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Two knights cannot force a checkmate, but a bishop pair or a
bishop and a knight can.
Though difficult, checkmating with a bishop and a knight is
not only possible but also presents a real test of a
player’s ability to coordinate the moves of those two
pieces. The bishop-knight checkmate has to be delivered within
the fifty-move draw limit without repeating a position three
times or reaching a stalemate.
The bishop-knight mate is accomplished in three steps:
- Force the king to the side of the board,
- Force the king out of the wrong color corner, if
required, and
- Deliver mate with the bishop in the lethal colored
corner, the color of the bishop.
The last two moves in the forced mating sequence are checks,
delivered first by the knight and finally by the bishop.
In the example below, White forces mate with a white bishop,
so the “wrong colored” corner squares are black. The
mating squares, of course, are the two white corners where
White’s white bishop is deadly.
Since White’s bishop can only cover white squares, the
king and the knight have to cover the black squares in the mating
sequence.
If you play on with only the king, against the bishop and
knight, try to keep the king in the center of the board away from
a side or corner as long as possible. Once the king is driven
from the center of the board, try to reach the wrong corner of
the board; in this case it’s a black corner since the king
can only be mated on a white corner square. However, if the king
missteps, checkmating on other squares is also possible. I point
out one such instance in the following mating sequence.
With best play from any board position, the bishop and knight
should be able to mate in 34 moves. To simplify the discussion,
here is an end game with the Black king, already at the side of
the board, on the “wrong color” corner square. Once you
master mating with your opponent’s king on the side of the
board, a logical next step would be to practice forcing the king
to the side of the board using the king, the bishop, and the
knight.
To get the most out of this discussion set up the following
position:

White to Move
1. Nf7+ Kg8
White begins with a knight check; Black’s king move is
forced.
2. Ba4 Kf8
White’s bishop maintains control of e8.
3. Kf6 Kg8
White’s king covers e7; Black’s king heads away from
a8.
4. Bc2 Kf8
White’s bishop covers h7.
5. Bh7 Ke8
White’s bishop covers g8.
6. Ne5 Kf8
White’s knight covers d7; Black’s king heads away
from square a8.
7. Nd7+ Ke8
White’s knight now covers f8; Black’s king has to
move closer to a8 again
8. Ke6 Kd8
White’s king maintains opposition and guards the knight.
9. Kd6 Ke8
White’s king maintains opposition; Black’s king
heads away from square a8.
10. Bg6+ Kd8
White’s bishop gains control of e8.
11. Nc5 Kc8
White’s knight takes control of b7
12. Bf5+ Kd8
Black’s king heads away from a8.
13. Ne6+ Kc8
If 13...Ke8 14.Bg6#.
14. Kc6 Kb8
White’s king maintains opposition to limit Black’s
king movements to only two squares.
15. Nc5 Ka7
White’s knight controls a6 to corner Black’s king.
16. Kc7 Ka8
Black’s king is limited to two squares though a different
two.
17. Kb6 Kb8
White’s king guards a6 from where White’s knight
will check.
18. Na6+ Ka8
“Gotcha!” says White.
19. Be4#

Although the bishop-knight mate can be forced, it is difficult
to achieve over the board within the fifty-move (with out a pawn
move or a capture) draw limit. If the bishop or knight is
captured, White can no longer win and has to accept a draw.
With the bishop and knight against a bare king, you have at
least a tie. If you have time on your clock, play the game out to
a win or a fifty-move draw. If you are short of time, your
opponent can achieve no more than a draw if your flag falls.
Playing as White, you have at least achieved a draw no matter
what happen in the rest of the game. The bishop-knight is a tough
win, but it is possible if you know the winning technique. I hope
that you have learned it here.
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