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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8 |    | #K |    |    |    |    |    |    |
|---------------------------------------|
7 |    | #R |    |    |    |    |    |    |
|---------------------------------------|
6 |    |    | ^K |    |    |    |    |    |
|---------------------------------------|
5 | ^Q |    |    |    |    |    |    |    |
|---------------------------------------|
4 |    |    |    |    |    |    |    |    |
|---------------------------------------|
3 |    |    |    |    |    |    |    |    |
|---------------------------------------|
2 |    |    |    |    |    |    |    |    |
|---------------------------------------|
1 |    |    |    |    |    |    |    |    |
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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: