Bishop and Knight
This one is the hardest of the basic checkmates. That's because it is no longer good enough to force the lone king into a corner: it has to be the corner of the color of your bishop. You simply cannot produce a checkmate anywhere else.
The Checkmate
The checkmates can take several forms. Here they are:
The bishop delivers the check. Knight and king act in supporting roles.
The bishop delivers the check. Knight and king act in supporting roles.
The knight delivers the check. Bishop and king act in supporting roles.
Driving the King
Here is a position well along the way to completion. You will notice that the lone king is very close to the wrong corner.
Phase one of this very complex checkmate is to drive the lone king to the edge of the board. In the diagram, that phase has already been completed. Phase two is to drive the king toward the more friendly corner, and it is done like this:
1…. Kc6.
White confines the Black monarch to the eighth rank.
1…. Ka8.
If Black wants to cooperate with 1…. Kc8 then White takes the b8-square away with 2. Ba7. But not 2. Bc7 stalemate!
2…. Nc7+.
This move drives the king out of his comfy corner. Another stalemate is produced by 2. Bc7.
2…. Kb8 3. Bc5.
A big key to chess strategy is to not give anything up if you can help it. White keeps all the squares she has gained and prepares to take more away from Black.
3…. Kc8 4. Ba7.
Now we have the lone king traveling in the right direction.
4…. Kd8 5. Nd5.
Notice how all the White pieces cooperate in the effort to keep Black from gaining squares.
5. Kc8.
Black tries to stay near his most comfortable corner. If he tries to go to the middle, he will wind up in the wrong corner: 5…. Ke8 6. Kd6 Kf7 7. Bf2 Kg6 8. Ke5 Kg5 9. Nf6 Kg6 10. Ke6 Kg5 11. Bg3 Kg6 12. Bf4. White keeps using all 3 pieces to gradually take squares away from the slippery Black monarch.
6. Ne7+ Kd8 7. Kd6 Ke8 8. Ke6 Kd8 9. Bb6+ Ke8 10. Nf5 Kf8.
Now White should transfer the bishop to a more useful diagonal.
11. Bd8 Ke8 12. Bf6 Kf8 13. Be7+ Kg8.
Black could end it prematurely with 13…. Ke8 14. Nd6 checkmate.
14. Kf6 Kh7 15. Kf7 Kh8.
This is a tricky situation. Although the Black king is in the proper corner, it's premature to try to cash in, since there is no good follow-up after 16. Bf6+ Kh7.
16. Kg6 Kg8.
Now we're ready for the final blow.
17. Nh6+ Kh8 18. Bf6 checkmate.
The Two Knights
This one is not possible except against a cooperative opponent. There simply is no way to force checkmate against a lone king when you have king and two knights. Incredible but true.
The only way to convince yourself of the truth of this statement is to try to do it. Any opponent who doesn't wish to get checkmated can simply head his king to the corner. There will always be a way out.
