pins the pawn with 5. Qe2. If 5...Kc3, then 6. Qdl puts an end to Black's counterthreats, so Black must try 5...Kell, getting out of the pin and hoping to queen. There follows 6. Qc4+ Kb2 (threatening to promote) 7. Qd3, getting on top of the pawn and forcing 7...Kc1; after 8. Qc3+ Kdl (forced), White has gained another free move, which can be used to bring the king even closer, 9. Kc4. At that point the king is so close several ideas will do. Play might reasonably conclude 9...Ke2 10. Qd3+ Kel 11. Qe3+ Kdl 12. Kc3 Kcl 13. Qxd2+ Kbl 14. Qb2 mate. 389) Queen vs. center pawn on seventh

Proceeding against an advanced knightpawn is even easier, since the defending king has fewer available squares. In Diagram 390 Black to play wins with 1...Qf6+ (forcing a block of g8) 2. Kg8 (and now Black has time for a king move) 2...Kg5 3. Kh7 (on 3. Kh8 the pawn remains pinned and Black can bring the king even closer) 3...Qh6+ 4. Kg8 (once again, the pawn is obstructed) 4...Kf6 5. Kf8 Qxg7+ 6. Ke8 Qe7 mate. 390) Queen vs. knight-pawn on seventh rank

Diagram 391 shows the problem with a rook-pawn on the seventh rank: stalemate may arise before the friendly king has time to get close enough. After I...Qg6+ 2. Kh8 Black doesn't have time to bring the king closer because of the looming stalemate. No progress can be made and the game is drawn. 391) Queen vs. rook-pawn on seventh rank

To defeat the rook-pawn the queen needs the help of the friendly king (it has to be closer). Or, in some cases, with a pawn or two more on the board, a certain tactical trick might be possible. I once had the position of Diagram 392 in a blindfold exhibition I gave at Rutgers University in the 1970s. I had just won the pawn race and with an extra move was able to continue 1. Qb4+ Kc2 2. Qa3 (getting on top of the pawn) 2...Kb1 3. Qb3+ Kal. White would ordinarily have to worry about the stalemate, but Black has an additional pawn, and the extra tempo it affords allows White to win, 4. Qc2! h2 5. Qc1 mate. 392) More is less

Occasionally the attacking king is close enough so that the pawn can promote and the game's still lost, as in Diagram 393. If 1. a8/Q+, Black has 2. Kb6, and White doesn't have a good move. 393) White to play loses

394) A rook can be as good as a queen

With the king and queen stumbling over each other in the corner it's not surprising how little can be done to fight off the constriction. In Diagram 394 White has just queened with check, but after l ...Kg6, White cannot ward off the menacing rook check coming at a8. Of course, sometimes the attacking king doesn't have to be in close proximity. It can be far away, and, with a little magic, might be able to perform wonders. In Diagram 395 the placement of the friendly king seemingly allows White to overcome the limitations of space and time: 1. Kb6! Kbl 2. Kc5+ Kc2 3. Qe5 Kbl 4. Qel+ Kb2 5. Qd2+ Kb 1; and now, 6. Kb4 (or 6. Kc4) 6...al/Q 7. Kb3. The best Black has is 7...Qe3+, hoping for 8. Qxc3?'?, but there's always 8. Kxc3, and that's that. Rook-pawns aren't the only pawns that can pose troubles in these endings. Bishoppawns can provide obstacles too. In Diagram 396 White can at once play 1. Qg3+. If I...KfI, the pawn is blocked and White has time to move the king to c5. But Black doesn't have to block the pawn. With I ...Kh I ! it's evident the pawn can't he captured without giving stalemate. The position is drawn.

395) Far away can be close enough

396) Bishop-pawns: a nuisance or a boon

397) Take with check

Diagram 397 otters an exception. True, White can't capture the pawn right away because of the stalemate. But by interposing I. Qfl+, after I...Kh2, White gets to capture the pawn with check, 2. Qxf2+, avoiding stalemate, and soon mating (2...Kh3 3. QgI, or 2...Kh1 3. Qe2). As a rule of thumb usually trj, to take with check, or fulfill an action of any kind with check, since it tends to maintain the initiative and keep the move. By taking with check the next free move (where you are not required to reply to your opponent) is likely to be yours. But the defending king can't always get to the corner for stalemate hope. Sometimes it's cut of), and the attacking king may he very close, ready to lend assistance. 398) White mates in two moves

In Diagram 398 it's quite close, and this is good enough to force mate in two moves. Since the position is one of those where the defender has very few possibilities, it may he helpful to work backward in trying to solve it. If it were Black's turn, Black would have two moves, Kfl -e l and KfI e2. I f the black king were suddenly on el, it would he mate if White's queen could he on dl. With that in mind, and also with the idea of preventing KfI -e2, White starts with 1. Qg4!, and that mates next

move. 399) Black to play draws

Bishop-pawns can he troublesome even when not as far advanced as the seventh rank. In Diagram 399 Black's pawn is on its fifth rank. But with the move the pawn can advance to a draw. After I...c3 White doesn't have a check. Be cause of the poor placement of the white king and queen, the pawn is guaranteed getting to c2. Thereafter the black king will head toward al, and the position is drawn. A sample continuation might be 2. Qe4 c2 3. Qd4+ Ke2 4. Qc3 Kd 1 5. Qd3+ Kc 16. Kd6 Kb 1, and Black holds. Give White the move, however, with the ability to prevent the pawn from getting to its seventh rank, and it's quite another matter. 400) White to move wins

In Diagram 400 White wins with 1. Qd4+ Kc2 2. Kc6 Kb3 3. Qd3 Kb2 (Black could try 3...Ka4, hoping for 4. Qxc3?? stalemate, but 4. Qc2+, among others, wins easily enough) 4. Qb5+ Ka2 5.

Qc4+ (getting on top of the pawn) 5...Kb2 6. Qb4+ Kc2 7. Kd5 (ever closer) 7...Kd2 8. Qd4+ Kc2 9. Kc4, and the pawn will be stopped. 401) Rook-pawn on its sixth rank loses

A rook-pawn on its sixth rank has similar trouble. Unless it reaches its seventh rank the queen has little trouble containing it. In Diagram 401 White to play wins with 1. Qd3+ (or 1. Kb6 a2 2. Qc 1) 1...Kb2 2. Qb5+ Kc2 3. Qa4+ (getting on top of the pawn) 3...Kb2 4. Qb4+ Ka2 5. Kb6, and now the pawn is lost next move. Time to move ahead to rooks.

Rooks can be fun, too So much for a queen stopping an advanced pawn. Let's see how a rook can do in comparable situations. In Diagram 402 Black to play has an easy win. It begins with a fifth rank cutoff (the fifth rank from the rook's perspective), 1...Rd4!. This prevents the participation of the white king. If White then does nothing, Black's king maneuvers to get in front the pawn, which would then shortly be lost. So White must try 2. a5, and after 2...Kf3, White can continue 3. a6. Now the rook attacks the pawn along the rank, 3...Rd6, compelling 4. a7. The pawn is then stopped and lost by placing the rook behind the pawn on the file, 4...Ra6. 402) Fifth rank cutoff wins

403) White to play wins

Without such a debilitating cutoff, getting the friendly king back in time can be crucial. In Diagram 403 White wastes no time positioning the king: 1. Kd5 Kf4 2. Kd4 Kf3 3. Kd3 (immediately moving the king back toward the pawn) 3...g3 4. Rf7+ (rooks often work best from behind) 4...Kg2 5. Keg Kh2 6. Kf3 g2 7. Rh7+ Kgl 8. Rg7 KhI. And now, one last trick, if 9. Rxg2, the game is over by stalemate. But White has a practical play, 9. Kf2, delaying capture, when 9...Kh2 10. Rh7 is mate. 404) Black mates in two moves

White is hoping for stalemate in Diagram 404 (by I...Kc7??). But why fool around, when the simple 1...Rdl (or moving the rook to any square from d 1h 1) mates next? Actually, if you have any doubt, and are nervous (say, you're in time trouble), moving the rook to h 1 tends to be practically wiser, the thinking being that the further away the rook is, the better and safer. After all, rooks are long range pieces and function admirably from far away. On a giant square board, with files and ranks reaching out to the end of the universe, a rook could be that far away from a king, almost at Star's End, in complete safety, and still be able to give check. Think about it. 405) Two ways to win

A discovery helps win the pawn in Diagram 405: 1. Ka3+ Kal 2. Rh8 Kbl 3. Rh1+ Kc2 4. Kxa2. Note that if White were to play 1. Rh8 initially, Black could try to complicate matters by promoting to a knight, giving check, l ...al/N+. But after 2. Kc3 Ka2 (2...Kc 1 allows 3. Rh I mate) 3. Rb8 wins the knight (and the game very quickly after that), since 3...Ka3 is met by 4. Ra8 mate. 406) How can Black stop the pawn?

Time for a tactical aside. In Diagram 406 White has a pawn ready to queen, Black's king can't get over to defend, and the presence of an extra rook for Black doesn't seem very consoling. But the rook enables Black to save the day, if offered as a sacrifice, 1...Rh4!. Obviously, White takes it, 2. Kxh4, drawing the king onto a checkable square, but then Black has the space-clearing sac, 2...g5+!, clearing g7 with a gain of time. After 3. KxgS Kg7, the table is turned, and it's Black who's winning. 407) Take a meaningful opposition

In Diagram 407, from a problem analyzed by Pal Benko on a theme of Richard Reti, it's a matter of making Black commit, while also making sure that, later on, time won't be lost if the rook's attacked by the black king. Right now the rook's on a bad square, being assailable by the black king from f3 or h3. With 1. Rgl!, however, anticipating an eventual, time-gaining attack by the enemy king at either f3 or h3, White ensures the rook's safety at a later critical moment, while getting a meaningful opposition and that leads to a win. If I...Kh4, then 2. Kf6 (going to the side where the black king isn't) 2...g3 3. Kf5 Kh3 4. Kf4 g2 5. Kf3, and the pawn is lost. If instead Black goes to the other side, I...Kf4, then White's king in turn switches the side of approach, 2. Kh6 KO 3. Kh5 g3 4. Kh4 g2 5. Kh3, and the pawn falls here too. The moral is, it's good to look ahead (as White does in the above problem, seeing that the rook might later be endangered with loss of tempo). When facing off against a dangerous pawn it's not always a picnic for the rook. In Diagram 408 Black to play wins with 1...b2, and White can't prevent the pawn from queening. If 2. Ra3+, for example, there would follow 2...Kc4 (but not 3. Kc2? Ra2, drawing) 3. Ra4+ Kc5 (and not 3. Kb5?, which allows 4. Rb8) 4. Ra5+ Kc6 (here, 4...Kb6 also works, since 5. Ra8 is met by 5...Kb7) 5. Ra6+ Kb7, and the pawn queens. 408) Badly placed rook

A version of Saavedra's position, named after the composer, is shown in Diagram 409. Black to play wins thusly: 1...f2 2. Re3+ Kg4 (on 2...Kf4 there follows 3. Re8, with a draw in hand; while 2...Kg2 3. Re2 also draws) 3. Re4+ Kg5 4. ReS+ Kg6 5. Re6+ Kf7, and it seems White is out of tricks. Yet he's not, 6. Re5!, since 6...fl/Q? allows 7. Rf5+! Qxf3 stalemate! But there's always the possibility of underpromotion. The surprising 6...f1/R! leads to a brilliant win. It avoids the stalemate shot and menaces mate at hl. The only way to stop that mate is by 7. RhS, when Black has the devilish 7...Kg6, threatening the rook and mate at f8. 409) Saavedra's idea

Rooks and connected passed pawns Rooks often have to deal with connected passed pawns. If there are no intervening threats and tactics, connected passed pawns, having reached their sixth rank in safety, can usually get the better of a lone rook. In Diagram 410 Black to play wins perforce, 1...d3, when 2. Kf5 e2 3. Rgl d2 4. Ke4 el/Q+ 5. Rxel dxel/Q+ is decisive.

