ChessKing, bishop and knight against a bare king is always a win, but it's the hardest of the basic mates. You can only mate in a corner the same color as your bishop, and the defending king will always run to the other one. You don't need to memorize every move. Just get two practical things down: recognize the right corner, and use the knight's "W" maneuver to drive the king there. Then if it ever comes up in a game of free chess, you'll be ready.
Key position
Remember this first: drive the king to a corner the same color as your bishop. A light-squared bishop mates in a8 or h1; a dark-squared bishop mates in a1 or h8.
How to play it
Step 1: the W maneuver, driving the king along the back rank
The black king keeps trying to hide back on h8, so White has to push it the other way along the 8th rank toward a8. The knight goes f7, e5, d7, b6, d5, which traces a "W". Together with the bishop and king, it pushes the black king across.
Every move in this line is a best move according to the tablebase. The point isn't to memorize it but to see who does what: the knight and bishop take turns covering the squares the king wants to run back to, and your king blocks it from the front.
Step 2: into the right corner and mate
Common mistakes
The last move is where stalemate happens most: the black king has only a square or two left, and one knight jump covers them all.
Two other common problems:
- Driving the king to the wrong corner: in a corner of the opposite color to your bishop, you'll never mate. You're just wasting moves.
- Sending the knight too far away: the knight has to stay close to the black king and help cover squares. If it wanders off, the king slips back to the wrong corner.
Practice puzzles
Show answer
1. Nf3# The knight checks from f3. The bishop on g2 covers h1 and h3, and the white king covers g1 and g3. Checkmate. Careful: Nh3?? is stalemate.
Show answer
1. Bg7+ Kh7 2. Nf6# The bishop checks from g7, and the king has to go to h7. Then the knight mates from f6: the white king covers g8 and g6, the bishop covers h8 and h6, and the bishop can't be taken because the king protects it.
FAQ
How many moves does the bishop and knight mate take?
According to the tablebase, up to 33 moves, so with the 50-move rule you have to be efficient. It's rare in practice, but if it does happen, knowing the W maneuver gives you a real chance to win.
Why can you only mate in the bishop's corner?
In the other corner, the bishop can't cover the corner square, and the knight only covers one color at a time, so the king always has a square left. That's why you have to drive it to a corner your bishop controls.
Do beginners need to learn this?
No rush. Get the queen mate and rook mate down first; they come up far more often. Save the bishop and knight mate for when your basics are solid.
Try it yourself
To see the other endgames, go back to Chess endgames. To try a bishop and knight mate yourself, play chess against the computer, trade everything off, and keep just a bishop and a knight.