Practical Chess Endings E-Book

Paul Keres

• Herausgeber: Batsford
• Kategorie: Lebensstil
• Sprache: Englisch

Seitenzahl: 629

Veröffentlichungsjahr: 2018

Beschreibung

An updated edition of Paul Keres' classic endgame instructor, designed specifically for practical players with over 500 extra diagrams to facilitate learning and memorisation of critical lines of endgame play. It is an essential practical book, for all chess players, from one of the world's greatest grandmasters. Keres remained an elite grandmaster throughout his life and is widely regarded as one of the s strongest ever players not to have won the world chess champion. His book is a comprehensive guide to the precise handling of all basic endgame positions. It features logical step-by-step explanations of procedures required to obtain the best possible results from frequently occurring queen, rook, bishop, knight and pawn endings. It includes commentaries on the final stages of selected tournament games, which demonstrate the art of favourable transposition from complex to clear-cut endgames.  

Leseprobe

Preface

In chess literature throughout the world countless books have been written on opening theory, the middlegame, chess tournaments and game selections. Within this vast production, however, books on the endgame are comparatively few in number, despite the fact that this is one of the most important parts of the game of chess.

It is indeed difficult to overestimate the value of good endgame play and time spent on this department is amply repaid. The purpose of this book is to give the reader practical help in endgame technique.

Many chess players are averse to studying the endgame, in the belief that it is boring. To a certain extent they are right, for most theoretical endings are relatively dry in content, requiring precise calculation and offering few opportunities for individual flights of imagination. Nevertheless, there is much of interest in this phase of the game, and all chess players should strive to improve their play by mastering the necessary technique.

In order to pinpoint basic principles, I have decided to cut down on the number of examples but to examine them in greater detail than is customary. In this way I hope to make endgame theory a little more palatable. This has necessarily led me to reject many purely theoretical analyses and restrict myself to material which will be of most benefit to the practical player.

In offering this volume to the reader I hope not only to stimulate interest in the subject matter but principally to raise the average level of endgame technique among chess players everywhere.

Paul Keres

Tallinn, July 1972

Contents

Preface

Introduction

1 Elementary Endings

King and queen against king

King and rook against king

King and two bishops against king

King and two knights against king

King, bishop and knight against king

King and pawn against king

2 Pawn Endings

King and pawn against king

King and pawn against king and pawn

A: Pawns on the same file

B: Pawns on different files

King and two pawns against king and pawn

A: Isolated pawns with a passed pawn

B: Isolated pawns without a passed pawn

C: Connected pawns with a passed pawn

D: Connected pawns without a passed pawn

a) When one pawn is blocked

b) Without blocked pawns

King and two pawns against king

King and two pawns against king and two pawns

A: Creation of a passed pawn

B: The distant passed pawn

C: The protected passed pawn

D: The blockade of enemy pawns

E: Other possibilities

Endings with more pawns

Practical examples

3 Queen Endings

Queen against pawn

Queen against rook (and pawn)

A: Queen against rook

B: Queen against rook and pawn

Queen against queen (and pawns)

A: Queen against queen

B: Queen against queen and pawn

C: Queen and pawn(s) against queen and pawn(s)

Queen against other pieces

A: Queen against two rooks

B: Queen against two bishops

C: Queen against two knights

D: Queen against bishop and knight

Practical examples

4 Rook Endings

Rook against pawn(s)

Rook and pawn against rook

A: Rook and rook’s pawn

B: Rook and pawn other than rook’s pawn

a) Pawn on the seventh rank

b) Pawn on the sixth rank

c) Pawn on the second to fifth ranks

Rook and two pawns against rook

Rook and pawn(s) on both sides

A: Rook and pawn against rook and pawn

B: Rook and two pawns against rook and pawn

Practical examples

Rook against minor pieces

Rook against bishop

Rook against knight

Rook and minor piece against rook

Rook and bishop against rook

Rook and knight against rook

5 Bishop Endings

Bishop against pawn

Bishop and pawn against bishop

Bishops of the same colour

Bishops of opposite colour

A: Bishop and two pawns against bishop

B: Bishop and pawn(s) on both sides

Bishop and pawns(s) against knight

Bishop against knight and pawn(s)

Practical examples

6 Knight Endings

Knight against pawn(s)

Knight and pawn against pawn

Knight and pawn(s) against knight

Practical examples

Introduction

A normal game of chess usually consists of three phases; opening, middlegame and ending. In the opening a player attempts to develop his forces in the most effective manner and create favourable middlegame chances. The middlegame is the richest and apparently the most difficult part of the game, in which the player aims for a decisive superiority or at least an advantageous endgame. And, finally, the ending is that part of the game in which we must convert into a win any advantages won during the opening or middlegame.

As a result, it is clear that the ending is one of the most critical stages of the game. A player can sometimes afford the luxury of an inaccurate move, or even a definite error, in the opening or middlegame without necessarily obtaining a lost position. This is explained by the fact that in both these complicated phases of the game there are great practical difficulties in detecting and exploiting our opponent’s mistakes. In the endgame, on the other hand, an error can be decisive, and we are rarely presented with a second chance.

There could be no clearer proof of the vital need to perfect one’s endgame technique. The world’s leading chess players pay special attention to this aspect of their game, and we can find numerous modern examples of finely conducted endgames.

It must be admitted that, from a purely technical point of view, endings are much less interesting to study than, for example, opening theory or the strategy of the middlegame. However, this study is essential, and there is at least the advantage that most endings lend themselves to exact analysis of winning or drawing possibilities.

In the following pages, we shall attempt to provide the reader with the most important principles for the correct handling of various practical endings. We all know that present endgame theory in its entirety would fill many hefty tomes, the mere sight of which is a deterrent. The aim of this book, therefore, is to lighten the burden somewhat by selecting from the vast material available those endings which are of most practical value. For example, we shall be examining all basic endgame positions, presenting an indispensable ABC of chess usage. Do not underrate such an approach. Even great players have been known to have weaknesses in this phase of the game.

1 Elementary Endings

In this section we shall examine positions which in fact belong to the ABC of every player and scarcely need any further elucidation. However, we mention them briefly here for the sake of completeness, first of all looking at the force required to mate a lone king.

King and Queen against King

This is always a win, the only danger being a possible stalemate.

One possible winning method from diagram 1 is the following: 1 ♕c3 ♔e4 2 ♔b7 ♔d5 The black king obviously wishes to remain in the centre as long as possible. 3 ♔c7 ♔e4 4 ♔d6 ♔f4 5 ♕d3 ♔g5 6 ♔e5 ♔g4 7 ♕e3 ♔h5 8 ♔f5 ♔h4 9 ♕d3 ♔h5 10 ♕h3 mate.

This is perhaps not the shortest way, 1 ♔b7 being possibly quicker, but the given method shows how easily the enemy king can be mated in such positions.