410) Connected pawns on sixth rank win

411) Get behind the most advanced pawn

In Diagram 411, however, the pawns have not yet reached their sixth rank as a team. Black can frustrate this and forge a win with the stultifying, 1...Re2!, getting behind the most advanced pawn. By being positioned behind the most advanced pawn, the rook stops either pawn from moving safely. After the obligatory 2. Kgl, Black's rook attacks the back-pawn, 2...Re5!. After 3. Kf2 RxdS, the epawn is soon captured as well. To be sure, a rook can often stop the advance of connected pawns by being placed behind the most advanced pawn. A practical example (Diagram 412) of this is a position from the twenty-first and last game of the Spassky-Fischer Match, played in Reykjavik, Iceland, in 1972. With the black pieces, and the move, Fischer played I...Ra2 (which was really Black's 39th move), getting behind White's advanced rookpawn and thereby stopping the connected pawn complex from moving. After 2. Be6 h5, Spassky sealed 3. Bd7, but resigned before resuming the game, and Fischer was the new champion.

412) Spassky-Fischer, Reykjavik 1972

A frontal rook attack doesn't always work as well as one from behind. But in Diagram 413 it does the job. With 1...Re7! 2. Kf3 Kd3 3. Kf4 Kd4 4. Kf5 KxdS the strength of the connected pawns has been eviscerated. 413) Frontal attack might work

414) The correct advance draws

As the pawns are further up the hoard, the situation is typically more immediate. In Diagram 414, for instance, Black's connected pawns have already reached their sixth and seventh ranks. It's still easy to lose, as I...b2? 2. Kxc2 illustrates. But Black can hold once it's realized that it's the result that counts, not how many pawns are present in the final position. After l...cl/Q! 2. Rxcl, Black is able to advance the b-pawn with a threat, so that there isn't time for the white king to get closer to the promotion square. Stalemate follows from 2. b2 M 3. Ka I! R02. Diagram 415 offers a spectacular case, where the pawns have already become deadly, both being on the seventh rank, about to queen. Nonetheless, there's a saving grace, and that's to threaten perpetual mate, due to the cooperative positioning ofthe black king and rook and the had placement of the white king. With 1...Rh6+ 2. Kgl Rg6+ 3. Kf1 Rh6 (menacing mate) 4. Kel Ke3 5. Kdl Kd3 6. Kcl Kc3 7. Kbl Black holds the draw by aping the same threats on the other side. Thus 7...Rb6+ 8. Ka2 Ra6+ 9. Kbl Rb6+ 10. Kcl Rh6 starts a new cycle, and White can make no progress. 415) Black has perpetual threats

416) Black to play draws

A similar situation exists in Diagram 416. Black can hold with perpetual threats, beginning with 1...Kf5, eyeing mate at hl. If 2. Kh4, then 2...Kf4 continues the threats, which become even more patent after 3. Kh3 Kf3 4. Kh2 Ra2+ 5. Kgl Ral+. And, of course, not 2. Kh6 because of 2...Rhl mate. 417) White fashions perpetual attack

Rounding off this section of drawing by perpetual attack is Diagram 417, which represents a problem analyzed by H. Weenik in 1927. Although Black has a mass of three dangerous pawns, with two pawns connected and on their seventh rank, the nature of the position is such that White can hold by perpetual attack beginning with 1. Kd7!. This defends the rook barrier, closing the door, and no matter which black pawn queens, the white rook can check endlessly, using the squares e8, e7, and e6 with full confidence. 418) Black to play draws

A comparable idea is seen in Diagram 418. Black can hold the draw with I...Rh4!. However White queens, Black's rook can check without interruption along its fifth rank, and the white king has no escape. 419) White to play draws

It's a fact that rooks don't always have to contend with connected pawns on the seventh rank. Occasionally, they must hold their own against split pawns on the seventh rank. Diagram 419 offers an instance in point. Here Black threatens to break the blockade with the king (Kd3-c2), so White must act with dispatch. White does so by 1. Rgl!. Now I...Kc2 is answered by taking the g pawn with check, and that reduces to a draw. But Black does have 1...Ke3, menacing to break the blockade on the other side by going to Q. White still keeps it together, however, shifting back the other way, 2. Rbl!, and Black can make no progress. The position is drawn. The section is over.

Minor pieces against pawns Unlike the queen or rook, unless additional units are involved, the bishop does not constitute a mating force when combined with its king. Typically, against a dangerous enemy pawn, the best the bishop can do is sacrifice itself to stop the pawn. In Diagram 420, for example, Black to play has I...Be5+. The bishop then has the ability thereafter to capture the pawn if it's advanced to the eighth rank. So the position would be drawn. But if it's White's turn, White has 1. Kd6, preventing the bishop from going to e5. Black could try 1...BeI, hoping to give a skewer check, but a further approach of the white king, 2. Ke5, once again threatens to win. Fortunately for Black, 2...Kg3 saves the day, since 3. b8/Q is dealt with by 4. Bf4+ and 5. Bxb8, a draw by insufficient mating material being the result. 420) White to play though Black draws

421) Discovered mate

To be sure, if the king and pawn are positioned badly, the bishop and king may be able to win. In Diagram 421 White has 1. Kf2 mate, but don't count on this happening every day. 422) Black mates in two moves

Here is another lighter moment, as reflected in Diagram 422. A comparable mate to that of Diagram 421, though arrived at very differently, occurs after the surprising, 1...Ng2!. This leaves Black but one move, 2. Bxg2, and that results in a kind of self-mate, 2...Bxg2 mate. In Diagram 423, it seems that White has plenty of time to deal with the dangerous h-pawn. Black could try to stop the bishop from getting to d6 with Ke4-d5, but White would then shift focus and play Ba3-cl, planning to move to P. The whole defensive edifice is shaken after I...b4+!. If 2. Kxb4, then the bishop's diagonal route to d6 is obstructed, and the h-pawn wins with direct advance. Ifinstead White takes with the bishop, 2. Bxb4, then 2...Kd5 guards A. White could still try to get on a defensive diagonal with 3. Ba5, hoping to play to c7, but Black thwarts all that with 3...Kc6, and the h-pawn will queen.

423) Sacking for interference

It's often surprising how suddenly deadly tactics can emerge. In Diagram 424, stopping the a-pawn appears to be impossible. Nevertheless, the repositioning I...Bgl! wins the pawn, since White doesn't have time for 2. a8/Q??, which encounters 2...Be3 mate! 424) Black to play wins

Why should bishops have all the joy? Knights can cope with dangerously advanced pawns too. In Diagram 425 Black to play draws with I...Ne8. For example, if 2. K17, the knight holds by moving to c7 or even d6, since 2...Nd6+ 3. Ke6 Ne8 4. Kd7 Nf6+ (or 4...Ng7) gets White nowhere, and the other way (2...Nc7) leads to F.rehwon. The first rule of thumb, therefore, is that the knight can hold the draw without immediate help if it safely occupies any square in front of the pawn, with one exception: a rook-pawn on the seventh rank, when the situation then depends on the placement of the kings.

425) Black to play draws

When, coming from one side, the knight is unable to occupy a square in the pawn's path directly, sometimes it can reposition itself effectively on the pawn's other side. And when it can't do that, it might still be able to cope with the pawn by allowing it to promote and then winning the queen (for a knight) with a forking check. 426) Black to play draws

427) Black to play draws

In Diagram 426, Black starts with 1...Nd7+, and White can counter aggressively with either Kf8-e8 or Kf8-e7. If 2. Ke8, Black shifts to the other side of the bishop-pawn, 2...Nf6+ 3. Kd8 Nh7, and the position is held. If instead White plays 2. Ke7, the position becomes Diagram 427. Here Black draws with 2...Ne5!, when 3. f8/Q is met by the forking check, 3...Ng6+, and that draws. Thus our second rule of thumb says that sometimes the knight can draw by attacking the pawn, such that, if the pawn advances to a queen, the knight then has a forking check. Now bishop-pawns and center-pawns can be handled similarly, since, against each kind of threat, it's easy enough for a defending knight to shift from one side to the other. But knightpawns, as they do in so many other endgames, pose their own set of problems. The key difficulty here being that, as the knight approaches the board's edge, it runs out of possible moves, so it's defensive tactics are reduced accordingly. 428) Black to play loses

In Diagram 428, therefore, Black to play cannot draw, since 1...Ne7+ 2. Kf8 (but not 2. Kt'1? Nf5! 3. g8/Q Nh6+) 2...Ng6+ 3. Ke8! leaves Black with nothing to do, and the pawn will queen shortly.

429) Each knight is three moves away from giving check

430) Each knight is one move away from giving check

Visual cues and knight distances Note that in Diagram 428, after 3. Keg, the white king is separated from the knight at g6 by one diagonal square. In comparable situations, it takes a knight three moves to maneuver into position to check the enemy king. This is good to know, knowing that your king isn't capable of being checked for three moves. Often this visual mnemonic, and comparable ones, can help in the analysis of more difficult endings. Picturing the situation enables you to reply more instinctively in situations when, for instance, you're short of time. Also, by having such shortcuts at your fingertips, it becomes possible to shorten analysis to a more manageable length. Thus, in Diagram 429, each knight is three moves away from checking the enemy king (assuming the enemy king doesn't move); in Diagrams 430 and 431 each knight is one move away; in Diagram 432 each knight is two moves away; in Diagram 433 each knight is one move away; and in Diagram 434

each knight is two moves away from checking the enemy king. 431) Each knight is one move away from giving check

432) Each knight is two moves away from giving check

433) Each knight is one move away from giving check

434) Each knight is two moves away from giving check

Question: How many knights can you place on a chessboard so that no knight can capture any other knight? Answer: thirty-two. Simply put them all on squares of the same color, which is the ultimate color rule. Diagram 429, where none of the knights can check the black king for three moves, has a helpful application for Diagram 435, which shows a position from a game between V. Smyslov and M. Illescas Cordoba played at Palma de Mallorca in 1989. In the position, White is in check. Playing the white king to the wrong square allows Black to sac his knight and draw. For example, if 1. KdS, then 1...Nc3+. If instead 1. Kc4, then 1...Nd6+. On 1. Kb6, Black can play either I...Nc3 or 1...Nd6, with a draw. White has several other possibilities, but by playing 1. Kc6! it becomes clear that Black's knight will not be able to check White's king for at least three moves, and the bpawn will prove unstoppable. In the actual game, Black resigned (1-0). 435) Thinking visually

Just when a knight may seem helpless, its proper placement can establish all kinds of unexpected barriers, salvaging apparently lost situations. Consider Diagram 436. After I...Nc7! Black stops the apawn temporarily and sets up various traps around an infuriating barrier line. Both d5 and e6 are guarded directly, and d6 and d4 indirectly, since both 2. Kd6 and 2. Kd4 are hit with the fork, 2...Nb5+, winning the a-pawn. So White has to step around the barricade. After 2. Ke4 Kg3 3. Kd3 Kf4 4. Kc4 Ke5 5. Kc5 Ke6 6. Kc6 Na8 7. Kb7 Kd7 8. Kxa8, Black stalemates with either 8...Kc7 or 8...Kc8. And if 2. Kf6, then 2...Kg3 3. Ke7 Kf4 4. Kd8 Na8 5. Kc8 Ke5 6. Kb7 Kd6 7. Kxa8 Kc7 also stalemates. 436) Creating a knight barrier

A similar barrier is established in Diagram 437 with I...Ng6!. Play might then continue 2. Kc7 Kb3 (Black's king is already on a critical diagonal of retreat) 3. Kd8 Kc4 4. Keg Kd5 5. Kf7 Nh8+ 6. Kg8 Ke6 7. Kxh8 Kf7 stalemate.

