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can be supported by a pawn on the next file they need not by any means be at a disadvantage against three united single pawns on the opposite side. For instance, in Diagram 64, if Black had a pawn at QKt3 instead of R2, White would have no winning chances. He could not attack the pawns, nor would any kind of manoeuvres force a passed pawn through. In the diagram, however, White wins through

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Diag. 64

1. K-B5; Black cannot then hold the pawn at B3. 1. … P-R3; 2. P-Kt4.

In this particular case the win is made easy by the fact that the White King is able to attack the Black pawn at once. But even without this advantage, the weakness of

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Diag. 65

doubled pawns usually entails the loss of the game. Diagram 65 may serve as an example.

1. K-Q4, P-B4ch; 2. K-B4, K-B3; 3. P-B3 K-Kt3; 4. K-Q5, P-B3ch; 5. K-B4, and wins.

Doubled pawns are a drawback, even when not isolated, should there be no way of obtaining a passed pawn by exchanging them against a smaller number of single pawns. This is illustrated in Diagram 66, in which Black wins because the three pawns on the King’s side hold up the four White pawns and the Black King can assail the White pawns from the rear,

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Diag. 66

the White King being fettered by the necessity of capturing the QBP. The proper formation for the Black pawns would be at B3, Kt2, R3, after which White cannot force a pawn through by playing P-B4 and P-Kt5, as Black can refrain from making any exchange. Black could not afford to leave the pawns where they are, because even if there were no White pawn at B2, White would, by playing P-Kt5, threaten to win in the following way:

1. P-Kt6, BPxP; 2. P-R6, and P-B6, etc.; or 1. … RPxP; 2. P-B6, with P-R6, etc. In a game Ed. Lasker-Moll (Berlin championship, 1904), from which the position is taken, Black played P-R3 in order to obtain the formation mentioned above, and White resigned after 2. P-B4? P-B3, P-Kt5, K-Q5. There was, however, a pretty win after Black’s P-R3, namely: 2. P-B6, PxP; 3. P-B4, K-Q5; 4. P-Kt5, BPxP; 5. PxP, K-K4; 6. PxP, K-B6; 7. K-B2 and Black is lost, because his own pawn obstructs the square B2, and the King must release the square Kt2, after which the White pawn queens.

This winning combination, however, is only an interesting exception to the rule that positions of this kind are generally won by the side which possesses the passed pawn. In this particular case Black could have made the position secure by obtaining the ideal position of B3 Kt2 R3 for his pawns earlier, before the White pawns could advance so far. In the position of Diagram 66 Black could still have won by playing P-B3. After 2. P-R6, PxP; 3. P-B4, K-Q4; the Black King has time to overtake the passed pawn which results on the Bishop’s file.

To conclude the study of pawn endings with an equal number of pawns on either side, we will discuss Diagram 67,

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Diag. 67

which illustrates a curious position occurring from time to time in practice. Whoever has the move wins by moving into distant opposition. White, therefore, should play K-K5 K-Q5 would lose, as Black would play K-Kt5, protecting his pawn and attacking the White pawn, the protection of which White has to give up next move. In the same way Black with the move cannot play K-Kt5 because White wins the pawn with K-Q5. After 1. K-K5 Black cannot avoid the loss of the game, e.g. K-R3; 2. K-Q5, K-Kt3; 3. K-Q6, and so on. Black with the move wins similarly with K-R5.

We have still to consider end-games in which a draw results in spite of a majority of pawns, or where a win can only be achieved by the sacrifice of an extra pawn.

Diagram 68 shows the latter case. Here White can only win in the following manner: 1. P-Kt4ch, PxPch; 2. K-Kt3, K any; 3. KxP, and wins. Any other way would allow

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Diag. 68

Black to assume the opposition and to force the draw, e.g. 1. K-B2, K-B3! 2. K-Q3, K-Q4, etc.

Not 1. K-B2, K-Kt5? 2. K-Kt2, K-B4, 3. K-B3, etc., as in Diagram

57.

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Diag. 69

A counterpart to this position is found in Diagram 69, which shows one of the few cases in which the possession of an extra pawn does not force a win. It seems at first sight as if White could win by simply assuming the opposition with 1. K-K4 continued: … K-K2; 2. K-Q5, K-Q2; 3. P-B5, K-K2; 4. K-B6, etc. But Black would reply 1. … P-B4ch! and after 2. PxPch, K-B3 followed by KxP ensure the draw.

We come now to those end-games in which pieces as well as pawns are left on the board.

As it is my aim to give typical examples, I shall confine myself to positions where there is only one piece besides the King. Most end-games with several pieces can be reduced to that.

In nearly all end-games with pieces the King’s manoeuvres used in pawn endings are of no avail, as far as opposition is concerned, as the advantage of opposition means that the opponent is forced to move his King, and as long as there are pieces on the board, such β€œforced move” positions are infrequent. However, the strength of the pawn position is of the same importance as in pawn endings, just as the command of as many squares as possible is essential for the King. A third and very important factor is again the mobility of pieces.

A good example is found in Diagram 70, a position from a game Post-Leonhardt (Berlin Jubilee Tournament, 1907).

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Diag. 70

Black’s pawn position is weaker, because the White pawns, being on Black squares, cannot be attacked by the Bishop, whilst Black has two isolated pawns on White squares. Furthermore the Black Bishop has less mobility than the White one, and finally the Black King is tied to his Q3, to prevent White’s entry at B5 or K5. These drawbacks decide the issue. 1. … B-R2; 2. P-R4, B-Kt3; 3. B-B2, P-R4. (After B-R2 White would command the square at Kt6 through P-R5); 4. B-Q3, B-R2; 5. B-B1, and Black resigns, for White threatens to establish his Bishop at B3, where the pawns at Q5 and R5 are both attacked, whilst the Black Bishop is at once forced to occupy the only square from which both pawns are covered, namely B2. As this square must be abandoned in the next move, Black loses a pawn and the game.

5. … B-Kt1; 6. B-K2, B-B2; 7. B-B3, and wins, or 5. … B-Kt3; 6. B-Kt2, B-B2; 7. B-B3, and wins.

A corresponding instance of KNIGHT V. BISHOP is the end-game Blackburne-Schlechter (p. 102).

It is difficult to gauge the relative value of Bishop and Knight in the end-game. The Knight has the advantage of access to all squares; against that the Bishop is able to fight at long range, and offers opportunities of gaining moves in certain positions where there is a β€œforced move” (compare p. 90).

As already stated, two Bishops are superior to two Knights because the limitation of the colour of squares ceases. A Rook generally wins against a Bishop or a Knight, sometimes even against a majority of one or two pawns, provided,

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