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of course, that there are still pawns on the Rook’s side, and that their exchange cannot be forced. The following position (Diagram 71), from a game Moll-Post, shows how to proceed in such cases.

Here White can force a win in the following way: 1. RxP, P-Kt6; 2. R-R6, PxP; 3. RxP, K-B2; 4. R-B2, B-Kt5; 5. R-B4, B-R4; 6. P-B4! The Black pawn position must first be torn up, if it is to be attacked successfully.

Now Black’s defeat is inevitable, whether the pawn is taken or not. The sequel would be 6. … PxP; 7. RxP, after which the Rook goes to KR5 and the Rook’s pawn must fall, or: 6. … K-Kt3; 7. PxP, PxP; 8. R-B6ch, K-Kt2; 9. R-B5, and the Bishop’s pawn is lost, unless Black gives up his passed pawn. In this case Black loses also: 9. R-B5, B-Q1; 10. KxP, K-Kt3; 11. K-Q3, B-B3; 12. R-B6, K-Kt2; 13. K-K4, K-Kt3; 14. R-R6, K-B2; 15. K-B5, B-Q1; 16. R-KKt6, followed by RxP, etc.

The Queen against a minor piece wins so easily that it is not necessary to give an example. It only remains to discuss end-

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Diag. 71

games of QUEEN V. QUEEN, ROOK V. ROOK, AND MINOR PIECE V. MINOR PIECE, in which one player has a majority of pawns, or an equal number of pawns, one of which is passed. As a rule the extra

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Diag. 72

pawn leads to a win. There are, however, exceptions frequently recurring in practice to which I must refer specially.

Diagram 72 shows an end-game with a Rook’s pawn and a Bishop β€œof the wrong colour.”

White draws with 1. Kt-Q2, P-B7; 2. Kt-K4ch, K-Kt7; 3. KtxP, and draws, as Black, in order to capture the White pawn, after KxKt must give the White King access to the Rook’s square, from which he could not be dislodged except by a Bishop on White squares.

In Diagram 73 White cannot win although his Bishop is of the β€œright colour” by 1. P-B7, KtxP; 2. BxKt, and White cannot win the Rook’s pawn. He can only attack the pawn from Kt7 or Kt8, both of which are inaccessible as the Black King gets to Kt1. It is a stalemate position. If the White

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Diag. 73

pawn were still at R5, White’s King could attack the pawn from R6 and secure the win.

In the position given, White could only win by keeping his passed pawn, and indeed it is possible to win by gaining a move with the Bishop. In the diagram it is White’s move. Black with the move could not play K-B2 because K-Q6 would follow. The Knight would have to move, allowing the pawn to queen. Therefore White must try to bring about the same position with Black to move. He can do this, for instance, in the following way:

1. B-Kt3, K-B2 (now 2. K-Q6 would be bad on account of Kt-Q5, 3. P-B7, Kt-Kt5ch, and KtxP); 2. B-R2, K-K2; 3. B-K5. Now White’s plan has succeeded; the same position has occurred, and it is Black’s move. As mentioned before, the King must not move, but Knight’s moves are of no avail. If 3. … Kt-Kt4; 4. B-B6ch, the Knight is lost, or alternatively the pawn queens. On 3. … Kt-B1, B-Q6ch decides, and on 3. … Kt-Q1; 4. B-B6ch, K-K1; 5. BxKt would follow.

On this occasion I should like to point out that it is impossible to gain a move with a Knight, as a square which is accessible to him in an odd number of moves cannot be reached by him in an even number. A simple instance is Diagram 74.

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Diag. 74

White loses, having the move. 1. K-R8, Kt-K4; 2. K-R2, Kt-Q2; 3. K-R8, Kt-B1; 4. P-R7, Kt-Kt3 mate.

Black with the move cannot win, as he cannot bring about the same position with White to move.

In end-games of BISHOP V. BISHOP, of which we have already had an example in Diagram 70, an extra pawn wins in most cases if the Bishops are of the same colour. It is generally possible to force an exchange of Bishops and obtain one of the well-known pawn endings.

On the other hand an ending with Bishops of different colour leads mostly to a draw, frequently even against a majority of two pawns. The position in Diagram 75 is a draw, because it is impossible for the White King to get round his Kt pawn to drive off the Bishop.

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Diag. 75

With two passed pawns distant from each other, a win can generally be forced, as in the following position (Diagram 76).

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Diag. 76

The King moves up to the pawn, the progress of which is barred by the Bishop (not the King). He thereby forces the sacrifice of the Bishop. If the Black King comes to the rescue of the Bishop, the other pawn proves Black’s downfall.

1. K-K4, K-K2; 2. K-Q5, K-Q2; 3. B-K4, B-K2; 4. P-Kt6, B-Q1; 5. P-Kt7, K-B2; 6. K-K6, and wins; or 5. … B-B2; 6. P-B6, B-R7; 6. B-B2, K-K1; 8. K-K6, B-Kt1; 9. B-Kt6ch, K-B1; 10. K-Q7, and wins.

When the pawns are united, one should observe this rule: if they are attacked, they should, if possible, move to squares of the colour of the opposing Bishop.

Therefore in the position set out in Diagram 77 White should not play P-B5, but P-K5. After 1. P-B5 there is no possible chance for White to assume the command of the Black squares, and in order to advance the pawns it is necessary

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Diag. 77

to force access to both White and Black squares. In the present instance play would proceed on these lines:

1. P-K5, B-R4; 2. K-K3, K-B2; 3. K-K4, K-K2; 4. P-B5, B-Kt5; 5. P-B6ch, K-B1; 6. P-K6, B-R6; 7. B-R4, B-Kt5. White can only get through with the King’s Pawn, as P-B7 is unavailing on the grounds set out above. But in order to play P-K7, the square K7 must first be covered a second time, so that the Bishop cannot be given up for the two pawns. Therefore: 8. K-Q5, B-R6 (B-B6; P-K7ch); 9. K-B6, K-K1; 10. K-B7ch, K-B1; 11. K-Q7, and wins.

In end-games with one Knight on each side, an extra pawn usually decides the game much in the same way as in end-games with Bishops of the same colour; frequently even with equal pawns, the possession of a passed pawn is sufficient, as it keeps either the King or the Knight busy, so that there is only one piece available for the defence of the pawns. An instructive example is the end-game Ed. Lasker-Rotlevi on p. 100.

End-games with Rook against Rook are the most frequent, as well as the most difficult. Here the possession of an extra pawn is seldom sufficient for a win, unless the stronger side has also an advantage in the greater mobility of the Rook. Diagram 78 is typical of such cases, frequent in practice, in

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