If the rook-pawn hasn't yet reached its seventh rank, there's more maneuvering room and other possibilities emerge. Thus, in Diagram 438, it seems that Black must abandon control of a7, enabling the pawn to push on. But 1...Nd6! draws, since 2. a7 runs into a forking check, 2...Nc8+. Nor does it help for White to play 2. Kc6, since 2...Nc8 3. Kc7 Na7 4. Kb7 Nb5 5. Kb6 Nd6 brings us back to start, and that draws. Accordingly, it can be said that the knight holds the draw if it occupies any square on the circuit, the ring of squares going from a7-b5-d6-c8-a7. 437) Another knight barrier

There are times when a knight can save the cause even if it can't win the pawn with a forking check. Sometimes, even after promotion, the attacker's king and new queen are so poorly placed that another way to draw arises. When the knight can't get back to cope with the pawn directly, and if the enemy king is cornered, the knight may still offer a surprise weapon: perpetual threat. In Diagram 439 Black can draw with I...Nb4, allowing White to queen, 2. c8/ Q, since 2...Na6+ 3. Kati Nc7+ 4. Kb8 Na6+ will soon produce a draw by threefold repetition. 438) On the circuit

439) Saved by a perpetual

440) Dangerous rook-pawn

Back to the rook-pawn: it doesn't always have to be on the seventh rank to get the better of a knight. Even on the fifth rank it can be a monster. In Diagram 440 Black to move wins with 1...h3. If the knight moves, the pawn will queen. But if 2. Kf2, then 2...h2 queens next move. A hidden version of this tactic is contained in Diagram 441. Black to play wins with 1...Nxb2+! 2. Nxb2 a3, and once again the rook-pawn can't be stopped. In Diagram 442 another stratagem comes into play: checkmate by forced obstruction. Black to play can force White to self mate, in a sense, with I...Nf8, when 2. h7 allows 2...Ng6 mate. Question: In Practice Position #6, how does Black force a win'? Solution, page 243. 441) Driving onto a bad square

Practice Position #6

442) Black mates in two moves

443) White mates in three moves

A logically earlier version of the same theme can be seen in Diagram 443. White mates in three moves, 1. Net Kal 2. NO (forcing Black to lock in the king) 2...a2 3. NO mate. An offshoot of the same concept appears in Diagram 444. After I...Nb5+ 2. Ka8, Black uses a king move for the decisive tempo, 2...Kc8, and then corners the locked in king, 3. a7 NO mate. Some of these cornered mates are not so easy, and a careful maneuvering scheme has to be worked out. In Diagram 445 it's a matter of maneuvering to get to a comparable position to that of Diagram 444. The winning line begins with 1. Nf5 Kal 2. Nd4!. Now Black can't play 2...a2 because of the mating check at b3. So the king must block the pawn, 2...Ka2, which allows enough time for 3. Net Kal 4. Nel a2 5. NO mate. 444) Black mates in three moves

445) White mates in five moves

An even lengthier set of maneuvers are seen in Diagram 446. Not only must the knight be repositioned; the white king must also do its part. It begins with 1. Nc2+ Ka2 and now 2. Nd4!, to keep b3 guarded. After 2...Kal, the other cog in the maneuver is put into action, the white king, by 3. Kc2!, which relieves the knight's need to guard b3 and also compels Black to move the king to avoid self mate (3...a2?? 4. Nb3 mate). The sequence accordingly concludes 3...Ka2 (obstructing the a-pawn, and therefore giving White an extra tempo to maneuver) 4. Net Kal 5. NO a2 6. NO mate. That's one way to end a section. 446) White mates in six moves

Minor piece and pawn vs. minor piece At this point we're ready to move to another set of endings, where minor pieces confront each other, but one side has a single extra pawn. In Diagram 447, which is a familiar position analyzed famously by Centurini, White has a dangerous knight-pawn on the seventh rank. Black's bishop discourages it from queening, with the black king helping out by preventing White from blocking the critical b8h2 diagonal at c7. It's also to he noted that the kings stand in direct opposition. In the first part of the solution White finds a way to drive Black's bishop off the b8h2 diagonal, beginning with 1. Bh4!. Without doubt, this sacrificial offer can be turned down, and must be, but the tactic gains time to transfer White's bishop to the a7-g l diagonal. After 1...Bh2 2. Bf2 Bf4 (or to another safe place on the b8-h2 diagonal) 3. Ba7! Bh2 4. Bb8, and now Black must surrender the critical diagonal. Fortunately for Black White's bishop blocks the promotion square. This means that Black will have one free move to maneuver the bishop to another defensive diagonal, namely the short diagonal, a7h8. There follows 4...Bgl, and after 5. Bg3 (for instance) 5...Ba7, White has the deflective sacrifice 6. Bf2!, and the pawn will queen shortly. If the shortest defensive diagonal (here, a7-h8) were one square longer, the black bishop would be able to avoid the deadend and still keep b8 guarded. Alas, such a square doesn't exist and White wins. 447) White wins

In Diagram 448, with the kings standing in diagonal opposition, and White's king on the short side of the pawn, Black doesn't even have the opportunity to reposition the bishop to the shortest defensive diagonal, since a7 is already guarded by White's king. Thus I. Rg5 Bg3 2. Be3 Bh2 3. Ba7 Bg3 4. Bb8 Bf2 5. Bh2 (among others) leave Black without resource and the pawn queens.

448) White wins

In Centurini's original position (Diagram 449) the black bishop started not at g3 but h2, so White doesn't have a time-gaining offer at W. Consequently, White maneuvers for time, waiting for the black bishop to come out of its cubby hole, ripe to be sniped at. If Black offers no resistance, White wins with 1. Bh4 Bf4 2. Bt2 Bh2 3. Ba7 Bg3 4. Bb8 Bf2 5. Bf4 Ba7 6. Be3. But let's say that after 1. Bh4 Black tries a more active defense, I...Kb5, aiming the king at a6, where it can additionally guard a7. White continues 2. Bf2 Ka6 3. Bc5 (a waiting move that forces the black bishop to move and expose itself) 3...Bg3 4. Bel (looking to an eventual block at c7) 4...Kb6 (racing back to guard c7 from c6) 5. Bd8+ Kc6. We're back in the starting position, with one difference: the black bishop is exposed to capture, now being on g3 instead of h2. White would now win with 6. Bh4! (forcing Black to waste a tempo saving the bishop, instead of using it to reposition the king) 6...Bh2 7. Bf2, and we're back to the basic winning idea. 449) Centurini's position

450) Black draws

In such endings knight-pawns pose problems for the defender, since the shortest defensive diagonal consists of but two squares (rook-seven and knighteight). Rook-pawns, on the other hand, can sometimes be very good for the defender, even though a rook-pawn on the seventh rank offers only one diagonal for the defending bishop. If there is no place on the diagonal to create an obstruction, the defending bishop merely temporizes, and the position is drawn as in Diagram 450. Of course, the black king plays a key role, in that it guards b7 and prevents White from blocking the diagonal by playing Bc8-b7. 451) Black draws

In Diagram 451, instead of a knightpawn, White has a bishop-pawn, which means the shortest defensive diagonal leading to the promotion square (here, a6-c8), is just long enough. With the kings

standing in direct opposition, on the long side of the pawn, the game is drawn after 1. Bb5 Bg4 2. Ba6 Bf5 3. Bc8 Bd3 4. Bd7 Ba6 5. Bb5 Bbl 6. Bet Ke6, Black has just enough room, and time to hold, with the position being drawn. 452) Easy draw

If a bishop-pawn provides a long enough secondary defensive diagonal leading to the promotion square, a center pawn makes the defender's job even easier, there being an additional square to work with. In Diagram 452 the black bishop can stop the pawn whether on the long (d8-h4) or short (a5-d8) defensive diagonal. 453) White wins

Even with a bishop-pawn, the short defensive diagonal having three squares, the kings can still play a decisive factor. Consider Diagram 453. If White's king were on the long side of the pawn at d8 (every pawn has a long and short side, except for the rook-pawn), with the kings standing in direct

opposition, the position would be drawn. But when the attacking king is on the short side of the pawn, with the kings standing in diagonal opposition, the secondary diagonal can be blocked at knight-seven (here, b7). White will win by forcing the black bishop off the c8-h3 diagonal. For instance, on 1. Bb5 Bg4 2. Ba6 Bh3 3. Bc8 Bfl 4. Bg4 Ba6 5. 130, and White will block the diagonal at b7 on the next move, with the pawn queening shortly afterward. 454) Another easy win

Make the shortest critical defensive diagonal a little longer, by one square, and it doesn't matter. If the kings stand in diagonal opposition, as in Diagram 454, the position is lost. The attacking king, being on the pawn's short side, enables it to support a block at c7. Since the black king isn't able to help out, standing as it does in diagonal opposition to White's king, White forges ahead with 1. Bb4 Bg5 2. Ba5 Bh4 3. Bd8 Bf2 (for instance) 4. Bg5 (or 4. Bh4) 4...Bb6 5. Bf4 Ba5 6. Bel, blocking the promotion square (d8) and winning. 455) Drawn

From Diagram 454, shift the defending king over to the short side of the pawn, with the kings then standing in direct opposition and the position becomes Diagram 455. This setup is drawn, since White has no safe way to offer a block at c7. Black's king guards that square and will join forces with its bishop when the time becomes necessary. A sample variation is 1. Bb4 Bg5 2. Ba5 Bh4 3. Bd8 Bf2 4. Bg5 Bb6 5. Be3 13c7 (or 5. Ba5), and Black holds. 456) White wins

But with a bishop-pawn instead of an adjacent center pawn, and the kings standing in direct opposition on the short side of the pawn, the superior side wins with a partial zugzwang (Diagram 456). For example, after 1. Bh5 Bf5 2. Bf3 Bh3 3. Bbl Bg4 4. Bc8 Bf3 5. Bg4 Bbl 6. Bet, Black doesn't have a good move. 457) Both players want to move

