Bishop and knight checkmate: the W manoeuvre

King, bishop and knight against king is a win, but the hardest of the basic mates. Mate only works in a corner your bishop covers. If the king runs to the other corner, you have to drive it along the edge to the right one, and the knight does that with a W-shaped walk, covering the squares the bishop can't.

The mate, played out

Black's king is in a8, a light corner, and your bishop runs on dark squares: there's no mate there. The mate will be in h8.

White to move. Step through all 23 moves.

Keep the king in the wrong corner, then drive it out

1.Nd3. First the knight comes over to keep Black's king near the edge (Nd3, Nc5, Na6, Nc7). Then 6.Ba7 takes b8, and the king has to leave the corner along the back rank.

The W

The knight now walks a W: 7.Nd5, 10.Ne7+, 15.Nf5, 16.Ng7+. From those squares it covers the light squares the bishop can't, so Black's king can't slip back. Your king and bishop follow it along: 11.Kd6, 12.Ke6, 13.Bb8, 14.Bc7.

The right corner

20.Kg6 shuts the king in h8's corner, and after 22.Nf8+ Kh8, 23.Be5 is mate, in the bishop's corner.

The mistakes

Leaving a piece loose. In the middle of the W, the knight and bishop need protecting: moves like 7.Kb5?, which leave the knight on c7 to be taken, give a draw.
Stalemate at the end. At the end Black's king in h8 has no squares left, so any bishop move that doesn't give check is stalemate: 23.Bc7?? or 23.Bd2??, for example.

The idea to remember

Mate only in a corner your bishop covers. Drive the king along the edge to it, with the knight walking a W to cover the other colour.

Train it

This is one of the endgame techniques OptiChess teaches as a walkthrough: the moves play themselves until a moment that matters, then you find the move, checked against the tablebase. Simpler mates first: with a queen and with a rook. More endings are in the chess endgame trainer.

Try it. Real positions, set at your level, every answer checked against the board. No account needed to start.

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