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Written by Yury Markushin
Sunday, 07 February 2010 21:21

Today I will discuss the Knight + Bishop endgame checkmate.  This endgame was well analyzed by Philidor long time ago, in 1749. It is not the most common mate you will see, it occurs once at every 5000 games, but it is definitely important to know how to use the Knight and a Bishop together.

I have seen many guides that are trying to explain how to actually checkmate a lone King with Knight and Bishop, but they’re very often failing to teach. They show moves, give some explanation and it even seems like you understand how to do it yourself at first, but… when trying to do it, it just doesn’t work.

The problem is that there is no exact guide for this mate available; at least I wasn’t able to find it.  This is a main reason why I’m writing and you’re (hopefully) reading this. I will systematically present the well known information and form an algorithm, how to do it.

I promise, you will be able to deliver this complex Knight and Bishop Checkmate to a lone King after you read and understand this. You ask why is it complex? Well, even grandmasters fail to do it in fifty moves, sometimes.  But you will!

Below is the endgame I played against Chessmaster GM edition (2800+ ELO) program. If you can checkmate the Machine in this endgame, I will do the same against human opponents as well.

Idea # 1

The only way to checkmate an opponent’s King is to force him to the right corner, the corner which matches the color of your bishop. Therefore, if you have the light square Bishop you need to force him to a8 or h1, which are light corners.

Idea #2

The safest place for the lone King to be is the opposite color corner, so the main difficulty is to force him out of the wrong corner and escort to the right one.

Idea #3

Here we go. Let’s checkmate this 2800 rated program in Knight and Bishop endgame. The first objective is to force an opponent’s King to the wrong square.

Idea #4

We divide the chess board onto three Triangles: Large Triangle, Medium Triangle and Small Triangle. These are represented in green, blue and red. On the diagram black's King is inside the Large Triangle. As you already know the only way to checkmate the King is to force him into the light square a8 (or h8) if we have the light square Bishop. We move the opponent's King from the Large Triangle to Medium and then to Small one, where checkmate will be delivered. See how in the game above.

It is the Large Triangle in action. Black's King cannot escape and only limited by 8 squares he can move at. Bishop is placed at its ideal square. Ideal square is on the diagonal (side of the Triangle), one square up: b3 or f7. The Knight is positioned on the ideal square also. The ideal square for the Knight is d3, it should be on the same row as the Bishop but one square apart.

Why are these ideal squares? When Bishop and Knight are placed in its ideal way they form a wall, preventing the black's King from breaking through.

Red X's show the squares controlled by white.

We have moved black's King to the Medium Triangle. The basic idea here it that the Bishop is at its new ideal square c7, which is on the side of the Triangle, one square away from the edge of the board. The Knight is also at its new ideal square d5, on the same column/row as the Bishop, but one square apart. White King pushes the opponent's King from the bottom towards the Small Triangle. Black King is only limited by 6 squares.

Our job is almost done here. Black's King is now at Small Triangle and is locked to only 2 squares. There is a checkmate in 2 at this position. But be careful, there is still a chance for a Draw here, don't let the win slip and make each move with a check from now on.

I hope my analysis was any use for you and you have learned how to checkmate the lone King with a Knight and Bishop. I recommend practicing delivering that checkmate against the computer. You will build confidence and never forget how to do it, after you checkmate Chessmaster, Rybka or Fritz multiple times. Just start up with random position and try to force the opponent's King to the right corner applying guidelines given above.
You may want to look through the game a few times and read the comments and the "ideas" in order to get the algorithm. But hey, it works and we did it. Let me know about your progress in the comments field.

If you're interested in the endgames I suggest to check out Famous Queen vs. Rook Endgame and to improve your endgame.

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Last Updated on Saturday, 14 January 2017 22:00

+2 #26 Yury 2014-07-23 21:07
Thanks Vasilis , I'm glad that it was useful for your chess !

+1 #25 Vasilis 2014-07-22 19:29
By what i knew since.. a while ago, the K+B+N against K chechmate was posible, oNLy to the Bishops color corner!!

+1 #24 Vasilis 2014-07-21 04:20
Fantastic explanation!!
I just start to understand how to manage this, with this kind of process!!

+1 #23 Nyakallo Letsela 2014-07-18 01:41
oh chess only checkmate and wind match eithr wht pawn or nght+bishop

+1 #22 `Quicky 2014-05-05 18:05
1. Kc2 Kd7 2. Kd3 Kd6 3. Kd4 Ke6 4. Ke4 Kf6 5. Nd3 Ke6 6. Bb3+ Kf6 7. Nf4 Kg7
8. Kf5 Kh7 9. Kf6 Kh8 10. Bc4 Kh7 11. Ng6 Kh6 12. Bg8 Kh5 13. Ne5 Kh4 14. Kf5
Kg3 15. Ng4 Kg2 16. Bc4 Kf3 17. Bd3 Kg3 18. Be2 Kh4 19. Ne3 Kg3 20. Nd1 Kh4 21.
Kf4 Kh3 22. Ne3 Kh4 23. Ng2+ Kh3 24. Kf3 Kh2 25. Nf4 Kg1 26. Kg3 Kh1 27. Ba6
Kg1 28. Nh3+ Kh1 29. Bb7# 1-0

+4 #21 orphee 2014-02-14 11:42
awesome learning thank you very much
could you please teach us the notorious Queen vs Rook endgame in this way?
maybe the impossible became posiible

+2 #20 Christopher Brooker 2013-02-27 20:17
Thank you for your informative analysis. I have played for many years and always dreaded having this end game. I have it in a game on the net at the moment for the first time. Your help is invaluable even if I fail, I have learnt something. I believe there's a typo when you refer to the Bishop at C7 in the medium triangle?

+2 #19 Kemas 2012-11-09 07:19
that's still difficult. say you are White. you already have King at c3 and a Bishop at b3. you also have a Knight at, say, e5.

Black King is at b1. he can't go anywhere far. but i still can't corner him. just what's going on?

+2 #18 Dr Waxter 2012-09-07 09:41
In my experience you must know Philidor's W method and Deletang's triangle method. White's move #9 is incorrect here. It should be K-f6, waiting 10 B-f7 and 11 N-g6. Then Philidor's method will quickly drive the Black K to mate at H1.
You cannot force checkmate in the "wrong" corner. You use Philidor's method if the opposing K retreats to the "wrong" corner, you use Deletang's method if it retreats to the "correct" corner. You must be able to switch methods if your opponent switches tactics.

+1 #17 Yury 2012-08-11 12:49
Quoting chess noob:
sorry I meant the #13 comment by admin. sorry it was a mistake, otherwise excellent article! excellent site, bookmarked

It's alright:) Humans make mistakes, otherwise no chess games would've been won! Good luck!