Let's move off the seventh rank and look at some situations where the pawn isn't that far advanced. Diagram 457 offers a crucial position where each player wants to move. If it's White's turn, the block 1. Bc7 ensures that the pawn will queen. But if it's Black's move a rear attack on the pawn by the defending king, I...Kc4!, stops White's aggression. White can't then afford to trade bish ops on c7 because the pawn will hang afterward. Meanwhile, there are two diagonals that go through the square h6, which is the place the pawn needs to get to next. There's the shorter one, a5d8, as well as the longer one, a7-g 1. The shorter defensive diagonal turns out to be long enough, and Black's bishop can ferry back and forth, between a5 and d8, with progress being impossible. 458) White wins

Take the same basic setup, however, placing the white king on the short side, so that the kings stand in diagonal opposition, and an offer of a trade at a5 will win. Thus, in Diagram 458, 1. Ba5 forces the black bishop off the a5-d8 diagonal. After I...Bf6 2. b6 Be5 3. b7 Kc5 4. Ka7 KO 5. Ka8, and Black cannot prevent the white bishop from going through winning maneuver to h8. Even if Black went first it wouldn't matter: there would still he no way to prevent Be I -a5, breaking the blockade. 459) Deflection

Move the pawn back a rank, swap darksquare bishops for light-square ones, and we have Diagram 459. It's a win too: I. Ba4 13177 2. b5 Kc4 3. b6 Bd5 4. Ka6 Kc5 5. Ka7 Be4 6. Bd7 Bf3 7. Bc8 Be4 8. Bbl Bf5 9. Bf3 Bc8, which brings us to Diagram 460. White then wins with the simple deflection, 10. Bg4!, and the pawn will queen. In Diagram 450 we reviewed some aspects of the rook-pawn on the seventh rank. We saw that once the defending bishop and king seized control of knight-seven on the adjacent knight tile, that the draw was secured. In Diagram 461, the pawn hasn't yet reached the seventh rank. It's on the sixth rank, and that allows White an easy win: 1. Ba7 Be5 (tor example) 2. Be3 Bb8 3. Bf4. 460) Winning by deflection

461) White wins

462) White wins

Change the color of the bishops, so they travel on light-squares, put the pieces in slightly different places, and we have Diagram 462, which is a win with White to move. With 1. Bbl the pawn's safe advance is guaranteed. But Black to play can keep it together with I ...Bc4!, threatening to take the pawn. To avoid that, White has to advance, 2. a7, which is contained by 2...Bd5, and Black controls the critical a8-h I diagonal, with White having no way to offer an obstructive trade. In Diagram 463 the rook-pawn is shifted back to its fifth rank, but that doesn't stop White. With the temporizing, 1. Bc6!, seizing the diagonal leading to the promotion square, Black is left without a good move. Black's bishop must stay where it is, at c8, and if Black tries 1...Kc4, the pressure is off the a-pawn, giving White time for the interposition, 2. Bbl, and the pawn will queen. In Diagram 464 it's a matter of who moves. If Black moves first the white bishop can be driven off and Black wins: I ...Be4 2. Kd6 Bc2 3. Bf3 b3 4. Bd5 h2 5. Bat Kb4 6. Ke5 Ka3. But if White moves first a draw is achieved by a rear attack with the king, preventing a bishop trade: 1. Kd6 Bb3 (I ...Be4

2. Kc5 Bc2 3. Bxc2 Kxc2 4. Kxb4) 2. Bg4 (for instance) 2...Kb2 (or 2...Bc2 3. Be6 Bd3 4. Kc5) 3. Kc5 Ka3 4.Kb6 Bf 5. BdI Be8 6. Ka5, with a drawn position. That's enough bishops for right now. 463) White wins

464) White to move draws

We come to endings of knight and pawn vs. knight. Diagram 465 offers one useful formation to remember. Black's center pawn is on the seventh rank. Both sides have their king and knight guarding the promotion square, and obviously the defending knight is happy to give itself up for the pawn. But the attacker has a neat ploy, I...Nd3!, offering the black knight in a deflection. The knight can't be captured without allowing the pawn to queen. So White has no choice other than 2. Ndl, obstructing the pawn, which immediately fails to another deflection, 2...NeI+ (or 2...Nb4+), and Black is lost. 465) Black wins

466) Black to play draws

In Diagram 466 we encounter another practical tactical motif, which here saves the position. White's knight is unable to give a check for three moves. Black's king, guarding the promotion square, is therefore temporarily secure. But reinforcements are needed, since promotion is imminent. The resource comes from 1...Nd8+!, when the knight can't be taken without simplifying to a draw. After 2. Kf8, Black continues to fight with 2...Ne6+ 3. Kf7 (on 3. KgS Black has 3...Ke8, which draws) 3...Nd8+4. Kf6 NO 5. Kf7 Nxe7, and that's a draw. 467) Black mates or wins the knight

Even in pedestrian looking positions there can he a dash of poison. Take Diagram 467. What does White do after 1...Kg2!, assailing the out-of-the-way knight'? If White innocently answers 2. Ng4, Black has 2...Nf3 mate waiting. And if White surrenders the knight, 2. Kg5, hoping to gain Black's remaining pawn, there follows 2...Kxh2 3. Kf6 Kh3 4. Kxe5 g5, and the pawn will queen. 468) White wins

Some of the most useful confrontations to familiarize oneself with are in endings of bishop vs. knight, with one side having a single extra pawn. A standard stratagem is illustrated in Diagram 468. White to play has the simple 1. Bd5!. After 1...Ke2 the knight falls to 2. b4!, and a new queen soon follows. 469) Black wins with a corral

Diagram 469 shows another version of the corral idea. Black to play has 1...Bd4!, winning at once, since it corrals the knight. That is, the bishop guards every square to which the knight could move. So if the knight moves it's captured, with the pawn queening afterward. Diagram 470 shows another bad scene for the knight. It gets trapped by I...Bf2!, stalemating White's king, and Black's only moves lose the knight immediately. 470) Black to play wins

Black is barely surviving in Diagram 471. The knight is attacked, but it can't be taken without losing the pawn, thanks to the black king being on it. The simple 1. Be4! reduces Black to losing moves. The knight has no safe play, and Black's king can't move without releasing the attack on the pawn. Thus, 1...Kd4 permits 2. Kxf8, and the pawn will queen. 471) White to play wins

472) White to play draws

Finally, there's a glimmer of hope for the knight, and we see it in Diagram 472. The knight seems to be almost corralled, but it's not. After 1. Ne 1 it's hard for Black to attempt progress. If 1...Bf2, for example, White can keep it together with 2. Nc2 Bb6 3. Nel Bc5 4. Nc2, and Black doesn't have anything effective to do. The position is drawn. The knight does even better in Diagram 473. It winds up blocking out the bishop, 1...Nb3+, which leads to the successful advance of the pawn. In Diagram 474, the knight gets the better of the bishop: not by blocking out the bishop, but by operating the way a bishop does in a corral, by taking away important squares. This it does with 1...Nf3!, which drives off the bishop, and the pawn will soon queen. A longer instance of the battle of a knight to block out and drive off a defending bishop is shown in Diagram 475. White begins with 1. Nd6, blocking out the bishop and preparing to advance the pawn. There might fellow 1...Bg1 2. c6 13146, temporarily stopping the pawn. White next improves the position of the king, 3. Ke6 Kg2 4. Kd7. Now after 4...Kf3 the direct attack 5. Nc4 drives off the bishop. The knight guards two key squares, a5 and b6; while the king guards the other two, c7 and d8. White soon queens. 473) Black wins

474) Black to play wins

475) White to play wins

But let's be fair. Bishops can corral knights, but sometimes knights can do a number on bishops. In Diagram 476 Black's knight uses a time-gaining check to shift to the other side of the board, 1...Nd4+, and no matter how White answers, the bishop falls to 2...Nf3. The team of connected pawns and minor piece with careful play usually get the better of a lone minor piece, but there are some useful-to-know exceptions. This brings us to another endgame generalization. Obviously, in minor piece and pawn vs. minor piece endings, one draws by sacrificing the piece for the remaining pawn. But in endings with two extra pawns for one side, the defender can't necessarily offer such a sac, since another pawn remains. 476) Black wins the bishop

Yet on occasion the lone piece might be sacrificed for just one of the pawns if the resulting situation is drawn positionally. In Diagram 477 Black can eviscerate the white pawns before they become too dangerous by 1...Ba5!. If the bishop is captured, 2. bxa5, Black has a positional draw, since White won't be able to force Black's king out of the corner. And if the bishop isn't captured, since the b-

pawn is pinned, it will be taken by the bishop next move, once again simplifying to a positional draw. 477) Black to play draws

(478) Black to play draws

479) White to play draws

In Diagram 478 we see a different way such endings can be drawn, when the players have bishops of opposite colors. It's often possible to establish control of the squares the pawns must pass over, with the defending king and bishop working together to fashion a blockade. A blockade refers to the obstruction and/or control of the pathway, preventing the pawn or pawns from advancing safely, or at all. Some units are good blockaders, some less so, with blockading ability naturally being affected by other conditions prevailing on the board. When the two defending pieces combine to create a blockade, the attacker, in bishop-ofopposite color situations, is not able to break the blockade, since the friendly bishop can't guard the same squares. Thus, the pawn or pawns can't move safely. In Diagram 478, if it were White to move, White would have 1. d5+, and the pawns would retain some dynamism. If it were Black to move, however, the blockading I...Be6! fashions a positional draw. Similarly, in Diagram 479, White to play has 1. Bc3!, when the pawns are frustrated in their movement. Moving the a-pawn will get nowhere (l...a2 2. Kb2). Otherwise, White simply temporizes with the bishop along the al-h8 diagonal. With White's bishop and king controlling b2, White is always prepared to sac the bishop for the two pawns, once the b-pawn advances. Meanwhile, Black's own bishop is helpless to help out. Such is the case with connected rook-pawns and knight-pawns. Move the pawns over a bit, creating a connected complex on the b- and c-files, with the pawns being advanced to the sixth rank, and the defender's control of the blockade squares can be broken, lifting the positional draw (Diagram 480): 1. Bf5+ Kb8 (on I...Kd8, White has a blindside attack, 2. Ka6 Bd6 3. Kb7 (guarding c7 for a second time and therefore breaking the blockade) 3...Be5 4. c7+ Bxc7 5. bxc7+, and queens next move) 2. Kc4 (coming around the other way, heading for d7) 2...Bg3 3. Kd5 Bf4 4. Ke6 Kc8 (if 4...Bg3, then 5. Kd7) 5. Ke7+ Kb8 6. Kd7 Bg3 7. c7+ (1-0). 480) White to play wins

481) Black draws

In Diagram 481 White has connected center pawns and they're stationed back on the fifth rank. Black's bishop is well placed at b8, restricting the movement of the white king, which can't get over to c6 (in order to support the d-pawn's advance) without leaving the a-pawn hanging. Accordingly, the position is drawn. Place the black bishop along the a3-f8 diagonal, however, and the conditions could change significantly, as in Diagram 482. While Black does guard d6 twice, White's e-pawn remains unthreatened, which frees the white king to meander toward c6 to break the blockade on d6. White therefore wins with 1. Kc4 Ba3 2. Kb5 Ke8 (if 2...Bb2 then 3. d6+ Ke8 4. e6) 3. Kc6 Bbl (might as well try something) 4. e6 Bc3 (for instance) 5. d6 Bf6 6. Kd5 (on 6.Kc7 Black has 6...Be5) 6...Bh4 7. Ke4 Kd8 8. Kf5 (aiming to get in at t7) 8...Bg3 9. e7+ Kd7 10. Kf6+. Let's get back to bishops of the same color, taking a look at a situation where the pawns aren't connected but split. In Diagram 483 White has an easy enough win.