King and Rook against King

This too is always a win. As in the above example, the enemy king must be driven to the edge of the board before he can be mated, although the task is slightly more difficult. Whilst the queen can drive the king to the edge without the help of its own king, it is essential for the rook and king to co-ordinate their action to achieve this aim.

In diagram 2, White’s task is not especially difficult. In order to force the black king to the side of the board, it is simplest to cut off the king by using the rook along the rank or the file, beginning with 1 ♖a4 or 1 ♖e1. However, as no further progress can be made without the help of the white king, the clearest method is 1 ♔b7 ♔e4 2 ♔c6 ♔d4 3 ♖e1 To force the enemy king towards the a-file. 3 ... ♔c4 4 ♖e4+ ♔d3 5 ♔d5 Now the black king is denied access to both the e-file and the fourth rank. 5 ... ♔c3 6 ♖d4 ♔c2 7 ♔c4 ♔b2 8 ♖d2+

8 … ♔c1 The king already has to go to the back rank. 9 ♔c3 ♔b1 10 ♔b3 ♔c1 11 ♖d3 ♔b1 12 ♖d1 mate. Note especially the use of waiting moves by the rook.

King and two Bishops against King

It is clear that king and one bishop cannot possibly mate a lone king, but two bishops easily force the win, as can be seen in the play from diagram 4.

The winning procedure is the same as in the previous examples. The black king is gradually driven to the edge of the board by coordinating the bishops to control its escape squares. The following line of play is readily understandable: 1 ♔b2 ♔e4 2 ♔c3 ♔d5 3 ♗f3+ ♔e5 4 ♗g3+ ♔e6 5 ♔d4 The black king is now completely cut off by the bishops and can easily be forced into the corner. 5 ... ♔f5 6 ♔d5 ♔f6 7 ♗g4 ♔g5 8 ♗d7 ♔f6 9 ♗h4+ ♔g6

The black king’s movements are even further restricted but he must be driven into the corner. 10 ♔e5 ♔f7 11 ♔f5 ♔g7 12 ♗e8 ♔f8 13 ♗g6 ♔g7

14 ♗e7 ♔g8 15 ♔f6 ♔h8 16 ♗f5 ♔g8 17 ♔g6 ♔h8 18 ♗d6 ♔g8 19 ♗e6+ ♔h8 20 ♗e5 mate.

There may of course be quicker ways but the winning method remains in all cases the same.

King and two Knights against King

Whilst it is clear that a single knight and king cannot mate the enemy king, it is not so obvious that there is no way to force a win with two knights. In this case there is a theoretical mating position, but White cannot bring it about against correct defence. Diagram 7 makes this clear, for White cannot strengthen his position even though the black king is in the corner.

The attempt to restrict the king’s movements by 1 ♘e7 or 1 ♘h6 leads to stalemate. White can try 1 ♘f8 ♔g8 2 ♘d7 ♔h8 3 ♘d6 ♔g8 4 ♘f6+

…and if 4...♔h8? 5 ♘f7 mate, but Black simply plays 4 ... ♔f8 and White must start all over again. However hard White tries, there is no forced way of mating the black king with two knights only.

King, Bishop and Knight against King

White can indeed force mate in this ending, and it is worthwhile to acquire the necessary technique. Once again the black king must naturally be driven into the corner of the board, and mating positions are possible in all four corners. However, mate can be forced only in the two corners which are of the same colour as the bishop controls. In the two other corners, mate is only possible if the defender makes a mistake, as was the case with the two knights.

This means that the task of the attacker is fairly tricky. Firstly, the enemy king has to be driven to the edge of the board, then into the corner, and finally into the other corner if the colour is the wrong one for his bishop. And whereas with the queen, rook or two bishops it was easy to cut the king off along the ranks, files or diagonals, with knight and bishop such control is more difficult. The two pieces constantly require the support of their own king, so that the knight and king can guard those squares which the bishop cannot control. Let us see how it all works by examining the play from diagram 9.

White must of course first bring up his king, whilst the black king tries to remain in the centre for as long as possible. As soon as he is driven away, he heads for the ‘wrong’ corner, a8 or h1, where he cannot be mated with correct defence.

Play might continue as follows: 1 ♔b2 ♔d3 2 ♘c7 ♔c4 To hold back the enemy king. 3 ♘e6 ♔d5 4 ♘d4 ♔c4 5 ♔c2 ♔b4 No better would be 5 ...♔d5 6 ♔d3. 6 ♔d3 ♔c5 7 ♗h2 As we can see, the white pieces supported by the king have taken many squares away from the black king. 7 ... ♔d5 8 ♘b3

8 … ♔c6 The king must retreat, so he heads for a8, whereas 8 ... ♔e6 9 ♔e4 would drive him towards h8. 9 ♔c4 ♔b6 Better than 9 ... ♔d7 10 ♔d5. 10 ♘c5 ♔c6 11 ♘a4

Reaching a similar situation to the one after White’s eighth move and showing a typical method of driving back the enemy king with bishop and knight. 11 … ♔b7 12 ♔b5 ♔c8 After 12 ... ♔a7 13 ♔c6 we reach a position which occurs later in the main variation. 13 ♔c6 ♔d8 14 ♔d6

14 … ♔c8 If Black tried to escape by 14 ... ♔e8, he would be driven over to h8 after 15 ♔e6 ♔f8 16 ♗e5, or here 15 ... ♔d8 16 ♘b6, without being able to slip away towards a8. 15 ♘b6+ ♔b7 16 ♔c5 ♔a6 17 ♔c6 ♔a5 18 ♗d6 ♔a6

19 ♗b8 Barring the king’s retreat towards a8 and beginning the manoeuvre to drive him towards a1. 19 ... ♔a5 20 ♘d5! ♔a4 White’s task is simpler after 20 ... ♔a6 21 ♘b4+ ♔a5 22 ♔c5 ♔a4 23 ♔c4 ♔a5 24 ♗c7+ etc. 21 ♔c5 ♔b3

22 ♘b4! A very important knight move and a typical way of driving the king from one corner to the other, 22 ... ♔c3 23 ♗f4 and we can see that the splendid position of the knight stops the black king escaping. 23 ... ♔b3 24 ♗e5 ♔a4 25 ♔c4 ♔a5 26 ♗c7+ ♔a4 27 ♘d3 ♔a3

28 ♗b6 A waiting move; the black king is now compelled to go to a1. 28 ... ♔a4 29 ♘b2+ ♔a3 30 ♔c3 ♔a2 31 ♔c2 ♔a3 32 ♗c5+ ♔a2 33 ♘d3 ♔a1

At last! The black king is now mated in three moves. 34 ♗b4 ♔a2 35 ♘c1+ ♔a1 36 ♗c3 mate.

