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Chess/The Endgame/Minor Piece endings

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If White has only one minor piece against a lone king, it is not possible to arrange the pieces so that the black king is checkmated. If White has a king and minor piece and so does Black, checkmate can occasionally occur (see below left), although it cannot be forced. If White has three pieces, the mate is easy. As we shall see, with two bishops[1] White's job is relatively easy, with a bishop and knight it is somewhat harder, and with two knights it is typically impossible (although it can happen against a very bad opponent).

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8a8 black kingb8 black kingc8 black kingd8 black kinge8 black kingf8 black kingg8 black bishoph8 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 white bishopg6 black kingh6 white 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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Checkmate in which Black and White each have a king and bishop.


King and Two Bishops vs. King

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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 white bishope3 white bishopf3 white 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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White to play

The diagram at left shows a mate in 6 with two bishops.

1. Bc2 Kf1 2. Bd2 Kg1 3. Kg3 Kf1 4. Bd3+ Kg1 5. Be3+ Kh1 6. Be4#

If Black plays 3. ... Kh1, instead of Kf1, White responds with the line: 4. Be1 Kg1 5. Bf2+ Kh1 6. Be4#, or 5...Kf1 6. Bd3#

The bishops coordinate by taking adjacent diagonals, thus cutting off the opposing king.

In the diagram position with Black to move, White can "gain a move" by triangulating his king:

1...Kd1 2. Kf4 Ke1 3. Ke4 Kd1 4. Kf3 Ke1. Now the diagram position is reached with White to move, and play proceeds as above. Black's king, hemmed in by the two bishops, cannot escape from the d1-e1 box.


King and Bishop and Knight vs. King

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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 white kingf6 black kingg6 black kingh6 black king6
5a5 black kingb5 white bishopc5 black kingd5 white knighte5 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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White to play

In order to mate with a bishop and knight, White must force Black's king to the corner that is the same color as his bishop - in this case the a8 square. This is not so easy to do, because the bishop and knight do not coordinate well in cutting off the opponent's king. Mate can always be forced unless Black can win a white piece, but, even with best play, the mate may take over 30 moves.

In the position at right, much of the hard work has already been done. Black is being pressed in the direction of the a8 corner. Nevertheless, nine more moves are required to mate.

1. Kd6 Kc8 2. Ke7 Kb7 3. Kd7 Kb8 4. Ba6 Ka7 5. Bc8 Kb8 6. Ne7 Ka7 (or 6. ... Ka8 7. Kc7 Ka7 8. Nc6+ Ka8 9. Bb7# ) 7. Kc7 Ka8 8. Bb7+ Ka7 9. Nc6#


King and Two Knights vs. King

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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 white knighth5 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 white kingh3 black king3
2a2 black kingb2 black kingc2 black kingd2 white knighte2 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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White to play

When White has two knights against a bare king, it is impossible to mate without cooperation from Black. The diagram at left illustrates his predicament. The black king is cornered, but White has no way to force checkmate. Moving either Nf3, or moving Nh3 all lead to stalemate. White can try for 1. Ne4 Kg1 2. Nf3+ Kh1?? 3. Nf2#, but instead Black plays 2. ... Kf1! 3. Nd4 (otherwise Black can play Ke2, and White must corner him again) 3. ... Ke1 and White still has a challenge to confine the black king.

a b c d e f g h
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 white kingg7 black kingh7 black king7
6a6 black kingb6 black kingc6 black kingd6 black kinge6 black kingf6 white knightg6 white knighth6 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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Checkmate!
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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 white knightg6 black kingh6 black king6
5a5 black kingb5 black kingc5 black kingd5 black kinge5 black kingf5 white knightg5 black pawnh5 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 rook3
2a2 black kingb2 black kingc2 black kingd2 black kinge2 black kingf2 black kingg2 black kingh2 black king2
1a1 black kingb1 black kingc1 white kingd1 black kinge1 black kingf1 black kingg1 black kingh1 black king1
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Checkmate! Notice how the checkmate is easier now that the black king is hemmed in by his own rook and pawn, and the king no longer has to be nearby.

However, checkmate can happen with king and two knights against king if the opponent makes enough foolish moves, ending with a checkmate position like those to the left. It is easier if the losing side's king is hemmed in by his own pieces, like that to the near left.

If Black has one pawn, White may be able to win by cornering the black king with a king and one knight, and avoiding stalemate by letting Black to advance his pawn, while the other knight administers mate. This is more likely to succeed if the black pawn is not far advanced, and needs at least three moves to become a queen. Alexey Troitsky, the famous endgame study composer, produced an extensive analysis of this endgame and composed several endgame studies with two knights against one pawn. Some positions require as many 70 moves without a pawn move or capture. This endgame has some historic interest - it was included in the amendment of the "50 move draw rule" to exclude those positions in which it could be demonstrated that more moves were required. (The exception to this rule has since been rescinded; the rule now dictates that either player may claim a draw after 50 moves without a capture or pawn move, regardless of the position on the chessboard. This means that the definition of the fifty-move rule now specifically excludes king-and-two-knights-versus-king-and-pawn positions.) The ending of two knights versus one pawn has occasionally occurred in practical tournament play.

  1. ↑ It is always implicitly assumed that the bishops of the same side are on opposite-colored squares, since same-colored bishops can only happen with an unlikely underpromotion. In fact, it is impossible for any number of bishops on the same color to checkmate a lone king.
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