482) White wins

483) Fischer-Keres, Zurich 1959

The position comes from a game played between Bobby Fischer and Paul Keres at Zurich in 1959. Keres resigned in the diagram, but do you know how to win it'? The win is not achieved by pushing the f-pawn immediately, 1. f7+?, since after the f-pawn is captured White is stuck with a rook-pawn and can't win. The right method consists in maneuvering the white king to e7, similar to the maneuvers considered in previous examples, so that the king, too, guards f7. Thereafter, a deflective sacrifice simply wins. A sample line is 1. Kf4 (moving on the dark squares avoids checks) 1...Bb3 2. Ke5 Ba2 3. Kd6 Bb3 (and not 4...Kf8 because of 5. h7) 4. Ke7; and now, after 4...Ba2, White wins with 5. Bf7+ Bxf7 6. h7+ Kxh7 7. Kxf7. The bad bishop Before leaving minor pieces for good I'd like to cover one more idea, and that concerns the bad bishop. Here it features bishops of the same color, one for Black and one for White. One side has a

bad bishop if it's mobility is severely restricted by its own pawns, usually fixed and obstructed pawns at that. To be sure, any ending with a bishop on the board could show a bad bishop. Sometimes a knight can be opposed to a bishop, and the knight can have a field day jumping over the obstacles the bishop has to contend with. 484) White to move must lose a pawn

485) Averbakh's bad bishop problem

Consider Diagram 484. Here White has a bad bishop in that its own pawns limit its mobility. In fact, White to move must drop a pawn. If 1. Kf3, then I ...Kd4; if 1. Kd3, then I...Kf4. And if the white bishop moves instead, one of White's pawns must hang. Perhaps the idea is better illustrated by a famous position analyzed by Averbakh and others (Diagram 485). In the position, Black to move would be in a generalized zugzwang, if we use the term loosely. That is, any move Black plays would lose at least a pawn, due to the black bishop's obstructed status

and the inferior placement of Black's king. But in the diagram it's White to move, so it's a matter of transferring the move to Black in the same position. The winning idea can be achieved several ways, but one line begins with I. Be2. Now Black has a choice. Black can play I...Beg or I ...Bg6.On I...Bg6 White continues with 2. Bd3 (holding the black bishop to a diagonal where it has but two squares to play with) 2...Bh7 3. Bfl Bg6 (or 3...Bg8, which fails to 4. Be2 Bt7 5. Bf3, mission accomplished) 4. Bg2 B17 5. Bt3, and White is in the desired setup, with Black to move and having to make concessions. Thus Black tries I...Beg, and that's met by 2. Bd3 Bg6. On 2...Bd7 White wins with 3. Bc2 Bg6 (note that 3...Beg puts the bishop in a place where it can't defend h5 after 4. BdI ). After 2...Bg6 there follows 3. Bc2 Bh7 (the only good move) 4. Bb3 Bg8 (the only good move) 5. Bd I Bt7 (the only good move) 6. Bf3, and it's Black's move, and that's Black's problem.

We now move into a group of endings that have great practical significance: those of rook and pawn vs. rook. These endings have different types of consequences from those between minor pieces, since the rook is a mating weapon. Thus one cannot sac a rook for the remaining pawn since that would still leave the opponent with a mating force. In our first block of positions we shall examine situations where the pawn is on the seventh rank, defended from in front by its rook and attacked from behind by the enemy rook. In Diagram 486, generally speaking, Black's rook is better placed, since being behind the passed pawn it has more available squares on the a-file to play with than White's rook does. Along the a-file, in fact, White's rook has no moves. But if it's White's turn there's an immediate win, and some teachers refer to it as the rook trick: 1. Rh8!, when 1...Rxa7 loses to the skewer, 2. Rh7+. But Black to play doesn't have to allow that winning idea. The draw is achieved by 1...Kg7! (Diagram 487). 486) The rook trick

Thereafter Black merely moves the rook up and down the a-file to safe squares, until White's king gets to b6. At that moment the white rook is released, but it being Black's turn, Black can give a series of checks along the files, with the white king having no place to find shelter. 487) White only draws

From Diagram 487 a sample drawing line would be 1. Kb4 Ra2 (for instance) 2. Kb5 Ral 3. Kb6. After 3...Rbl+ 4. Kc5 Rcl+ 5. Kb4 Rbl+ 6. Kc3 Ral we're back at the start, a draw in hand. To show how egalitarian this idea is we offer Diagram 488. Instead of having an a-pawn on the seventh rank, White has a b-pawn on the seventh rank, and it doesn't do any better. White's king here also has no place to find shelter or escape the checks. 488) Having a b-pawn doesn't win either

489) Gaining time wins

An even more obvious winning situation than the rook trick occurs in Diagram 489. White to play checks at f8, with promotion coming up next move. Of course, if it were Black's turn to start, Black would have I...Kg7, avoiding the check threat and stopping the rook trick as well. The attacker can even have another rook-pawn on the other side of the board, and there's still no win, as in Diagram 490. White can advance the h-pawn to h6, even give check, and it won't matter because Black's king will obstruct it from V. White will still be unable to make any progress. Make the extra kingside pawn a g-pawn and that doesn't affect the result either. Black still draws, keeping the king at g7 and playing moves with the rook along the a-tile, as in Diagram 491. It doesn't even help that White's king could find shelter from checks along the ranks by using the g-pawn as a shield. White still can't make progress. 490) Only a draw

491) Still only a draw

But add an f-pawn, as in Diagram 492, and Black's defensive edifice collapses. The winning technique consists in moving the f-pawn up to f6. It doesn't even need support. Thus 1. f4 Ra5 2. f5 Ra6 3. f6+. The pawn can't be captured by either rook or king. If instead 3...Kh7, then 4. f7 will win outright. And if 3...Kf7, our old friend the rook trick pops up, 4. Rh8!, and White will win Black's rook. 492) White wins

Undeniably, rook tricks don't always win, and sometimes they can even lose, especially when one doesn't bother to look. In Diagram 493 White mustn't mechanically play 1. Rh8??, expecting 2. Rxa7 Rh7+, since Black turns the tables against White's poorly placed king with 1...Rhl+, skewering White's king and rook, say 2. Kg5 Rxh8, once again in a position to stop the a-pawn and now win it shortly. But there are many surprising ways the rook trick idea can suddenly materialize. In Diagram 494 White may seem to he holding the draw, but 1...Rh1+ 2. Kxd2 (forced) 2...h2 3. Kc2 (or 3. Keg) loses

to the tricky rook, 3...Ral 4. Rxh2 Ra2+. 493) No rook trick here

You can sometimes feel a rook trick in the air, though even when you see one coming there may be very little to do about it. In Diagram 495, for example, after 1...h2!, White doesn't have much in the way of resources. Taking the pawn loses to the skewer check theme. And moving the king, say 2. Kc2, loses to the insidious, 2...RaI, menacing promotion, and essentially compelling 3. Rxh2 Ra2+. Meanwhile flank checks to the black king get nowhere fast, 2. Rh8+ Ke7 3. Rh7+ Kf8 4. Rh8+ Kg7, and White isn't any better off. 494) Converting to a rook trick

The rook trick isn't always out there on the surface. It can he hidden, as in Diagram 496. White seems to have shelter along the second rank, so I ... Rh I clearly fails to 2. Rxa2, and there's no check. But by first offering a pawn, I...e3!, White is in deep trouble, since Black is planning to take White's f-pawn

and then play a rook trick. If 2. fxe3, then 2...Rhl scores at once. Nor can White answer with 2. Kxe3, since Black can then clear at with a gain of time, 2...Rel+, followed by queening with support. 495) Black to play wins

In Diagram 497, Black to play has the inner workings of 'a rook trick but has to go about it precisely. What wouldn't work is the immediate I...RaI'?, hoping for 2. Rxh2'?, when 2...Ra3+ forces White's king onto the second rank for a skewer check. It wouldn't work because White can answer I...Ral by interposing a disruptive check, 2. Rh5+!. After Black's king retreats, say 2...Ke6, then White can follow through, 3. Rxh2, since 3...Ra3+ then doesn't force the white king onto the second rank (it can go to the fourth rank instead, avoiding a rook trick altogether). The correct approach is to take advantage of the kings being where they are at once, starting with l...Ra3+!. The right triangle check forces the white king onto the second rank, say 2. Kc2, and then 2...Ral! proves decisive. After the pawn is captured, 3. Rxh2 (flank checks to the black king will he fruitless), the rook trick 3...Ra2+ proves just as handy. The analysis of Diagram 497 introduced another significant generalization, this one concerning analysis. Whenever you analyze a complicated line with ramifications, even if you think you're fairly sure about where you're going, ask yourself a simple question before proceeding: Is there anything such as a check, capture, or threat that I haven't considered, or have considered but minimized or marginalized, that might affect my analysis and thereby change my evaluation? You'll be surprised how the mere posing of this question (or one like it) serves as a valuable check against letdowns, oversights, and plain old blunders. 496) Hidden rook trick

497) Black sets up a rook trick

498) Checking to upset the defense

Onto Diagram 498, where White to play would hit Black with 1. Re7!, a cutoff that prevents Black's own looming threat. If it were Black's turn, however, the a-pawn would be lost to 1...Ra6+!, forcing the white king onto the seventh rank, 2. Kf7 (or 2. Kg7, but not 2. Ke7? Rxa7+), when the pawn is captured for free, 2...Rxa7+. In Diagram 499 Black might feel initially safe enough, since the e-pawn, being on the second rank, helps avert a skewer check. But there's much more to it. White to play wins with 1. Rh8! anyway. Oh, Black can take the pawn before it queens, 1...Rxa7, and there is no rook trick to fret over. But there is an end to the game, 2. Rh5 mate! 499) Rook trick or mate

In Diagram 500, inspired by a game of Botvinnik's, we see how the threat of mate, like the possibility of a rook trick, can allow the stuffed up rook to move freely. After 1...Rcl! White can do no better than harass with 2. Ra3+, when 2...Rc3 3. Rxa2 Rc4 is mate. Note that Black had to play the rook to

cI in order to block the check from a3, while still maintaining the mate threat at c4. 500) Black wins

In Diagram 501, the defending rook is not placed behind the passed pawn, instead attacking it along the seventh rank. Black's immediate survival is based on the rook remaining at h7: keeping an eye on the pawn, while also controlling the h-file and safeguarding the black king. Upset that balance and Black will lose. Thus White wins with 1. R18!, threatening to promote, when 1...Rxa7 is squashed by 2. Rh8+ Rh7 3. Rxh7 mate. Note that White can't play any old move with the rook along the eighth rank, since something like 1. Rg8? would not be answered by I...Rxa7'?, rather Black would interpose I ...Rf7+!, driving away White's king and avoiding mate. After 2. Ke6 Black could safely take the apawn, 2...Rxa7, there no longer being a mating check along the h-file. 501) White to play wins

Another instance where the defending rook is not placed directly behind the advanced pawn is shown

in Diagram 502. Once again the defending rook is preventing a rook-file check (here, on the a-file), but since the kings are not directly aligned there's no mate threat in the air. Still, there's no good reply to I...Kb3!. Ifthe rook retreats toward the white king, 2. Ra4, then Black can safely move out his own rook, 2...Rb8, and the h-pawn will cost White a rook. And if the white rook responds by going elsewhere along the second rank, say 2. Rg2, the time-gaining 2...Ra2+ ensures promotion. 502) Where does the rook go?