The reader will now realize that this ending is by no means easy. It is worth noting standard positions such as those after White’s 8th, 19th and 22nd moves, and the beginner would do well to try to drive the black king into the corner from various positions on the board, in order to get used to the way in which the three white pieces co-operate. It must not be forgotten that the king must be mated within 50 moves, or else a draw can be claimed. This makes it all the more imperative for us to be thoroughly conversant with the winning method, so as not to lose valuable time driving the enemy king back.

King and Pawn against King

We could have examined this ending in the section on pawn endings, but as we are dealing with simpler examples here, it seems best to include it in this section on elementary endings. In this type of ending it is difficult to give general principles, as everything depends on the placing of the pieces. It goes without saying that a win is only possible if the pawn can be promoted, so our task is to establish when this can or cannot be done.

Of course, White wins easily when the enemy king is too far away to prevent the pawn queening. It is equally clear that the game is drawn when the white king cannot prevent the capture of his pawn. We are primarily concerned with those positions where the black king is placed somewhere in front of the pawn. Let us begin by examining the basic situation given in diagram 17, with the pawn on the sixth rank and the black king on the back rank in front of the pawn.

On the left is a typical position in this ending, always attainable even with the pawn originally further back, as its advance to the sixth rank cannot be prevented. The win here depends on who has the move. With White to move the game is drawn, as 1 c7+ ♔c8 2 ♔c6 gives stalemate, and White cannot bring about the same position with Black to move. For instance, after 1 ♔d5 ♔c7 2 ♔c5, Black plays the correct move 2 ... ♔c8! and now both 3 ♔d6 ♔d8 and 3 ♔b6 ♔b8 amount to the same situation. Black’s defence is easy: he keeps his king for as long as possible on c7 and c8 until the white king reaches the sixth rank when Black must immediately place his king directly in front of the white king.

In connection with this ending, I would like to stress one extremely important point concerning the position of the two kings. In all pawn endings, when the kings face each other as above (i.e. standing on the same rank or file with one square in between), they are said to be in ‘opposition’ or more specifically in ‘close opposition’, as compared with ‘distant opposition’ when the kings are 3 or 5 squares apart. Diagonal opposition occurs when there are 1, 3 or 5 squares between both kings.

We say that a player ‘has the opposition’ when he has brought about one of the above-described positions with his opponent to move. In such cases the latter has lost the opposition. We could now define the left half of diagram 17 as follows: the win in this position depends on who has the opposition. If White has it, he wins; if Black has it, the game is drawn.

This rule applies to all similar positions, except those where a rook’s pawn is involved. For example, in the right half of diagram 17, White cannot win even with the opposition, as 1 ... ♔h8 2 h7 gives stalemate.

If the pawn is not on the sixth rank but further back, Black’s drawing chances will increase significantly. Consider the bottom half of diagram 18.

This and similar positions are drawn, whoever has the move. Black defends according to the principles we have given above, with the play going as follows: 1 c3+ ♔c4 2 ♔c2 ♔c5 3 ♔d3 ♔d5 4 c4+ ♔c5 5 ♔c3 ♔c6 6 ♔d4 ♔d6 7 c5+ ♔c6 8 ♔c4 ♔c7 9 ♔d5 ♔d7 10 c6+ ♔c7 11 ♔c5 ♔c8! 12 ♔d6 ♔d8! and we have reached the known drawing position in which Black has the opposition.

One might think that we have now finished with the king and pawn ending, but this is far from being the case. What happens, for instance, when the white king occupies a square in front of his pawn? In this case equally there are no general rules for winning, but White’s winning chances are much greater, especially if the pawn is advanced, as in the upper half of diagram 18.

The white king has managed to reach the important square in front of his pawn and this fact ensures the win in all cases, whoever has the move and however far back the pawn may be. With Black to move, there is a simple win after 1 ... ♔a8 2 ♔c7 or 1 ... ♔c8 2 ♔a7, followed by the advance of the pawn. Even with White to move, there are few problems, for after 1 ♔a6 ♔a8 2 b6 White has the opposition, so wins as we have seen above. All similar positions are won, except for those which again involve the rook’s pawn.

It is, however, worth pointing out one small fact about positions with a knight’s pawn. Returning to the upper half of diagram 18 with White to move, it may seem at first sight that White can also win with 1 ♔c6, as 1 ... ♔c8 2 b6 is lost for Black. However, 1 ♔a6! is the correct move although White can reach this position again even after 1 ♔c6 which Black answers with 1 ... ♔a7!.

If White now carelessly plays 2 b6+? Black replies 2 ... ♔a8! with a draw, for both 3 ♔c7 and 3 b7+ ♔b8 4 ♔b6 give stalemate. So White must swallow his pride and play 2 ♔c7 ♔a8 3 ♔b6! ♔b8 4 ♔a6! returning to the winning plan.

If the white king is in front of the pawn but not so advanced, we arrive at the left half of diagram 20.

In this typical position the win depends on who has the move. If White has the opposition, then Black loses after 1 ... ♔b7 2 ♔d6 ♔c8 Or 2 ... ♔b8 3 ♔d7. 3 c5 ♔d8 4 c6 ♔c8 5 c7 etc. However, with White to move, Black draws after 1 ♔d5 ♔d7 2 c5 ♔c7 3 c6 ♔c8! 4 ♔d6 ♔d8 with the well-known drawing position.

From this example, it is clear that White wins easily if his pawn is further back, for in this case he can always gain the opposition by moving the pawn. Hence a useful rule for conducting this type of ending is as follows: the white king is advanced as far as possible in front of his pawn (of course, without losing the latter), and only then is the pawn moved.

The right half of diagram 20 illustrates the application of this rule. If Black has the move, he draws easily with 1 ... ♔g4 or 1 ... ♔f4, but White to move wins in the following instructive way: 1 ♔g3! Gaining the opposition, as compared with 1 ♔f3? ♔f5! when Black has the opposition and draws. 1 ... ♔f5 2 ♔f3! Maintaining the opposition; note that 2 f4? ♔f6 would again draw. 2 ... ♔e5 3 ♔g4 ♔f6

4 ♔f4! Once more White takes over the opposition and applies our rule of advancing his king without moving the pawn; a mistake would be 4 f3? ♔g6 5 ♔f4 ♔f6! drawing. 4 ... ♔e6 5 ♔g5! ♔f7 6 ♔f5 6 f3 is possible, but not 6 f4? ♔g7! drawing. 6 ... ♔e7 7 ♔g6 ♔e8 8 f4 Only now, with the white king on the sixth rank, is the pawn advanced; 8 ♔g7 would be pointless, as 8 ... ♔e7 9 f4 ♔e6 would force 10 ♔g6. 8 ... ♔e7 9 f5 ♔f8

10 ♔f6! It is vital to gain the opposition once more, as 10 f6? ♔g8 only draws. 10 ... ♔e8 11 ♔g7 ♔e7 12 f6+ and the pawn queens.

