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or K7, or R7 and mate next move.

 

Position 2.β€”White: K at QKt3, RKR2

Black: K at K4

 

1. K-B4, K-Q3; 2. R-K2, K-B3; 3. R-K6ch, K-Q2; 4. K-Q5, K-B2; 5. K-B5, K-Q2; 6. R-K1, K-B2; 7. R-K7ch, K-Q1; 8. K-Q6, K-B1; 9. K-B6, K-Kt1; 10. R-K1, K-R7; 11. R-K8, K-R3; 12. R-R8 mate.

 

Position 3.β€”White: K at QRsq, B at KKtsq, BatKKt2

Black: K at KRsq

1. K-Kt2, K-Kt2; 2. K-B3, K-B3; 3. K-Q4, K-K3; 4. B-R2, K-B3; 5. K-Q5, K-B4; 6. B-K5, K-Kt4; 7. K-K6, K-Kt5; 8. B-QR8, K-Kt4; 9. B-B3, K-Kt3; 10. B-KB6, K-R3; 11. K-B7, K-R2; 12. B-Kt5, K-R1; 13. B-Q1, K-R2; 14. B-B2ch, K-R1; B-B6 mate.

It is more difficult to mate with KNIGHT AND BISHOP. It is only possible to mate on a corner square commanded by the Bishop, as the following argument shows clearly. A mating position in the corner which the Bishop does not command would have to be of the type set out in Diagram 42. Here the Bishop plays on White squares, and the Knight in order to checkmate must move on to a White square; in other words, he must come from a Black one. Therefore, when the Bishop checked on the previous move and drove the King away, the King had the option of two black squares, and had no need to go into the corner one. He is only mated in consequence of a wrong move.

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A B C D E F G H

 

Diag. 42

 

As stated above, however, it is possible in all cases to mate in the corner square which is of the same colour as the Bishop. The King is driven into the corner in this way: the Knight cuts him off such squares as the Bishop does not command. Diagram 43 will serve as an illustration.

1. K-Kt2, K-Kt2; 2. K-B3, K-B3; 3. K-Q4, K-K3; 4. Kt-Kt3, K-B3; 5. B-B3, K-Kt4; 6. K-K5, K-Kt3; 7. Kt-K4, K-Kt2; 8. K-B5, K-R1; 9. K-B6, K-Kt1; 10. Kt-Kt5, K-R1; 11. Kt-B7ch, K-Kt1; 12. B-K4, K-B1; 13. B-R7, K-K1; 14. Kt-K5, K-Q1; 15. Kt-B4, K-B2; 16. B-K4, K-Q2; 17. K-B7, K-B2; 18. K-K7, K-B1; 19. K-Q6, K-Q1; 20. B-Kt6, K-B1; 21. Kt-R5, K-Q1; 22. Kt-Kt7ch, K-B1; 23. K-B6, K-Kt1; 24. K-Kt6, K-B1; 25. B-B5ch, K-Kt1; 26. Kt-B5, K-R1; 27. B-K6, K-Kt1; 28. Kt-R6ch, K-R1; 29. B-Q5 mate.

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A B C D E F G H

 

Diag. 43.

It is impossible to force a mate with the KING AND TWO KNIGHTS. On the same grounds as given with respect to Diagram 42, the mate can only be attained through the opponent making a bad move. But a mate can be forced if the weaker side has a spare move which prevents the stalemate, e.g. Diagram 44.

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A B C D E F G H

 

Diag. 44

1. Kt(K3)-Q5, K-Kt2; 2. K-B5, K-R3; 3. K-Kt4, K-Kt2; 4. K-Kt5, K-R2; 5. Kt-B7, K-Kt2; 6. Kt(B7)-K8, K-R2; 7. Kt-Q6, K-Kt1; 8. K-Kt6, K-R1; 9. Kt-Q7, P-B4; 10. Kt-Kt5, P-B5; 11. Kt-B7 mate.