In Diagram 503 the defending rook is the one occupying the square in front of the pawn, with the attacking rook guarding the pawn along the second rank. The black rook also cuts off the white king along that rank. Together with the black king they prevent the white king from getting over to the battle zone. After I...Kb4! White is in trouble. 503) Squeeze out

504) Creating shelter

505) White to play wins

A sample conclusion might be 2. Ke3 Kb3 3. Rdl Kb2. Another useful technique is shown in Diagram 504. White to play has the annoying 1. Rg8+, but Black to play still has a win by creating a certain kind of shield, protecting the h-pawn. It begins with 1...Rg3+. After 2. Ke4 Black obstructs the h-file with 2...Rh3, when 3. Rg8+ Kh4 4. Kf4 threatens mate. Note that 4. Rh8+, instead of 4. Kf4, would have been answered by 4...Kg3, and the black king gets out. But in reply to 4. Kf4, and the mate threat, Black has the retort, 4...Rf3+!, when 5. Kxf3 permits the h-pawn to queen with check. But if the attacking rook can't escape from its corner by a check or threat of rook trick another tactical idea sometimes can work: setting up a discovery. In Diagram 505 White to play wins with 1. Rc8!, when I...Rxa7 loses to 2. Kb6+. In Diagram 506 White is barely surviving, escaping checks because of the placement of the black king. With that in mind, Black tries to maneuver to expose the white king to such a check, and thereby is the path to victory: 1...Kc5 (threatening check along the b-tile) 2. Kc7 Kd5 (again, threatening

check) 3. Kd7 (once again, using the enemy king for shelter) 3...Ke5 4. Ke7 Kf5 5. Rf8+ (if 5. Kf7, then 5...Kf4 6. Kf6 Rfl threatens a discovery, so that 7. Rxh2 would be met by 7...Kg3+, as in Diagram 505) 5...Kg6 6. Rg8+ Kh7 and Black wins. 506) Black to play wins

507) White to play draws

508) White to play draws

But sometimes one can use the enemy king for shelter and it does work, as in Diagram 507. White is able to hold with 1. Kb4 Kc2 2. Kc4 Kd2 3. Kd4 Ke2 4. Ke4 Kf2 5. Kf4 Kg2 (Diagram 508). This position of Diagram 508 illustrates an idea seen earlier (Diagram 416), where a rook and king held a position by virtue of perpetual threats. Such is the case here, with White being able to check away by 6. Rg8+ Kh3 7. Rh8+ Kg2 8. Rg8+ Kf2 9. Rh8 Rfl 10. Rxh2+ Kgl+ 11. Kg3, and the position is drawn. 509) Black wins

A question that arises is what to do when the pawn hasn't yet reached the seventh rank. In some instances it may be better placed on the sixth rank, where it's still dangerously advanced yet offers a place to shelter the king from checks. In Diagram 509 Black has an easy win, beginning with I...Kg3, when 2. Rg8+ Kh2 provides temporary shelter from the storm. After 3. Rg7 Rg 1 4. Rh7 Kg2 5. Rg7+ Kh l 6. Rh7 h2 7. Rh8 Kg2 8. Rg8+ Kf3 it's clear that White's king will be able to approach the rook

until it runs out of checks. 510) Black to play wins

In Diagram 510 the winning idea involves a debilitating tactic: a deadly crosspin. It begins with a simple check, 1...Rh6+!, forcing the white king into line with the rook and pawn, say 2. Kb7; whereupon the shot, 2...Rxh7! costs a rook but ensures the d-pawn's promotion. Naturally, it's assumed one knows how to win queen vs. rook. 511) Black to play wins

A similar idea occurs in a well-known example analyzed by Emanuel Lasker (Diagram 511 ). Through a series of checks and threats White's king is eventually forced into line for a losing tactic: 1...Kb1 (threatening to promote) 2. Rb7+ Kal (threatening to promote) 3. Rc7 Rf3+ 4. Ka4 Kb2 (threatening to promote) 5. Rb7+ Ka2 6. Rc7 Rf4+ 7. Ka5 Kb2 (threatening to promote) 8. Rb7+ Ka3 9. Rc7 Rf5+ 10. Ka6 Kb3. And now 11. Rb7+ Ka4 12. Rc7 Rf5+ 13. Kb7 Rxf7 forces a queen vs.

rook ending. 512) White to play wins

In Diagram 512, Black's rook is in line with the white pawn, but must also stay on the e-file to prevent White's rook from moving to e8 with check. With the move White has a simple plan: to move up with the king. After 1. Kc5 Rc7+ (if I...Ke6, then 2. KW if I...Ke4, then 2.Kd6) 2. Kb6, and White's rook is now free to move, with the pawn promoting shortly thereafter. So far we've been looking at positions where the rooks are in the main fight to attack and support the pawn. In different instances the friendly king is the unit that's actually defending the pawn so that the friendly rook is free to do other things. In Diagram 513 White to move has an easy win: 1. Rb8 (to break the cutoff) 1...Rc1 2. Kb7 Rbl+ 3. Ka6 Ra1+4. Kb6 Rbl+(and now the king is free to approach the rook, ending the checks) 5. Kc5 RcI+ 6. Kd4 Rd I+ 7. Ke3 Ref+8. Kd2 (or 8. Kf2), and Black has run out of hope. 513) White to play wins; Black to play draws

But if Black is to move, the position is held by 1...Ke7!, when 2. Rb8 Ral 3. Rb7+ Kc8 4. Rb2 Rcl and Black stops the checking threat (along the c-file), with White's own king remaining hemmed in. This illustrates a general principle in these endings. Whenever there's time, the defending king should move back toward the pawn, and toward the territory in front of the pawn, to tight against the pawn's advance and to hinder the opposing king from helping out. 514) White to play draws; Black to play wins

In Diagram 514 Black's king upholds the pawn but is trapped in by the rook cutoff along the g-file. The winning method is to break the cutoff, and to do it with dispatch, before the defending king can get back to participate. So with Black to play the win is achieved after 1...Rel 2. Kd2 RgI 3. Rh7 Kg2 4. Rg7+ KF3 and White will soon run out of checks. But with White to play the extra tempo helps the king get back just in time: 1. Kd2 Ra6 2. Keg Ra 13. Kf2 Rgl 4. Rh7 (4. Rt7 Rg2+ 5. Kfl Rat 6. Rf8) 4...Rg2+ 5. Kfl, and the position is drawn. 515) White to play wins

Question: In Practice Position #7, how does Black force a win'? Solution, page 243. Diagram 515 reflects another one of the innumerable situations that depend on who moves. Black to play draws with the already considered idea of I...Kc7. White to play, however, beats Black to the punch with 1. Rb8 Rcl 2. Kb7 Rbl+, and Black's king prevents White's king from moving up the hoard. But the white king can hide somewhere else, along the eighth rank, and that wins after 3. Kc8 Rcl+ 4. Kd8 Rhl 5. Rb6+ Kc5 6. Rc6+ Kb5 (taking the rook allows White to promote with check, as in Diagram 504) 7. Rc8 (shielding the back rank and a8) 7...Rh8+ 8. Kc7 Rh7+ 9. Kb8. Practice Position #7

In the group of examples that follow the friendly king is trying to unblock the pawn) to escape from in front of it) so it can promote. With the defending king cut off by one file, the attacker is trying to gain further space by converting to a two-file cutoff. That affords the attacking king more breathing room. As the friendly king moves out from in front of the pawn it must find shelter from the enemy rook. In Diagram 516 the winning way is accomplished by creating shelter on the a-file: 1. Rat! Kc6 (on I...Rb3 2. Ka8 Kc7 3. Rc2+, drives away the king and wins) 2. Kati! Rxb7 (what else?) 3. Rc2+ Kb6 4. Rb2+, and wins the black rook. 516) Simple win

Diagram 517 shows a standard technique, which again involves the creation of shelter for the friendly king. Black's rook has control of the a-file, so the method of the previous problem doesn't work here. On the other hand, White's rook already cuts off the enemy king from the pawn along the c-file by one file, but White seeks even greater space, beginning with 1. Rd2+. Now Black has two choices, I...Kc6 or 1...Ke7. Moving the king to c6 allows White's king to escape toward the kingside, 2. Kc8, when 2...Rh3 is punished by 3. Rc2+, with White soon promoting. After 1...Ke7 White has established a two-file cutoff. Play could then continue 2. Rd4 (putting the rook in an ideal place to cope with the upcoming checks) 2...Ral 3. Kc7 Rc1+4. Kb6 Rb1+5. Kc6 Rb2 (on 5...Rcl+, White has 6. Kb5 Rbl+ 7. Rb4, and the pawn will queen shortly) 6. Rd5 Rc2+ 7. Kb6 Rb2+ 8. Rb5. Having stopped the checks by a technique known as building a bridge, or Lucena's position, named after a player who analyzed it way back, White now promotes the b-pawn for sure. 517) Lucena's position

In Diagram 518 Black's king is cut off by one file, once again on the short side of the pawn (remember, every pawn, except the rook-pawn, has a long and a short side). Here we meet up with

another concept, that of the checking distance, which is the minimum distance at which a rook can operate effectively; that is, it's the distance at which a rook is able to attack without fear of being counterattacked by the enemy king. Generally speaking, the rook is a longrange piece, and works best from far away. As the following variation shows Black's rook has full power: 1...Ra8+ 2. Kd7 Ra7+3. Kd6 Ra6+ 4. Kc7 (try - ing to approach the rook) 4...Ra7+ (hut it's driven back to safeguard the pawn) 5. Kd6 Ra6+ 6. Kc5 Re6 and the pawn will fall. 518) White wins; Black draws