In conclusion we would like to mention two exceptional cases involving the rook’s pawn. The defence has better chances in this type of ending, drawing from positions that would be hopeless with any other pawn. For example, in the left half of diagram 23, even with the move White cannot win.

After 1 ♔a7 ♔c7 2 a6 ♔c8 3 ♔a8 Or 3 ♔b6 ♔b8. 3 ... ♔c7 4 a7 ♔c8 White himself is stalemated for a change. As a rule we can state that Black draws if he can reach the critical square c8 (or f8 on the other wing). An obvious exception to this rule is when the white king already occupies c6 or b6 and 1 a7 can be played.

The right half of diagram 23 gives us another draw for Black in a situation that would be a loss against any other pawn. Again White cannot win even with the move, as 1 h5 ♔f6 2 ♔h7 ♔f7 3 h6 ♔f8 gives us the drawing position we have just seen. So in general Black draws against a rook’s pawn.

With this example we complete our treatment of elementary endings and move over to more complicated cases, dealing in turn with pawn, queen, rook, bishop, and knight endings. We shall however examine only those positions illustrating general principles which can be applied to various endings. As already stated, we are not compiling an endgame reference book but presenting important basic positions which every chess player must know how to handle.

2 Pawn Endings

It may perhaps seem rather strange that we should begin with pawn endings, but there are good reasons for this. Firstly, pawn endings are relatively simple in form (though not necessarily in content!), consisting as they do of few men, and thus provide us with the best overall view of endings and their treatment. Secondly, pawn endings usually arise from other endings and represent so to speak the cornerstone of the whole of endgame theory.

We have already examined those elementary pawn endings which are the basis of all pawn endings. If these examples have given the reader the impression that pawn endings are the easiest of the endgames, he is sadly mistaken. As we shall see later, some pawn endings are very complex and difficult to play for the uninitiated.

King and Pawn against King

We return again to this ending which we have already examined in our section on elementary endings. As a test-piece we shall consider diagram 24 which cannot be solved immediately by applying our given principles. We shall also explain more fully the term ‘distant opposition’.

If Black has the move he cannot be prevented from reaching f4 with a draw, as we have already seen. The matter becomes more complicated, however, if White has the move. What will the result be then? To answer this question, we must examine the position in a little more detail. As we have seen in previous examples, White wins if his king can reach f6 with Black to move. His first move is naturally 1 ♔e2 (or 1 ♔g2 giving similar variations) and it is Black who must select the best defence. Obviously after 1 ... ♔f5? 2 ♔f3! White has attained his objective, and the same applies after 1 ...♔e5 2 ♔e3 ♔f5 3 ♔f3. The only correct defence lies in 1 ... ♔e6! in order to answer 2 ♔e3 with 2 ... ♔e5 and 2 ♔f3 with 2 ... ♔f5 gaining the opposition and drawing. The move 1 ... ♔e6! gave Black the distant opposition and this is converted into the close opposition as the kings approach each other. This example shows us the basic form of the distant opposition; we shall later examine far more complex examples of its application.

The theory of the opposition is important and reasonably straightforward, but a player can manage without it if he understands the theory of ‘related squares’. This theory is sometimes even more comprehensive and comprehensible than the application of the opposition rule, so let us examine it further by returning to diagram 24.

What are ‘related squares’? Let us assume that the white king is on f3 and his black counterpart on f5, when it is now known that White wins if it is Black to move. We can call these ‘related squares’ i.e. when the black king is on f5, White’s king needs to be on f3 to win; or if Black wishes to draw, he must play his king to the related square after White’s king goes to f3.

Now let us try to find other pairs of related squares, from the defender’s point of view. We know that the white king cannot be allowed to reach f4, when he wins in all variations. This means that if the white king is on e3, threatening to go to f4, the black king must be ready to play to e5, f5 or g5; but g5 is no good, for with ♔e4 White wins at least the f4 square; nor is f5 suitable for the black king, as he must be ready to occupy this square, in case the white king goes to f3. There remains only e5, making this the related square of White’s e3. To continue this logic, which black square corresponds to White’s e2? As White can go to e3 or f3 from this square, Black must have a related square from which he can reach e5 and f5, i.e. e6 or f6.

By means of this process we have rediscovered the correct defence for Black. After 1 ♔e2, only 1 ... ♔e6! is sufficient to draw. As we have seen above, all other moves lose.

This is, of course, a simple illustration of related squares, but we shall later give instructive examples of the usefulness of this method of calculation.

King and Pawn against King and Pawn

Once again, for this type of ending there are no general rules for winning or drawing, as everything depends on the placing of the pieces. Normally these endings result in a draw, so we are primarily interested in those cases where White can force a win. First of all, let us divide our material into two groups:

The Pawns are on the same file

In this case, we can take diagram 25 as our basic position.

Such positions are drawn whoever has the move and however many ranks back we move the pawns. If White has the move, Black has the opposition and clearly draws after 1 ♔g4 ♔g6 2 ♔f4 ♔f6 etc. If Black has the move, then he must lose the pawn as follows:

1

…

♔e6

2

♔g5

♔e7

3

♔f5

♔d6

4

♔f6

♔d7

5

♔e5

…and the pawn falls, as 5 ... ♔c6 6 ♔e6 would still win it. However, Black can still draw by applying the principles we gave in our elementary endings.

5

...

♔e7!

6

♔xd5

♔d7!

Gaining the opposition and drawing as already seen.

The situation changes drastically, however, if the pieces in diagram 25 are moved up one or two ranks. Admittedly, White to move cannot win, but if Black has the move, he is lost. He loses his pawn as we have just seen, but the white king meanwhile reaches the sixth rank, with pawns other than the rook’s pawn, to produce the same result. An exceptional case is when the black pawn is on g7 or b7. The black king can then head for the corner where he is stalemated if the white king approaches. Rook’s pawn positions are drawn, as always.

Let us next examine a few positions in which both kings have more room to manoeuvre, beginning with diagram 27.

Such positions often occur in practice and their correct evaluation is therefore important. We know that White wins if he can capture the pawn, and if he has the move he can win comfortably, as Black cannot gain the opposition. Play might continue as follows:

1

♔c4!

The only way to win. If 1 ♔d4 ♔d8! Black has the opposition and draws.

1

...

♔d7

2

♔b5!

Again taking the diagonal opposition. Not 2 ♔c5? ♔c7! drawing.

2

...

♔c7

3

♔c5

♔d7

4

♔b6

♔d8

5

♔c6

♔e7

6

♔c7

♔e8

7

♔d6

♔f7

8

♔d7

…and wins.

This is one possibility, but Black can also attempt to set up a counterattack on the white pawn by 1 ... ♔f7.

