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Chess/The Endgame/King and Queen vs. King

From Wikibooks, open books for an open world
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8a8 black kingb8 black kingc8 black kingd8 black kinge8 black kingf8 black kingg8 black kingh8 black king8
7a7 black kingb7 black kingc7 black kingd7 black kinge7 black kingf7 black kingg7 black kingh7 black king7
6a6 black kingb6 black kingc6 black kingd6 black kinge6 black kingf6 black kingg6 black kingh6 black king6
5a5 black kingb5 black kingc5 black kingd5 black kinge5 black kingf5 black kingg5 black kingh5 black king5
4a4 black kingb4 black kingc4 black kingd4 black kinge4 black kingf4 black kingg4 black kingh4 black king4
3a3 black kingb3 black kingc3 black kingd3 black kinge3 black kingf3 black kingg3 black kingh3 black king3
2a2 black kingb2 black kingc2 black kingd2 black kinge2 black kingf2 black kingg2 black kingh2 black king2
1a1 white kingb1 white queenc1 black kingd1 black kinge1 black kingf1 black kingg1 black kingh1 black king1
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Sample starting position for K+Q vs. K mate

Delivering checkmate with a king and queen against a lone king is quite easy. The basic technique involves driving the king to the edge of the board, which the queen can do by herself. It's faster if you use your king and queen together, but this increases the probability of a stalemate, so beginners should do it without the king. The technique described below will accomplish the mate in about 10 to 15 moves.

Here's an example (see diagram on right):

1.Qb5

Cutting the black king off along the fifth rank.

1...Ke6

1...Kc7 2.Qa6 limits Black's king to the last two ranks.

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8a8 black kingb8 black kingc8 black kingd8 black kinge8 black kingf8 black kingg8 black kingh8 black king8
7a7 black kingb7 black kingc7 black kingd7 black kinge7 black kingf7 black kingg7 black kingh7 black king7
6a6 black kingb6 black kingc6 black kingd6 black kinge6 black kingf6 black kingg6 black kingh6 black king6
5a5 black kingb5 black kingc5 white queend5 black kinge5 black kingf5 black kingg5 black kingh5 black king5
4a4 black kingb4 black kingc4 black kingd4 black kinge4 black kingf4 black kingg4 black kingh4 black king4
3a3 black kingb3 black kingc3 black kingd3 black kinge3 black kingf3 black kingg3 black kingh3 black king3
2a2 black kingb2 black kingc2 black kingd2 black kinge2 black kingf2 black kingg2 black kingh2 black king2
1a1 white kingb1 black kingc1 black kingd1 black kinge1 black kingf1 black kingg1 black kingh1 black king1
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Position after 2.Qc5

2.Qc5 (see diagram)

During this phase, notice how White's queen always stays a knight's move away from the black king, and how no checks are necessary (or even desirable). Moves like 2.Qc6+? only allow Black's king more freedom after 2...Ke5.

2...Kf6 3.Qd5 Kg6 4.Qe5 Kf7

After 4...Kh6 5.Qg3 White's goal has been achieved: the black king is trapped on the edge. White will then bring his king to f6 to force mate.

5.Qd6 Kg7 6.Qe6 Kh7

Black's king is forced to the edge of the board no matter what he does, e.g. 6...Kf8 7.Qd7.

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8a8 black kingb8 black kingc8 black kingd8 black kinge8 black kingf8 black kingg8 black kingh8 black king8
7a7 black kingb7 black kingc7 black kingd7 black kinge7 black kingf7 black kingg7 black kingh7 black king7
6a6 black kingb6 black kingc6 black kingd6 black kinge6 black kingf6 black kingg6 black kingh6 black king6
5a5 black kingb5 black kingc5 black kingd5 black kinge5 black kingf5 black kingg5 black kingh5 black king5
4a4 black kingb4 black kingc4 black kingd4 black kinge4 black kingf4 black kingg4 white queenh4 black king4
3a3 black kingb3 black kingc3 black kingd3 black kinge3 black kingf3 black kingg3 black kingh3 black king3
2a2 black kingb2 white kingc2 black kingd2 black kinge2 black kingf2 black kingg2 black kingh2 black king2
1a1 black kingb1 black kingc1 black kingd1 black kinge1 black kingf1 black kingg1 black kingh1 black king1
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Position after 8.Kb2

7.Qg4 Kh6 8.Kb2 (see diagram)

Now that Black's king is stuck, the white monarch comes in to finish off his adversary.

8...Kh7 9.Kc3

9.Qg5 doesn't spoil anything, but it isn't necessary. Unlike the king and rook vs. king mate, here Black's king doesn't have to be trapped in the corner.

9...Kh8 10.Kd4

10.Qg6?? stalemate was what Black was hoping for. Beware of this trap!

10...Kh7 11.Ke5 Kh8 12.Kf6 Kh7 13.Qg7#.

A detailed analysis of this endgame based on the computer-generated database is in Analysis of KQK Endgame. This shows that for any "King and Queen vs. King" endgame, white to move can force checkmate in at most ten moves.

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8a8 black kingb8 black kingc8 black kingd8 black kinge8 black kingf8 black kingg8 black kingh8 black king8
7a7 black kingb7 black kingc7 black kingd7 black kinge7 black kingf7 black kingg7 white queenh7 black king7
6a6 black kingb6 black kingc6 black kingd6 black kinge6 black kingf6 white kingg6 black kingh6 black king6
5a5 black kingb5 black kingc5 black kingd5 black kinge5 black kingf5 black kingg5 black kingh5 black king5
4a4 black kingb4 black kingc4 black kingd4 black kinge4 black kingf4 black kingg4 black kingh4 black king4
3a3 black kingb3 black kingc3 black kingd3 black kinge3 black kingf3 black kingg3 black kingh3 black king3
2a2 black kingb2 black kingc2 black kingd2 black kinge2 black kingf2 black kingg2 black kingh2 black king2
1a1 black kingb1 black kingc1 black kingd1 black kinge1 black kingf1 black kingg1 black kingh1 black king1
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The final checkmate.