519) Black's rook doesn't have the checking distance

On the other hand, if it's White's turn to play, as in Diagram 519, White wins with 1. Rg2+ Kh7 (now there's a twotile cutoti, so that White's king could operate on both sides of the pawn) 2. KB, and the menacing pawn will compel Black to sac the rook. If Black were to answer 1. Rg2+ with I ...Kf6, White wins with 2. KIN Rxe7 (it's often had to have a long-range piece, such as the rook, placed so that it needs to be guarded by its king, since a pesky check might drive away the defending king and

the rook falls) 3. Rf2+, forcing 3...Ke6, and then 4. Re2+ skewers rook and king. In Diagram 519, even with the move, Black cannot draw, since the black rook is too close to the king and pawn complex: it doesn't have the checking distance. (Usually a safe checking distance is four or more squares from the target the king, the pawn, or, in some cases, the promotion square. Accordingly, 1...Rb8+ (or I...Ra7 2. Rg2+, when 2...Kf6 is met by 3. KN Rxe7 4. R'2+ Ke6 5. Re2+, winning the black rook by skewer) 2. Kd7 Rb7+ 3. Kd8 (note that on 3. Kc5'?, Black wins the pawn by 3...Re6, which is Diagram 520) 3...Rb8+ 4. Kc7 Ra8 (trying to get the checking distance) 5. Ra2! (ofcourse, it's assumed White knows how to win when up a queen for a rook) 5...Re8 6. Kd7 Kf7 (once again, the black rook and king need each other, and that's a bad sign) 7. Rf2+, winning the rook and the game. 520) White loses the pawn

521) White to play wins

The placement of the defending rook is key, but the position of the defending king can also be critical. Change Diagram 520, shifting the black king from g7 to g8 (Diagram 521), give White the move, and the position is won by 1. Rf8+. The pawn is promoted with protection on the next move. In Diagram 522 we're dealing with a knight-pawn, and though White's king is cut off by one file from the pawn, this time the king is on the long side of the pawn. Being on the long side of the pawn may interfere with the action of the defending rook. In the position of Diagram 522 White is trying to break the cutoff by trading rooks, seeing the possibility of reducing to a drawn kingand-pawn ending, l ...Rxc l 2. Kxc l . White's king is then able to get in front of the pawn to draw. But with the smart 1...Re4! Black permits a rook trade when it's best for Black, since 2. Rxc4 Kxc4 simplifies to an easy king-and-pawn win. The black king then muscles in by the opposition. Nor does 2. Rc3 help, since Black has 2...Kb4. A possible try after I...Rc4! is to activate the white rook, 2. Rh I, but that fails to 2...Kb4, and even after 3. Rh8, Black will maintain the cutoff, maneuver his king up the board, eventually sheltering in front of the b-pawn. Once the pawn advances to its seventh rank Black will achieve a two-file cutoff and build a bridge. 522) Black still wins

A number of things to remember about rooks: 1. Rooks belong behind passed pawns. 2. Look for rook tricks. 3. Try to find shelter from enemy rook checks. 4. Aim to cutoff the enemy king. 5. Remember how to build a bridge. 6. Keep the rook at a safe distance. 7. Be careful to avoid skewer checks. Let's consider another set of examples. In these positions, the defending king sits in the pawn's path, and the defending rook must choose to play it passively (merely stopping a back rank mate or other annoying checks); or play it actively, checking or attacking from behind the passed pawn, at a safe distance, or switching appropriately to the flank, in a timely way, as the situation calls for it. The kind of pawn involved is often important. Here we distinguish between rook-pawns, knight-pawns, bishop-pawns, and center pawns. Starting with passive defenses, in Diagram 523 it doesn't matter who moves. White can make no progress, with the white rook tied to the sixth rank to avoid enemy rook checks. The position is therefore drawn, since all Black has to do is temporize with the rook along the home rank, checking White's king when the necessary moment arises. 523) A positional draw

524) Bishop-pawn wins against passive defense

In Diagram 524 Black has a bishop pawn and it's White who tries a passive defense. But it doesn't work. Black wins perforce with I...Ra2+ 2. Kbl c2+! 3. Kcl Ral+, skewering king and rook. From this we see that a passive rook defense doesn't work against a bishop-pawn because of this tactical maneuver, leading to a skewer. But a passive rook defense does work against a knight pawn. In Diagram 525 Black to play has an easy draw with 1...RfM. Thereafter, shifting the rook along the home rank, merely preventing an enemy rook check, is good enough to hold. And if White gets too bold it could even lead to defeat, as in the strained line 2. Raj (be careful about placing your rook in a position needing protection from your king) 2...Rh8 3. b7?? Rh6+. So here the tactical maneuver seen in Diagram 524 doesn't apply and the passive rook defense keeps it together. 525) Passive defense draws against knight-pawn

Give White doubled knight pawns, however, and the win is easy enough to find, since White can use

the extra pawn to force a rook trade and reduction to a winning king-and-pawn ending. In Diagram 526 White wins with 1. Rc7 Rh8 2. Rc8+! Rxc8 3. bxc8/Q+ Kxc8 4. Ka7, and the remaining bpawn queens. 526) White wins

Even with a bishop-pawn, having the skewer maneuver as a possibility, one must still go about employing it correctly. So in Diagram 527 immediately positioning the rook (I. Raj) without first giving a time-gaining check (l. Rb7+!) doesn't work, since Black's rook can then afford to leave the back rank, there being no longer a mating check possibility. Black could pin the pawn with I ...Rg6. But White still wins by shifting the rook back to the other flank, threatening mate. So only time would be wasted. The correct procedure would be to start with a check, 1. Rb7+!, when I...Ka8 is then met by 2. Ra7+ Kb8 3. c7+, and so on. Note that responding to 1. Rb7+! with I...Kc8 wouldn't help, since White would still play 2. Ra7 and win in the same manner. 527) White wins

Winning with the skewer maneuver can be even easier with a center pawn, since there's more room to operate. The rook is able to get sufficiently tar away without having to set up with a time-gaining check. Thus in Diagram 528 Black is up the creek after 1. Raj (1. Rb7 also works, as does 1. Rc7 Kd8 2. 17+). Mate can be avoided, and Black's rook isn't lost, but the pawn can't be stopped. 528) An easy win

But occasionally there are other tricks, as in Diagram 529. If it were Black's turn I...RaI+ 2. Rfl 12+ would follow. But with the move White can gain a breather by the surprising 1. Rg2+!, when taking the rook is stalemate. After I...Kt4 (or I...Kh3) White has time for 2. Rg7, and the battle continues. White holds the draw thanks to the better placement (far away, and capable of giving checks) ofthe white rook. 529) White to play and draw

The possibility of stalemate can be most welcome to an oppressed defender, and Diagram 530 offers another way it can come about. White has to stop the mate at h 1, and the simplest way is to block the black rook, 1. Rh7!, preventing it from getting there. Curiously, wherever Black places the rook on the eighth rank White's rook can oppose it on the seventh rank and the game is drawn. For example, if I ... Rg8, then 2. Rg7 produces the same idea; if I ...Rf8, then 2. R17; and White draws with this perpetual threat. 530) White to play draws by perpetual threat

Another very important idea is reified in Diagram 531. The defending king sits in the pawn's path. The attacking rook is well disposed on the seventh rank. And the attacking king is about to advance to its sixth rank, with various threats in the offing. But it's Black's move. And with that move Black can stop the approach of White's king by a third rank cutoff, I...Rf6!. After this stoppage of the intended invasion, there's only one way to attempt any progress, and that's to advance the c-pawn, 2. c6, hoping to create some shelter for the king to move up a rank. But once the pawn has advanced, and there's no way for the attacking king to hide in front of it, the black rook heads for the back rank, 2...RfI, to

check the white king from behind. This leads to a draw. If in Diagram 531 it had been White's move to begin with, White would move his king to the sixth rank. But not 1. Kc6, when I...Rf6+ would force it back. Rather White's best initial move would be 1. Kb6!, so that however Black checks it's possible to find shelter. That is, after I. Kb6!, if I...Rf6+, then 2. c6. Or if I ...RbI+ instead, then 2. Kc6, and the king escapes further rook checks. The question is, after 1. Kb6 from Diagram 532, what is Black's best continuation? 531) Philidor's drawing idea

If it's White's move in Diagram 532 the winning line is 1. Rh8+ Kd7 2. c6+ (this is the problem, that the pawn can advance with check) 2...Kd6 3. Rd8+ (a right triangle check, driving Black's king toward the kingside) 3...Ke7 4. c7 Rb 1 + 5. Ka5 (the king approaches the black rook) 5...RaI+ 6. Kb4 RbI+ 7. Ka3 Ra I + 8. Kb2, and the pawn queens next move. With Black to move, however, there is the possibility of coping with this threat by 1...Rc1!. If White then continues 2. Rh8+, forcing 2...Kd7, both the black rook and king work together to guard the square c6, and the c-pawn can't advance safely. With correct play from here, the game can he held. So from Diagram 532 the best move for Black is to get behind the passed pawn, 1. Re P. 532) White to play wins Black to play draws

Let's look at another idea, as exhibited in Diagram 533. White to play would mate in one move. But Black to play still has a chance to survive. It would be wrong to play it passively, merely trying to stop mate by I...Re1, hoping to interpose at e8, since 2. Ra8+ Re8 3. Rxe8+ Kxe8 4. Kg7 reduces to a king-and-pawn win. So the black king must bail out. A question arises: Should Black's king move toward the queenside, 1...Keg, or toward the kingside, I ...Kg8? 533) Black to play draws

On I...Ke8, which looks more natural, since the king thereby has further escape room, Black actually gets into trouble after 2. Ra8+ Kd7 3. RN and Black has trepidation. A possible continuation might then be 3...Rt2 4. Kg7 Rg2+ 5. K17 Rf2 6. f6 Rfl 7. Ra8 Rf2 8. Ra I Rt3 9. Rd I+ (a right triangle check) 9...Kc7 10. Kg7 Rg3+ 11. Kt8 Rt3 12. P Rt2 13. Rd4 (starting the action ofbuilding a bridge) I3...Rfl 14. Ke7 Rel + 15. Kf6 Rfl+ (or 15...Re2 16. Rd5) 16. Ke6 Rel+ 17. Kf5 Rfl+ 18. Rf5 and White wins. On the less natural looking I...Kg8, however, Black definitely draws. After 2. Ra8+ Kh7 3. RtR, a key position is reached, which is shown in Diagram 534.