We then have:

1

♔c4!

♔f7

2

♔c5

♔g6

Once again, this is a common situation, with both kings coming in at the pawns from opposite wings. A typical error would now be 3 ♔d6? when 3 ... ♔f5! would even win for Black! A useful rule to remember in such situations is that the winner must be able to attack the pawn from one square below (here d7), in order to maintain the attack whilst guarding his own pawn next move (♔d6). So White continues:

3

♔c6!

As before the white king heads for d7, whereas Black heads for f4. It is clear that in this case White arrives first.

3

...

♔g5

If 3 ... ♔f5 4 ♔d6 wins at once.

4

♔d7!

♔f5

5

♔d6

…and wins.

Of course, with rook’s pawns the winning chances are reduced, but diagram 29 shows us a subtle and unexpected winning manoeuvre.

This position occurred in a tournament game W. Schlage – C. Ahues, Berlin 1921. With White to move, Black must obviously lose his pawn, but this seems unimportant for, in the five moves it takes White to win the pawn, the black king can reach the drawing square c7. Is the position drawn then? The game continuation was in fact 1 ♔e6 ♔c3 2 ♔d6? ♔d4 3 ♔c6 ♔e5 4 ♔b7 ♔d6 5 ♔xa7 ♔c7 etc, with a draw.

But White could have won by choosing the correct route for his king. In pawn endings it is sometimes possible for the king to choose a diagonal route which is no further in move count but which restricts the route of the enemy king. White should have played:

1

♔e6

♔c3

2

♔d5!

As can be seen, White still captures the pawn in five moves but prevents the black king’s approach via d4, e5 and d6. As a result he cannot reach c7 in time and is lost.

2

...

♔b4

If 2 ... ♔d3 3 ♔c6 ♔e4 4 ♔b7 ♔d5 5 ♔xa7 ♔c6 6 ♔b8 wins.

3

♔c6

♔a5

4

♔b7

♔b5

5

♔xa7

♔c6

6

♔b8

…and the pawn queens. A simple but instructive example.

It is interesting to note that if Black’s king had originally stood on the seemingly worse square h2, instead of b2, the game would have been drawn, as White cannot prevent the approach of the black king without wasting time himself.

The Pawns are on different files

In such positions, if the pawn can be stopped by the opposing king, the result is usually a draw, unless White can capture the enemy pawn under favourable circumstances. As an example of this, consider diagram 30.

F. Dedrle 1921

White easily wins the black pawn and it appears as if 1 ♔c3 ♔e5 2 ♔b4 ♔d5 3 ♔xa4 etc would clinch matters. However, Black has the resource 1 ... a3! which draws after both 2 bxa3 ♔e6 3 ♔c4 ♔d6 and 2 b4 ♔e6 3 ♔b3 ♔d6 4 ♔xa3 ♔c6 5 ♔a4 ♔b6 etc. In order to win, White must plan for this black defence and be ready to capture the pawn with his king whilst keeping his own pawn as far back as possible, as follows:

1

♔b1

a3

The best defence, as White wins easily after 1 ... ♔e5 2 ♔a2 ♔d4 3 ♔a3 ♔c5 4 ♔xa4 ♔b6 5 ♔b4! etc.

2

b3!

As will soon be seen, 2 b4 would only draw.

2

...

♔e5

3

♔a2

♔d5

4

♔xa3

♔c5

5

♔a4

♔b6

6

♔b4!

…and wins. It is clear that, with the pawn on b4, this last move would be impossible, whereas now we have reached a well-known winning position.

There are very interesting possibilities when both passed pawns cannot be stopped. Often the game can be won by instructive king manoeuvres, using the above-mentioned idea that in chess the shortest distance between two points is not necessarily a straight line. Let us examine an ending by Grandmaster O. Duras (diagram 32).

A cursory glance might lead us to believe that the position is equal, for both pawns still stand on their original squares and the placing of the white king is only slightly better. In the event, however, this minimal advantage, combined with the fact that White has the move, surprisingly gives him a forced win. Nevertheless, he must play most accurately to achieve this result, in particular when choosing the correct positioning of his king.

1

♔c5!

Clearly the white king must in some way support the advance of his pawn, as otherwise the black king can stop it. But why this move which apparently places the king on an unfavourable square, in the firing line of a future black queen? The remaining moves provide an explanation.

A

1

...

♔g6

Black attempts to stop the white pawn. 1 ... g5 will be discussed in B.

2

b4

♔f7

3

b5

♔e7

4

♔c6!

Now we see why 1 ♔c5 was essential. The game would be drawn after both 4 b6 ♔d7 and 4 ♔b6 g5 5 ♔c7 g4.

4

...

♔d8

The point is that the black king is now unfavourably placed on the back rank where he can subsequently be checked by the white queen.

5

♔b7!

g5

6

b6

g4

7

♔a7 g3

8

b7

g2

9

b8♕+

…and wins.

B

1

...

g5

Instead of trying to stop the advance of the enemy pawn, Black attempts to push his own through, a line which is all the more tempting because he would queen with check. However, the white king now reveals his flexibility with the following subtle win:

2

b4

g4

3

♔d4!

The black pawn will now require support from his king, but this means that White can drive the king onto a square from which he can be checked. Note that 3 b5? g3 would win for Black.

3

...

♔g5

3 ... g3 4 ♔e3 ♔g5 5 b5! would lead into the text variation, but not here 5 ♔f3? ♔f5 drawing.

4

b5

g3

If Black tries to hold off the white king with 4 ... ♔f4 then the white pawn queens first with check.

5

♔e3

♔g4

6

b6

♔h3

7

b7

g2

8

♔f2

♔h2

9

b8♕+

... and wins.

A magnificent study, revealing with limited material the complexities that some pawn endings can contain. Among countless compositions we could quote many other examples illustrating surprisingly deep ideas arising from relatively simple positions.

For the moment, let us consider one more study which is probably the most famous example in chess literature of king and pawn on either side.

R. Réti 1922

Although White is to move, he appears hopelessly lost, for the black pawn is going to queen and White needs at least two tempi to stop it. His own pawn seemingly offers little hope as it can easily be stopped by the black king. However, the geometrical motif once more comes into play, as the white king performs wonders:

1

♔g7

h4

2

♔f6

♔b6

So White has already won one tempo by forcing Black to make a time-wasting move. If instead 2 ... h3, then 3 ♔e7 h2 4 c7 draws, as both pawns queen at the same time. Black’s first two moves could have been inverted, for after 1 ... ♔b6 2 ♔f6 the threat of 3 ♔g5 would force 2 ... h4.

3

♔e5!

The point of the whole play. As White now threatens to catch the pawn with 4 ♔f4 Black has no choice.

3

…

h3

4

♔d6

h2

5

c7

h1♕

6

c8♕

...with a clear draw.

Who would have assumed this possible in the initial position? These examples are by no means comprehensive, but they indicate some of the various possibilities contained within the simplest pawn endings. Later we shall meet further examples, when more complicated positions simplify during the solution.

King and two Pawns against King and Pawn

Positions with king and two pawns against king and pawn represent a very complicated section of pawn endings. There are many and varied possibilities so we must be systematic if we are to obtain an overall picture of collected material. As a rule, the side with the greater material wins especially if his passed pawn is at a distance from the other pawns and can thus drag the defending king away.

There are also, however, many positions which admit of no easy win, and it is these positions which interest us most and to which the following section is mainly devoted.

Isolated Pawns with a Passed Pawn

We intend to classify endings of two pawns against one by separating them into various groups depending on the position of the white pawns. Firstly we shall examine those in which the white pawns are isolated and one of them is passed. As already mentioned, White wins fairly easily here if the pawns are some distance apart, so we shall only examine those positions where there is one file between the pawns, which means that the passed pawn cannot take the black king too far away from the scene of action. A typical position is diagram 38.

As could be expected, this position is a win for White, whoever has the move. Let us assume that White is to move.

1

d5

♔d7

White wins easily after 1 ... ♔c5 2 ♔e5 ♔xb5 3 d6 ♔c6 4 ♔e6 etc.

2

♔e5

♔e7

3

d6+

♔d8!

The most cunning defence, setting White a few problems. After 3 ... ♔d7 4 ♔d5 wins, whereas now 4 ♔d5 ♔d7 or 4 ♔e6 ♔e8 5 d7+ ♔d8 would not help White. However, White can now transpose to one of the elementary endings.

4

d7!

The simplest winning method, giving up the pawn but gaining the opposition, then capturing the black pawn with a standard win. There is a more complicated way to victory by 4 ♔d4 ♔e8 5 ♔e4 ♔d8 6 ♔e5!, a possibility we shall come back to again.

4

...

♔xd7

Or 4 ... ♔e7 5 d8♕+ ♔xd8 6 ♔d6 wins.

5

♔d5

♔c7

6

♔e6

…and wins.

Now let us see what happens if we bring the pieces one rank further back, giving us diagram 40.

This position is equally won for White, but he must here be more careful about a counterattack on his own pawn. Play could continue:

1

d4

♔c4

Hopeless would be 1 ... ♔d6 2 ♔e4 ♔e6 3 d5+ ♔d7 4 ♔e5 ♔e7 5 d6+ ♔d7 6 ♔d5 followed by 7 ♔c5 winning.

2

♔e4

♔xb4

3

d5

♔c5

Black has to place his king on this unfavourable square to stop the white pawn queening first.

4

♔e5

b4

5

d6

b3

5 ... ♔c6 6 ♔e6 would not alter the situation.

6

d7

b2

7

d8♕

b1♕

Both sides have a queen but Black’s queen is lost after:

8

♕c8+

♔b4

9

♕b7+ winning.

One might think that all positions like diagram 40 are won for White but there is a surprising exception. This is when the black and white pawns are on the bishop’s file as in diagram 42.

At first glance there seems no difference, as after 1 e4 ♔e6 2 ♔f4 ♔f6 3 e5+ ♔e7 4 ♔f5 ♔f7 5 e6+, or 1 ... ♔d4 2 ♔f4 ♔xc4 3 e5 ♔d5 4 ♔f5 c4 5 e6 c3 6 e7 c2 7 e8♕ c1♕ 8 ♕d8+ followed by 9 ♕c7+, White wins in the same way we have seen above. However, there is one subtle difference, as follows:

1

e4

♔d4!

2

♔f4

♔xc4

3

e5

3

…

♔b3!!

With this move Black exploits the peculiar fact that a queen cannot win against a bishop’s pawn on the seventh rank when the king is too far away. Insufficient would be 3 ... ♔d3 4 e6 c4 5 e7 c3 6 e8♕ c2 7 ♕e3+ winning.

4

e6

c4

5

e7

c3

6

e8♕

c2

…and the ending is drawn because White cannot stop Black’s king reaching b2. We shall look at this in more detail in our section on queen endings but feel that it is worth a mention here.

It is clear that if positions similar to diagram 40 are moved one rank down, they are drawn, as Black can always attack the white pawn. Yet, surprisingly, if we push the position two ranks up, so that the black pawn is on its original square, this also limits White’s winning chances. The black king remains in front of the pawns and usually escapes with stalemate, but it would lead us too far astray to examine this aspect now.

In conclusion we should mention that positions similar to diagrams 38, 40 and 42 are easily won for White, if Black has the move. In this case, the white pawn cannot be attacked, so White has only to advance his passed pawn, the sole exception again being positions with the black pawn on its original square.

Usually, rook’s pawns significantly reduce White’s winning chances, but in the positions examined this is surprisingly not the case. Consider diagram 45.

H. Fahrni – S. Alapin

This position could have arisen from our analysis of diagram 38 moved one file to the left with White having advanced his passed pawn. With Black to move the win is easy, but how does White win if he is to move? The same play as in diagram 38 does not work here, as 1 ♔d5 ♔c8 2 c7? ♔xc7 3 ♔c5 ♔b7, or here 2 ♔d6 ♔d8 3 c7+ ♔c8 both give Black a draw. So the win is not to be achieved by simple means and we must look a little deeper. As White would win if Black had the move, could we perhaps lose a tempo and bring about this situation?

Let us for a moment return to our theory of related squares. We have seen that Black must answer ♔c5 with ... ♔c7 and ♔d6 by ... ♔d8, so here are two pairs of related squares. Which black square corresponds to White’s d5? The white king can go to c5 or d6 from this square, so the black king must be able to go to the related squares c7 and d8. The only square is then c8, giving us another pair of related squares.

Continuing this process, we find that White’s c4 (controlling d5 and c5) corresponds to Black’s b8 and d8 (controlling c8 and c7); it can indeed happen that two squares relate to one only. And what about White’s d4? As this square controls d5 and c5, Black’s related squares are b8 and d8.

By doing all this preliminary work, we have already solved our problem. Let us assume that White has played ♔c4 and Black has selected the related square b8. White then plays his king to d4, compelling Black to go to the related squares b8 or d8. But he is already on b8 and cannot move two squares to d8. So he has to move to an unrelated square, when he loses. Let us see how this works out in a given sequence of moves:

1

♔d5

♔c8

2

♔c4

It does not matter here whether c4 or d4 is selected, as they both lead to the same result.

2

...

♔d8

Or 2 ... ♔b8.

3

♔d4!

♔c8

If 3 ... ♔c7 4 ♔c5 wins quickly.

4

♔d5!

♔c7

5

♔c5

…and White has reached the diagrammed position with Black to move. After 5 ... ♔d8 6 ♔d6 ♔c8 7 c7 ♔b7 8 ♔d7 ♔a7 9 ♔c6 (not 9 c8♕ stalemate) White mates in two moves.

