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win is by sacrificing the extra pawn, I shall treat of end-games in which positional advantages ensure the victory although the pawns are equal. Here we shall find simple cases in which pawn manoeuvres bring about the win, and more intricate ones in which King moves are the deciding factor.

Of the former the most important type is the end-game with the β€œdistant passed pawn.” A typical example is the position in Diagram 58, in which Black wins.

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A B C D E F G H

 

Diag. 58

The King’s moves are outlined by the necessity of capturing the opposing passed pawn, after which the Black King is two files nearer the battle-field (the Queen’s side), so that the White pawns must fall.

1. K-Kt2, K-Kt2; 2. K-Kt3, K-B3; 3. K-Kt4, K-K4; 4. P-B4ch, K-B3; 5. K-Kt3, P-R4; 6. K-R4, K-B4; 7. KxP, KxP; 8. K-Kt6, K-K4, and so on.

For similar reasons the position in Diagram 59 is lost for Black. White obtains a passed pawn on the opposite wing to that of the King. He forces the Black King to abandon his King’s side pawns, and these are lost. I give the moves in full, because this is another important example characteristic of the ever recurring necessity of applying our arithmetical rule. By simply enumerating the moves necessary for either player to queen his pawnβ€”SEPARATELY for White and Blackβ€”we can see the result of our intended manoeuvres, however far ahead we have to extend our calculations.

 

1. P-R4, K-K3; 2. P-R5, PxP; 3. PxP, K-Q3

Now the following calculations show that Black is lost. White needs ten moves in order to queen on the King’s side, namely, five to capture the Black King’s side pawns (K-K4, B5, Kt6, R6, Kt5), one to free the way for his pawn, and four moves with the pawn. After ten moves, Black only

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A B C D E F G H

 

Diag. 59

gets his pawn to B6. He requires six moves to capture the White Queen’s side pawns, one to make room for his pawn at B3, and after three moves the pawn only gets to B6. White then wins by means of many checks, forcing the Black King to block the way of his own pawn, thus gaining time for his King to approach. As we shall see later on (p. 97), if the pawn had already reached B7, whilst under protection by his K, the game would be drawn.

It is necessary to make it a rule to examine positions in which each side has a passed pawn, by counting the moves in the way first shown. It is just because end-games can be calculated to a nicety, there being no moves of which the consequences cannot be foreseen, that we note in contemporary master play a tendency to simplify the middle-game by exchanging pieces, as soon as there is an infinitesimal advantage in the pawn position (compare the game Charousek-Heinrichsen, p. 108).

We will now turn our attention to positions in which the pawns opposed on each wing are of equal number and no passed pawn can be forced through. Everything depends on the relative position of the Kings. The deciding factor in valuing the King’s position is whether pawn moves are possible, or whether they are already entirely or nearly exhausted, so that only manoeuvres by the King are possible. The following illustrations make the position clear. We shall see that the importance of getting the opposition is paramount. Diagram 60 shows a simple instance in which there are no

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A B C D E F G H

 

Diag. 60

more pawn moves. Whoever has the move wins by assuming the opposition. The opposing King must then give the way free to one of the pawns.

The state of affairs in Diagram 61 is similar to that in Diagram 60. Having the move, White plays into opposition and forces his way to Q5, after which Black’s Bishop’s pawn is lost.

1. K-K4, K-Q3; 2. K-B5, K-Q2; 3. K-K5, K-B3; 4. K-K6, K-B2; 5. K-Q5, K-Kt3; 6. K-Q6, and so on (compare Diagram 57). If Black has the move he can only draw, because the White Bishop’s pawn is covered even though Black gains the square at Q5.

1. … K-K4; 2. K-Q3, K-B5; 3. K-Q2!! and whatever Black plays White wins the opposition, so that the Black King’s ingress is stopped; 2. K-K2 loses the game because of 3. … K-K5; 4. K-Q2, K-Q5; 5. K-B2, K-K6; 6. K-B1, K-Q6; 7. K-Kt2, K-Q7; 8. K-Kt1, K-B6; 9. K-R2, K-B7, and wins.

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A B C D E F G H

 

Diag. 61

I shall take this opportunity of explaining what is called β€œdistant opposition.” In Diagram 62, White with the move wins by 1. K-K2, thus assuming β€œdistant opposition” (squares of the same colour!!). If Black now enters his second rank, White immediately plays into opposition on his third rank, e.g. 1. … K-Q2; 2. K-Q3, and still maintains it by 3. K-K3 if Black plays a waiting move such as 2. … K-K2. Now Black has no further waiting moves, as White threatens to capture one of the pawns. But playing into the third rank is of no use, as White then assumes the direct opposition, and wins as in Diagram 60. Black must allow White access to one side or the other. He could not have remained on the first rank at the outset either, for after 1. … K-Q1, White advances through a square, to which Black cannot assume the opposition, namely, 2. K-B3. If now Black wishes to answer the threat of K-B 4-Kt5 and plays K-K2, White answers 3. K-K3 as before.

2. K-K3 or KQ3 would be wrong, as Black would then succeed in assuming the opposition at K2 or Q2, and would be able to maintain it. White would be unable to circumvent this or to attack the pawns.

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A B C D E F G H

 

Diag. 62

In this position, too, there is ample scope for the study of the opposition.

If the pawns are still standing behind, the King who has the most advanced position has always the advantage, because he threatens to attack the opposing pawns should they leave their base. White has more pawn moves at his disposal, and will nearly always succeed in assuming the opposition. For instance, in Diagram 63, White, having the move, wins because his King gets first into the centre of the board.

1. K-K3, K-Q2; 2. K-B4, K-K2; 3. K-Kt5 K-B2; 4. K-R6, K-Kt1; 5. P-KB4, K-R1; 6. P-B5, PxP; 7. K-Kt5, K-Kt2; 8. KxP, K-B2. Black has now the opposition but cannot maintain it, having no pawn moves available. The White King threatens to capture any pawn that ventures forward.

9. K-K5, K-K2; 10. K-Q5, K-Q2; 11. P-B4, P-B3ch; 12. K-K5, K-K2; 13. P-B5, and wins, as Black will soon be compelled to play K-Q2, after which a manoeuvre shown previously gives White the Queen’s Bishop’s pawn.

l3. … P-KR4; 14. P-KR4, P-R4; 15. P-R4! K-Q2; 16. K-B6, K-O1: 17. K-K6, and so on.

If in Diagram 63 the King stood at Q2 instead of B1, he could just manage to draw. White takes eleven moves to capture the Black King’s side pawns, and to queen one of

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A B C D E F G H

 

Diag. 63

his own, as can be easily seen. In eleven moves Black captures the opposing QBP and queens his own. We see here how the King’s position can be counterbalanced by the weakness of a pawn, and lead to a draw. If the White QBP was not isolated but standing, for instance, at QKt2, Black would be lost, as calculation easily shows.

The strength or weakness of a pawn position, which, as we saw, had so deciding an influence in the end-game position just treated, is one of the most important factors in a game of chess, and should have full consideration in the middle game. A pawn, when isolated, is naturally weaker than when it is or can be protected by another. It may easily lead to the loss of a game, as the mobility of the King or a piece is reduced by having to protect the pawn (compare End-game, p. 102).

It is frequently and erroneously thought that DOUBLED pawns as such are a weakness. Doubled pawns are weak when ISOLATED, for they cannot support each other. But if doubled pawns

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