534) Black to play draws

In Diagram 534 Black to play has I...Ra1!, shitting to the flank. With this sudden activity from the wing Black can hold a draw. On 2. Rt7+ there follows 2...Kg8 3. Rg7+ Kt8 4. Raj Kg8 5. Ra8+ Kh7 and White hasn't made any real progress. Ifafter I...RaI White attempts to block Black's threats with 2. Reg the black rook goes back to attacking the pawn from behind it, 2...Rfl!. If White's rook then goes in front of the pawn, hoping to play Kf6-e7 (so that Kh7-g7 could be answered by f5-f6+, without hanging the rook at t8), Black's rook counters once again with a flank attack, Rfl -aI. 535) Black to play draws

Thus, we have a mnemonic to play with here. When White's rook goes to f8, in FRONT of the pawn (FRONT beginning with the letter "f'), then Black's rook goes to al, to the FLANK (FLANK beginning also with the letter "f'). On the other hand, when White's rook goes to e8, to BLOCK the checks (BLOCK beginning with "b"), then Black's rook goes to fl, BEHIND the pawn (BEHIND also

beginning with "b"). In Diagram 535 we meet up with another idea. It's Black's turn and White has f5- f6 in mind. Black's best move is I...Kg7!, with the king and rook working as a team to guard f6 and prevent the pawn's advance. As a rule of thumb in similar and related positions (already pointed out in slightly different context), if you have the time to do so, it's usually a good idea to bring the king back and use it as a defensive weapon. Thus after I ...Kg7 White could try 2. Ra7+ Kf8. But with 3. Kf6 (Diagram 534), menacing mate, the black king flees toward the kingside again, 3...Kg8, and we're back where we were earlier. To offer another reminder, if you have to bail out with your king, fleeing toward the kingside or queenside, head toward the short side of the pawn (the side of the pawn having the fewest number of files between it and the closest file edge). Simplification Perhaps the most basic winning endgame plan of all is that of simplification. In accordance with it one aims to maintain control of he situation by choosing lines that avoid complications and make the position more intelligible and manageable. The basic simplifying idea is just that: reducing the amount of material on the board so that it's harder to be mislead. In doing so one also diminishes the possibility of counterplay, especially if in the process the opposing queen can be gotten off the board. This is no place to treat the subject exhaustively, but the following positions all show rook endings and the process of simplifying to king-and-pawn wins. In Diagram 536, for instance, White has a most simple winning plan. It consists in (a) trading the rooks, (b) moving the king toward the h-pawn, and (c) using the a-pawn as a decoy. After the pinning 1. Rd2!, Black has nothing better than I...Rd7 2. Rxd7+ Kxd7 3. Kd4 Kd6 4. Ke4 and that's really that, since the presence of the white a-pawn makes defense of the kingside impossible. 536) White forces a rook trade

Diagram 537 shows another aspect to it. After simplifying White must create a passed pawn and then win using it as a lure. Thus the winning plan is to (a) trade rooks, (b) exchange off all the kingside pawns, (c) capture the e-pawn, then (d) beat Black to the queenside, and (e) promote the b-pawn. The win is executed by 1. Rxf6+ Kxf6 2. g5+ hxg5 3. hxg5+ KxgS 4. KxeS, and White indeed gets to the queenside first, captures the b-pawn, and wins. 537) White simplifies to a win

538) White checks to force a swap

The final example here merely reinforces what we've already seen. In Diagram 538 the plan is to (a) check on f8, when (b) either Black blocks and allows a rook trade or walks into a pin allowing a rook trade, and (c) the white king advances to clear a path for the e-pawn, which (d) then beats Black's g-pawn to promotion and wins. Thus 1. Rf8+ Kc7 (I...Rd8 2. Rxd8+ Kxd8 3. Kf7) 2. Rf7

Rxf7 3. Kxf7 g5 4. e6 g4 5. e7 g3 6. e8/Q wins. Queens and all that We close out with a few queen endgame ideas. This class of closings, as with the others, could be covered more deeply, but here we just want to bring up a few themes that tend to have value for amateur players. For instance, in the battle to escort home a passed pawn, the friendly king often has to make an entrance. At that point the opposing queen will surely start checking and threatening. It will probably become necessary to seek shelter to escape the checks. There are various ways to try doing this. One of the most effective methods is to block a check with a check - that is, give a crosscheck. 539) White to play wins

540) White to play wins

In Diagram 539 White wins immediately by the simplifying 1. Qe6+, forcing a trade of queens, and that leads to promotion on the next move. In other cases, the enemy queen functions as a blockader, literally preventing the pawn's advance to promotion. The win is then achieved, if it can be forced, by breaking the blockade. A standard way is to maneuver one's own queen into position, to offer a trade on the promotion rank, with the friendly queen protected by the pawn, so that if a trade takes place the pawn becomes a new queen when it takes back. In Diagram 540, with White having a bishop-pawn on the seventh rank, we see how this might transpire. White begins with a check, 1. Qe6+!, centralizing the queen. This gains time while aiming the queen at e8, planning a trade. After l...Kb2 2. Qe8 Qb4 3. f8/Q Qc4+ White ends the counterattack with a crosscheck, 4. Qe2+, meeting a check with a check, and Black can resign. 541) White to play wins

Diagram 541 shows more of the same, this time, against a center pawn. The win here is achieved by 1. Qd4+ Kbl (or I...Ka2) 2. Qd8 and White queens the pawn next move. No matter how Black plays it, once White has two queens on central files, with one already established in the middle, it will be easy enough for White to end the checks. Another motif is seen in Diagram 542. Here the friendly king has to cope with the pawn being pinned. In general the friendly queen must join the fray, some times breaking the pin by interposition, 1. Qf7. But there are usually checks to he answered, 1...Qg3+ 2. KfS, and new pins, 2...Qa3; and new replies, 3. KgS, maneuvering in the end to answer a check, 3...Qg3+, with a queen trading crosscheck, 4. Qg7+ (I 0). 542) White to play wins

543) Perpetual

Still, there's an ever-present danger of the opposing queen being able to check endlessly, with no means to end the checking. We call it a perpetual check, though long before the position goes on to perpetuity it will incur a threefold repetition, and the draw will be claimed as it's about to happen. In Diagram 543 the black queen gets monotonous, checking hack and forth, between a5 and d8: 1...Qd8+ 2. Ka7 Qa5+ 3. Kb8 Qd8+. Most players soon agree to a draw. In Diagram 544 White expect to block I ...Qg8+'? with the crosspin 2. Q18. But that's not what's going to happen. Black instead plays 1...Qf7+!, drawing by stalemate, no matter how White takes the queen. 544) Black to play and draw

But we don't want to imply that all the humor belongs to the defender. The attacker also has a few potential jokes. In Diagram 545, after 1. Qd7+, Black has a choice: to abandon the queen, say by l ...Kf6; or to defend the queen and get mated; if I...Kg8, then 2. Qe8 mate; if instead I...Kg6, there's 2. Qe6 mate. Let's leave it at that. Occasionally it's the superior side that gets mated. In Diagram 546 Black to play turns the tables with I...Qg8+ 2. Kd7 Qc8 mate (a swallow's tale mate). That's what can happen if one gets too cocky. 545) White to play wins

546) Black mates in two moves

547) White to play wins

In Diagram 547 a different concept comes into play. It's not always obvious how to deal with an annoying pin of the pawn. If the pawn is on the seventh rank it may be possible to employ the tactic of sacking the queen to break the pin, in the process, luring the enemy queen to a bad square, so that when the pawn queens it skewers king and queen, winning the opposing queen. In other words, from Diagram 547, White triumphs with 1. Qh2+! Qxh2 2. b8/Q+ and White gains Black's queen. A similar idea materializes in Diagram 548. Once again White sacs the queen, 1. Qbl+!, forcing Black's queen to capture on a bad square, 1...Qxb1, thereby unpinning the pawn. The pawn then queens, 2. b8/Q+, skewering king and queen. This brings back the idea of a pawn race, resulting in both sides queening, with one of the queens being won by the other. Thus in Diagram 549 White wins after 1. c8/Q b1/Q 2. Qa8+! (forcing Black's king onto the b-file) 2...Kb4 3. Qb7+, acquiring Black's queen. 548) White to play wins

549) White to play wins

Finally, let's close this section with the final position from Searching for Bobby Fischer, which is a simplified version of the same notion. In Diagram 550 Black wins the pawn race but loses the game after I...a2 2. h7 al/Q 3. h8/ Q+ Kc4 4. Qxal. Smile: you've just won the National Championship. 550) Black to play loses

Final advice For studying the endgame further I suggest you obtain a number of good endgame books. You should have at least one or two textbooks that cover all endings. To this end, to this and that endgame, I recommend Dvorets/n's Endgame Manual as well as Rueben Fine's Basic Chess Endings as revised by Pal Benko. I think you might additionally enjoy Van Perloc Endgame Tactics. It has a lot of fun stuff in it. Two other notable texts, worthy of any chess student's library, are Fundamental Chess Endings by Karsten Muller and Frank Lamprecht, and Silman: Complete Endgame Course by Jeremy Silman. I would also look at the game collections of great endgame players, such as Capablanca, Rubinstein, Petrosian, Smyslov, Lasker, Karpov, and Korchnoy. All kinds of illuminating strategies and techniques come out in their play. But the truth is it can't hurt to add ten or twenty other endgame books to your library as well since you'll probably need good source material to reinforce your study and supply sufficient illustrations. How do you get better at endgame play? There's no automatic approach here that would satisfy everyone's needs, especially when considering differences in playing strength and knowledge. You're simply going to have to work at it and see. At least in training games I'd play into endings as often as I could reasonably. You wouldn't want to force a situation that might be undesirable. But obviously the more practice you get the better. After those practice games have been played you should analyze them, turning back to your library to find supportive ideas and perhaps the right ideas, techniques and lines. A good exercise is to consider resigned positions between strong players. Most of these resignations occur when there's still some work yet to do. I would play these positions out against a good piece of software such as Fritz. You know your technique is decent if you can win ninety percent of these positions. Finally, no matter how much you've learned, regardless of all the examples you've seen, despite all the helpful visuals and mnemonics, never take your adversary or your situation for granted. Even disheartened players look for ways to save themselves, and that includes the most deceptive tricks ever invented. And at your end no trick of the trade can be relied on with total assurance. No, there are no tricks that guarantee success. Yet what you do have is a mind capable of always examining

what's before you. It can judge good and bad, weigh options, compare and contrast, filter out the unlikely, and help you make a decision based on finding objective truth. With the hardest work and most sincere effort you still might not find it. But that's what you have, and that's what you must count on, your own mind. Giving it full and open range, powered by total commitment, is the best you or anyone can ever do.

Solution to Practice Position #1: If I...Bxa7, then 2. NO mate! Who said two knights can't beat two bishops'? Solution to Practice Position #2: You can win the rook, just like Kramnik, with 1. Qf6+ Kh7 2. Qf5+ Kh8 3. Qe5+ Kh7 4. Qe4+. In the actual game, Black here resigned, since 4...Kh8 5. Qd4+ forks king and rook. Clearly, d4 is the desired connection point. Solution to Practice Position #3: After I...Nc3!, White must lose his knight. Rook-pawn or not, Black shouldn't have trouble winning after that. Solution to Practice Position #4: After 1. Ng7!, Black has no choice but to selfmate with I ...Bxg7 2. Bxg7 mate. Solution to Practice Position #5: White holds the position with 1. Rh P, when I...Kxhl is met by 2. Kfl and a draw. Solution to Practice Position #6: White wins with 1. Bxg2! Nxg2 2. h3. Solution to Practice Position #7: Black scores with l ...Rb2!, and White's rook is lost, since 2. Rg I is met by 2...Rh2 mate. Yes, Practice Position #7 is the same as Diagram 369 on page 173. I thought you'd enjoy seeing it one more time. Acknowledgements Besides my trusty computer, and the one I had to get to replace it and the one that came after, I would like to thank several people. Daniel Lucas, editor-in-chief of Chess Li/i', having read my closing remarks, gave me some very good advice when I was about to make some very bad mistakes. I thank him, as I do Roselyn Abrahams for a number of her insights on presentation. Further appreciation must go to Mark Donlan for his artistry in setting the text and designing the layout, as well as for his astute input. Finally, but not really last, since as a publisher, editor, impresario, and connoisseur he clearly stands out, I would like to extend my gratitude to Hanon Russell for his omniscient and guiding perspective, for curtailing my tendency toward extravagance at its most liberal, and for ensuring the overall integrity of the enterprise. I couldn't have done this book without any of these people, and even with their help I'm still surprised.

(numbers refer to diagrams)

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