Let us close this section with one example of this type of ending.

White’s task is made extremely difficult by the fact that his passed pawn is on the rook’s file and that he has no manoeuvring space for his king to the left of this pawn.

His only chance is to attack from the right, when he must continually reckon with a counterattack by the black king. For example, after the direct attempt 1 ♔c3 ♔a4 2 ♔d3 Black plays 2 ... ♔b4! (not 2 ... ♔a3 3 ♔e4 ♔xa2 4 ♔d5 winning easily), winning one of White’s pawns, with a clear draw. Again we must look a little deeper.

In order to win, the white king must reach d5 without allowing Black in the meantime to capture the a-pawn and be in a position to guard his pawn by ... ♔b4. When Black plays ... ♔b4 White must be in a position to play ♔d3 after which Black is in zugzwang and cannot prevent ♔e4-d5. So our first pair of related squares are White’s d3 and Black’s b4.

Let us proceed further. When the black king is on a3, threatening to take the a-pawn, White must be ready to answer this threat with ♔d5, so White’s e4 and Black’s a3 are related squares. Consequently Black’s a4 (controlling a3 and b4) corresponds to White’s e3 (controlling e4 and d3), and Black’s a5 (controlling a4 and b4) corresponds to White’s d2 (controlling d3 and e3).

Once again we have now carried out the most difficult part of our task. There only remains for White to reach d2 by careful manoeuvring and Black cannot prevent the white king’s advance to d5. For completeness we might mention that if the black king is on a6 or b6, the white king can occupy c1, c2 or c3, when he can always answer ... ♔a5 with ♔d2.

From our last comment it is clear that Black to move loses quickly, for after 1 ... ♔b6 (or a6) White plays 2 ♔c3 (or c2) 2 ... ♔a5 3 ♔d2! immediately. With White to move, matters are more complex, but the win can be forced as follows:

1

♔a3!

The only move, otherwise Black plays 1 ... ♔a4 and White’s king is too far from the related square e3. The text move wins an important tempo.

1

...

♔b6

2

♔b2

2

…

♔a5

The best, as other moves allow 3 ♔c3 with an easy win. It goes without saying that Black would get nowhere by playing his king to the centre.

3

♔b3!

Again winning a tempo.

3

...

♔b6

4

♔c3(c2)

♔a5

If 4 ... ♔a6 White wins by ♔c2(c3)-d3-e4 d5 etc.

5

♔d2!

The winning move, not found until later by Kling. The theory of related squares, however, makes it all so easy!

5

…

♔a4

6

♔e3!

♔b4

7

♔d3

...and White reaches his goal, winning easily after 7 ... ♔a3 8 ♔e4 ♔xa2 9 ♔d5 or here 8 ... ♔a4 9 ♔d5 ♔b4 10 a3+ etc.

There are many such examples in which the apparently complicated solutions can be readily understood in the light of related squares, whose importance will be seen in other positions to which we shall now proceed.

Isolated Pawns without a Passed Pawn

This kind of position gives the defending side much greater chances of obtaining a draw, especially if the attacker has no tempo moves available with his pawns. The deciding factors here are the placing of the kings and the gaining of the opposition. Consider diagram 52.

This is a typical situation in which at first glance it is difficult to say whether White wins or not. A thorough analysis is required. As a general rule, we can say that the defending side should restrict as far as possible the freedom of the white pawns, so that they have no tempo moves at their disposal. On the other hand, the attacking side must try to maintain this freedom and attempt to bring his king as far forward as possible. If the reader keeps these points in mind, he will easily understand the following variations. We shall begin with the simplest case, with Black to move.

1

...

e5!

2

f4

King moves do not help, e.g. 2 ♔e4 ♔e6 or 2 ♔d2 ♔e6 3 ♔c3 ♔d5 etc. The text move is the sole winning attempt.

2

...

♔f5

Black’s only move to draw, as 2 ... exf4+ 3 ♔xf4 ♔e6 4 ♔e4 ♔d6 5 ♔d4! would win for White, whereas now 3 fxe5 ♔xe5 is completely drawn.

Apart from this simple line, Black also has another drawing method, requiring accurate play, as follows:

1

...

♔e5

But not 1 ... ♔f5 2 d4 ♔g6 3 ♔f4 ♔f6 4 ♔e4 followed by 5 ♔e5 winning, as will be seen later.

2

♔e2

After 2 d4+ ♔d5 or 2 f4+ ♔f5, Black threatens 3 ... e5 and if 3 f4 (or d4), we would arrive at a symmetrical position to the one arising after Black’s 1 ... e5.

2

...

♔f4

Other king moves also draw, but the text move is the most instructive.

3

d4

3

…

♔g5!

This time the only move, for 3 ... ♔f5? 4 ♔e3 wins for White as we have seen. Black must make sure that he can answer ♔e3 with ... ♔f5, and the draw is forced, as White cannot strengthen his position.

Going back to diagram 52, with White to move, he wins as follows:

1

♔e4!

Obeying our rule about advancing the king as far as possible! This is the only way to win, as 1 ♔f4? e5+ 2 ♔g4 ♔g6, or 1 f4 ♔f5 2 ♔f3 e5 only draw, as does 1 d4 ♔f5 2 ♔d3 ♔f4 3 ♔e2 ♔g5! etc.

1

...

♔f7

The best chance. After 1 ... e5 2 f4! or 1 ... ♔e7 2 ♔e5 ♔d7 3 d4 ♔e7 4 f4 ♔d7 5 d5 (or 4 ... ♔f7 5 f5) White wins comfortably.

2

♔e5

♔e7

3

f4

♔d7

3 ... ♔f7 loses at once to 4 f5.

4

♔f6!

If 4 d4? ♔e7! Black would draw, as the reader can check for himself.

4

...

♔d6

5

d4

Winning the opposition and the game. Also possible is 5 ♔f7, as 5 ... e5 6 f5 wins.

5

...

♔d7

6

♔f7

♔d6

7

♔e8!

♔c6

8

♔e7

♔d5

9

♔d7

♔xd4

 10

♔xe6 and wins.

It is worth noting that White won this ending only because he had the tempo move 5 d4 at his disposal. For instance, if we look at the position after White’s sixth move and give him the move instead of Black, with best defence it is only a draw. Let us examine this in more detail.

In order to win, White must gain the opposition with his king on f7 when Black’s king is on d7, as we have seen. Other related squares are White’s f6 and f8 corresponding to Black’s d6 and d8, and if White’s king is on the knight’s file, then g8 and g7 correspond to Black’s e8 and e7. But what about g6? Black’s e6 is occupied by his pawn so he has here only the distant opposition on c6, a square to which Black must be ready to play as soon as White plays ♔g6.

