From the wrong corner to the right one
The W manoeuvre
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Win
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Step through the moves with the arrows, or click a move.
Lesson 4 of 4
King, Bishop and Knight Against King
The hardest basic mate: it can only be forced in a corner of the bishop's colour. If the king runs to the other corner, the knight's W manoeuvre drives it along the edge to the right one.
King, bishop and knight can mate a lone king, but only in a corner the bishop controls: with a light-squared bishop, a8 or h1. With the stronger side to move, the mate takes at most thirty-three moves from almost any position. A defender who knows this runs to the wrong corner.
From there, the knight walks a route in the shape of a W, from f7 to e5, d7, c5 and b7, while the bishop and king keep the enemy king on the edge. Step by step, the king is pushed along the back rank from h8 to a8, where the mate comes.
Every move in this lesson is checked against a tablebase. You get three conditions, each with the move that keeps the win and one that throws it away, the whole W manoeuvre move by move, and four positions to solve.
The idea
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The wrong corner
White's bishop runs on light squares, so the mate can only be forced on a8 or h1. Black's king has gone to h8, a dark corner: it has to be driven along the edge to a8.
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The W
The knight has gone f7, e5, d7 and now c5: four points of the W. With the bishop and king it keeps Black's king on the back rank, moving towards a8.
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The mate
In the right corner: the bishop checks along the long diagonal, the knight covers b8, and the king covers a7 and b7.
Before you play it: the checklist
Each condition with two positions: one where it holds and the move works, one where it is missing and the same move fails. The number is Stockfish's evaluation after the move, from the attacker's side.
1.Keep the knight out of reach
The knight works close to the enemy king. Never put it where the king can take it.
It works
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6.Nd7Win
6.Nd7! is the third step of the W, and the knight is safe.
It fails
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6.Nc6Draw
6.Nc6? puts the knight next to Black's king, and after 6…Kxc6 it is a draw.
The engine prefers Kd5 (Win).
2.Keep the pieces protected
When the king moves, check that it still protects the knight.
It works
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16.Kb6Win
16.Kb6 takes b7 and a7 away and keeps the knight protected.
It fails
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16.Kd7Draw
16.Kd7? abandons the knight on b7, and after 16…Kxb7 it is a draw.
The engine prefers Kb6 (Win).
3.Mate, not stalemate
In the corner, a quiet bishop move leaves the king without a move.
It works
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21.Bc6#Win
21.Bc6#.
It fails
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21.Bh3Draw
21.Bh3? gives no check, and Black has no move: stalemate.
The engine prefers Bc6# (Win).
Move by move
Click a move or use the arrows. Under each note you'll find the defender's other choices and how to answer them. The number under the board is Stockfish's evaluation from the attacker's side.
Your turn
Each position has one best move. Find it, then check the solution.
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Exercise 1
White to move. Black's king is heading for d7. Find the fastest mate.
Show solution
4.Ne5
4.Ne5! stops the king escaping via d7. Every other move is slower.
Bishop and knight against king, the W manoeuvre.
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Exercise 2
White to move. Find the fastest mate.
Show solution
6.Nd7
6.Nd7! cuts off b6 and c5. Careful: 6.Nc6? loses the knight.
Bishop and knight against king, the W manoeuvre.
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Exercise 3
White to move. Find the fastest mate.
Show solution
13.Nc5
13.Nc5! cuts off b7. Then 13…Kd8 14.Nb7+ reaches the last point of the W.
Bishop and knight against king, the W manoeuvre.
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Exercise 4
White to move and mate in one. Most bishop moves are stalemate.
Show solution
21.Bc6#
21.Bc6#.
Bishop and knight against king.
From history
Philidor and Delétang
Philidor gave a method from the wrong corner in 1777, with the knight route now called the W manoeuvre. Another method, Delétang's triangles, was published in 1923. The ending is rare, about once in every 6,000 games according to Wikipedia, but it is one of the four basic checkmates.
Take these into your games
The right corner
The mate can only be forced in a corner of the bishop's colour.
The W
From the wrong corner, the knight walks a W, f7, e5, d7, c5, b7, keeping the king on the edge.
All three pieces work
The bishop covers one colour, the knight the other, and the king takes the squares in front.
Protect the knight
The knight works next to the enemy king. Keep it protected or out of reach.
Count the squares
Near the corner, check every quiet move for stalemate.