Having decided as to the smallest amount of material advantage with which it is possible to force a mate, we will now turn our attention to simple game endings (still without pawns). To judge such endings correctly, it will only be necessary to find out whether it is possible to obtain the minimum advantage mentioned. It is sufficient to discuss cases in which a piece on the one side plays against a stronger one on the other, because in endings where several pieces are left on either side, fortuitous circumstances are generally the deciding factors, and it would be impossible to characterise and classify positions of that kind, by giving typical illustrations. Besides, they are reduced sooner or later by exchanges to such end-games as have been treated already, or are going to be shown now.

The Queen wins against any other piece; the Rook alone may give trouble. In Diagram 45 we illustrate a

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A B C D E F G H

 

Diag. 45

position which is one of the most favourable to the weaker side.

1. Q-R6 leads to nothing, as R-B2ch follows, and after 2. K-Kt6 Black forces a stalemate with R-B3ch.

It is necessary for White to gain a move in this position; in other words, White must try to transfer to the other side the onus of having to move. If then the Rook moves away from the King, it gets lost after a few checks, or if Black’s King plays to B1, the Rook is equally lost through Q-R6.

White plays therefore: 1. Q-K5ch, K-R1; 2. Q-R1ch, K-Kt1; 3. Q-R5, and wins. For example, 3. … R-B2; 4. Q-K5ch, K-R2; 5. Q-K3ch, K-R1; 6. Q-K8ch, and so on.

The Rook can win against a minor piece in exceptional cases only. In endings of ROOK AGAINST BISHOP the weaker King must take refuge in a corner square of different colour from that of his Bishop. For instance, Diagram 46:

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A B C D E F G H

 

Diag. 46.

1. R-Q5, B-B5 (or R2); 2. R-Q8ch, B-Kt1, and Black is stalemate unless the Rook leaves the eighth Rank. Any outside square which is not of the same colour as that of the Bishop is dangerous for the King. Imagine the pieces in Diagram 46 shifted two squares towards the centre of the board, as in Diagram 47, and White wins with

 

1. R-QKt5 B-R5

2. R-Kt8ch B-K1

3. R-R8

The Bishop is lost, as it is Black’s move.

In endings of ROOK AGAINST KNIGHT, the weaker side loses, where the Knight is cut off from his King.

For instance, in Diagram 48, 1. R-Q5! In this β€œoblique opposition” the Rook takes four of the Knight’s squares: 1. … Kt-K8; 2. K-B5, Kt-B7; 3. K-K4, Kt-R6 (Kt-Kt5?; 4. R-Kt5ch! wins the Knight). In this ending there is always a fatal check at some point, and the position in the

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A B C D E F G H

 

Diag. 47

diagram is not in any way a chance win. 4. K-Q3, K-B2; 5. R-QR5, Kt-Kt8; 6. R-R1, and wins.

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A B C D E F G H

 

Diag. 48

As soon as the Knight can obtain the King’s support the game is drawn even when the King is already forced on to the edge of the board.

 

Positionβ€”White: K at K6, R at K5

Black: K at K1, Kt at QR2

1. R-QB5, K-Q1; 2. K-Q6, Kt-B1ch; 3. K-B6, Kt-K2ch, draw. In this case the King must avoid the corners, as the Knight would be bereft of his efficiency.

 

Positionβ€”White: K at KR6, R at KR4

Black: K at KR1, Kt at K2

1. R-K4, Kt-Kt1ch; 2. K-Kt6 and wins.

We come now to the more interesting part of end-game play, namely, PAWN ENDINGS. The best course will be first to study how to turn a material superiority in pawns to decisive advantage, after which we shall note particular positions, in which a win is possible with an equality or even an inferiority in pawns.

The ending of KING AND PAWN AGAINST KING is one of the simplest albeit one of the most important of elementary cases. The stronger side will evidently try to queen the pawn. But generally this is not possible if the adverse King has command of the queening square. One important condition, though, must be complied with: the weaker King must move into β€œopposition,” and β€œopposition” is one of the characteristic and deciding factors in most pawn endings. It is absolutely necessary for the learner to understand fully the meaning of the term β€œopposition,” and its value in elementary cases This knowledge is of far reaching influence in end-games.

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