This means that the game might continue 1 ♔f6 ♔d6 2 ♔g7 ♔c7! Not 2 ... ♔e7? 3 ♔g6! ♔d6 4 ♔f6 ♔d7 5 ♔f7 winning. 3 ♔g6 ♔c6! 4 ♔f7 ♔d7 5 ♔g8

5 … ♔c8! Again the only move, as both 5 ... ♔e8 6 ♔g7 ♔e7 7 ♔g6! and 5 ... ♔c6 6 ♔f8 ♔d6 7 ♔e8 lead to a loss. 6 d5 There is nothing else. 6 ... ♔d7!. Not 6 ... exd5? 7 f5 and White queens with check. 7 ♔g7 Or 7 dxe6+ ♔xe6 and 8 ... ♔f5. 7 ... exd5 and both pawns queen together.

If White’s two pawns are doubled, he can only hope to win if his rear pawn has important tempo moves available. Consider the interesting position in diagram 60.

As the black king is much more actively placed than the white king, it seems at first unlikely that White can win. However, his pawn on f3 gives him a vital tempo at the critical moment, and he wins nicely as follows:

1

♔f5!

If his pawn were on f2 he would have no problems and could win at once with 1 ♔g5 ♔e5 2 f3, but in this position 1 ♔g5 would only draw after 1 ... ♔e5 2 f4+ ♔e6 3 f5+ ♔e5, and 1 ♔g4 fails to 1 ... ♔e6 2 ♔g5 ♔e5 when he is in zugzwang. He must first bring his pawn to f4 to guard e5 from the black king.

1

...

♔d6

White was threatening 2 f4 followed by the penetration of his king to h6 via h5. For example, if 1 ... ♔d4 2 f4 ♔d5 3 ♔g4! (not 3 ♔g5 ♔e6! and White is in zugzwang) 3 ... ♔d6 4 ♔h5 ♔e6 5 ♔g5 and 6 ♔h6 wins. So Black goes back with his king to prevent entry.

2

f4

♔d7

3

♔g4!

Again 3 ♔g5? ♔e6! draws for Black.

3

...

♔e8

4

♔h5

As will be seen later, 4 ♔g5 ♔f8 again puts White into zugzwang.

4

...

♔f8

5

♔g5

Now it is Black who is in zugzwang and he must allow White in on one side or the other.

It is interesting to note that if the whole position were one rank further back, Black would draw by 5 ... ♔f8! waiting to see which way White goes, but he lacks the necessary space here.

5

...

♔g8

Or 5 ... ♔e8 6 ♔h6 ♔f8 7 ♔h7 winning easily.

6

♔f5

6

…

♔h7

It is now too late for 6 ... ♔f8 7 ♔e5 ♔e8 8 ♔d6 ♔d8 9 f5! (the winning tempo!) 9 ... ♔e8 10 ♔c7 winning.

7

♔e4!

White must still proceed carefully. 7 ♔e5 ♔g6! gives Black a draw, as White wants this position with Black to move.

7

...

♔h6

8

♔d5

♔g6

9

♔e5

♔h5

 10

♔d6

♔h6

 11

♔e7

♔g6

 12

f5+ and wins.

A beautiful study with a subtle solution.

Connected Pawns with a Passed Pawn

When White’s pawns are connected and one of them is passed, he usually has excellent winning chances. Black’s defensive possibilities are limited and he can only hope for a draw when White’s pawns are not very advanced or if the black king has an unusually favourable position. In the following we try to indicate the factors by which a position can be evaluated.

Let us start by examining positions with the pawns on the a- and b-files. At the same time we shall consider how far advanced the pawns are, and in this way cover all types of position.

Diagram 65 is a key position in this ending. As it does not matter whose move it is, we shall make White’s task a little more difficult by giving Black the move.

1

...

♔c5

2

♔d3

♔d5

3

♔e3

♔e5

4

♔f3!

We immediately realize the tremendous advantage of a protected passed pawn which does not need the white king to remain near it and yet greatly restricts the enemy king’s activity. In this example the black king dare not leave the quadrant represented by the b5-b8-e8-e5 squares, or else the b-pawn queens. This means that 4 ... ♔f5 cannot be played, so Black is forced to relinquish the opposition.

4

...

♔d5

5

♔f4

♔d6

6

♔e4

White would make no progress with 6 ♔f5 ♔d5, when he would have to return to the fourth rank.

6

...

♔e6

7

♔d4

♔d6

8

♔c4

♔c7

So Black has been compelled to concede White the fifth rank, but he has various defensive possibilities.

9

♔c5

A simpler win is 9 ♔d5 ♔b6 10 ♔d6 ♔b7 11 ♔c5 etc, but we shall give the longer win in order to show one or two instructive points.

9

...

♔b7

 10

♔d5!

White would spoil everything with 10 b6? ♔a6! 11 ♔c6, giving stalemate, and after 10 ♔d6 ♔b6 11 ♔d7 ♔b7 Black keeps the opposition.

 10

…

♔c7

 11

♔e6

♔b6

If 11 ... ♔b7 12 ♔c8 wins.

 12

♔d6

♔b7

 13

♔c5(d7)

…with an easy win.

If the position in diagram 65 is moved one rank up (white pawns on a5 and b6 etc), it can no longer be won. Although the white king reaches c6, the b-pawn cannot be advanced because of the stalemate we have already seen. Equally drawn is the position one rank further up (White’s pawns on a6 and b7 etc), for the black king can clearly not be driven from the b8 and c7 squares.

If this position in diagram 65 is moved one rank down (white pawns on a3 and b4 etc), it is still won, but two ranks lower (white pawns on a2 and b3 etc) brings about a change. White to move still wins, 1 ♔c2 ♔c5 2 ♔d3! ♔b4 3 ♔d4 ♔b5 4 ♔c3! ♔c5 5 b4+ etc, but Black to move can draw by counterattacking the pawn with 1 ... ♔c3 2 ♔d1 ♔b2!, when White must force stalemate.

Let us now turn to positions where the white pawns are on the b- and c-files. Move the position in diagram 65 one file to the right (white pawns on b4 and c5 etc) and it is even easier for White to win, as is the same position one rank further down (white pawns on b3 and c4 etc). Further explanation seems unnecessary.

It is equally clear that this position moved two ranks down (white pawns on b2 and c3 etc) or two ranks up (white pawns on b6 and c7 etc) cannot be won for White, just as in the corresponding positions already examined. There is, however, a difference if the position in diagram 65 is moved one file to the right and one rank up, giving us diagram 67.

This position is won for White as follows:

1

...

♔d6

2

♔e4

♔e6

3

♔f4

♔d6

The passed pawn severely restricts the black king’s movements, so that White can immediately advance his king.

4

♔f5

♔c7

5

♔e6

♔c8