I have recently taken an interest in the famously difficult ending which arises when one player - whom for the purpose of this article we will assume to have the White pieces - has king, bishop and knight against Black’s king, with no pawns or other pieces on the board.
As you probably know, White can forcibly checkmate Black’s king, but must do so within 50 moves from the capture which brought about the ending; otherwise Black may claim a draw. White must also avoid other events, such as stalemate, or if the same position occurs three times or five times, and of course the capture of bishop or knight, all of which will result in a drawn game, either automatically or through a claim by (normally) Black.
A couple of years ago I decided to get to grips with this ending. There is more than one technique for winning it and - after viewing a few YouTube videos - I settled on the triangle method. I got rather hooked on this technique, and must have practised it several hundred times on my iPad, often placing the pieces completely randomly to ensure that I can win any such position that might arise in a real game.
I emphasise the importance of practice. I have found that if I allow a few months or even weeks to go by without practising this ending I forget some of the technique and have to find the YouTube video and relearn it.
While searching for the video that taught me the triangle method I came across an even better one by a YouTuber called Majnu2006. (I assume he pronounces Majnu as “my noo” rather than “madge noo”.) You might think that this man’s name would appear somewhere on his YouTube channel but, this is the age of pseudonymity on social media. My best guess is that he is Majnu Michaud, a Netherlands player born in 1965 who possesses no FIDE rating or title. But whoever he is, our Majnu is an extremely good teacher. His video is here.
I suggest you view Majnu’s video after studying this article.
This ending, by the way, has faced me only once, during a casual game with a friend in a pub where I had the bishop and knight. I was in practice, and played the ending well enough. No-one was recording or counting the moves, but I’m pretty sure they didn’t exceed 50 because my opponent’s king didn’t “escape” at any point, and in any case he made no claim for a draw (in fact he didn’t know about the 50-move rule until I mentioned it after the game). Annoyingly, my friend resigned when he could see the coup de grâce coming. In this case I really wanted to deliver checkmate, even though it was no more than a formality, and told him, “I don’t accept your resignation - play on!”, which he obligingly did.
But now it is time to plunge into the ending itself, with the illustrative “game” which I played against Chess Pro and later imported into Lichess here.
I randomly generated the starting position using one of Excel’s random number functions. Your thinking before starting your mating campaign should be along these lines:
1… Kd2 2. Bg6
Keeping my bishop on the b1-h7 diagonal, but why do I retreat it to g6 and not to (say) e4, f5 or h7? Because I am planning to move the bishop later to the d1-h5 diagonal, which means moving the bishop from g6 to h5. But I must first confine the king within the right-angled triangle b1-h7-h1, whose right angle is the corner square (h1) on or near which I intend to mate the Black king.
2… Kc3 3. Nc6 Kb3 4. Ke6
I am moving my king towards the a1 safe corner, which seems paradoxical. But that is where the Black king is headed, and I must follow him in order to exclude or eject him. Does a good general not chase a fleeing army in order to force it onto the killing ground?
4… Kb2 5. Kd5 Kc3 6. Nd4 Kb4 7. Nc2+
The check is coincidental. My knight is now positioned on c2, as planned, and is protected by my bishop on g6. Black is still aiming for the a1 corner, as he should.
What if he doesn’t? Good question, and difficult to answer because I practise this ending on an app supposedly playing stronger than a super-grandmaster (though I did once beat it in a normal game when set to 2000 Elo, so it can’t really be that strong), and which tends to play correctly. But if in this game the Black king suicidally headed to a8, I would establish my bishop on the a2-g8 diagonal and confine the king using my three pieces in much the same way as you’re about to see.
The danger is that the Black king might merely be making a feint designed to draw White’s pieces away from the a1 corner and, with that aim accomplished, might attempt to head for the other escape square, h8, or back towards a1. If this tactic were to succeed, checkmate would almost certainly require more than 50 moves and Black could claim a draw at that point.
I suggest we put this question on hold for the moment while you absorb the conventional process, whereby Black heads directly to one of his two safe corners and doesn’t deviate. After I’ve shown you how to checkmate Black when he plays sensibly, I will deal with the “pretend selfmate” scenario by reference to Diagram 8. Perhaps I should explain here, in reference to Black’s moves, that since Black can do no more than delay checkmate - and then only to a limited extent - against an opponent versed in one of the correct techniques, I regard a move by Black which delays mate as being in principle a good move; and I consider a move by Black that accelerates checkmate as being in principle a bad move which should be marked accordingly.
7… Kc3 8. Kc5 Kb3 9. Kd4 Kb2 10. Kc4 Kb1 11. Kb3 Kc1
This completes the first stage of my plan. The knight prevents the Black king going to a1 and I am going to force the doomed monarch towards the h1 corner. To prepare for the coming manoeuvres, my knight is now going to join the bishop in a two-move dance to its next home, which is e6.
12. Nd4 Kd2 13. Ne6
White’s task was to confine Black’s king behind the diagonal controlled by the bishop. This has already been accomplished, as is shown by the marked squares, which are attacked by White’s pieces. These form an impenetrable wall against the Black king, who is now confined to a quasi-triangle of 17 squares. The White king’s next task is to push the Black king behind the d1-h5 diagonal, place the bishop on g4 (or e2), and thereby prepare to confine the king to an even smaller triangle.
13. … Ke3 14. Kc3
Majnu2006 offers a general principle applicable to the White king’s chase of the Black king towards the killing corner (h1): the White king should attack the square which the Black king has just vacated, in this case d2. I suggest you treat Majnu2006’s advice as guidance, since it doesn’t always push the Black king in the right direction. If you need an example: 15 Kc2 (not Kd4).
14…Ke2 15. Kc2 Ke3 16. Kd1 Kf3 17. Kd2 Kf2 18. Bh5 Kg3 19. Ke3 Kh4 20. Be2
As Diagram 5 shows, Black’s king is now confined to the shorter d1-h5 diagonal, in which he has only seven squares he can move among. (It doesn’t matter whether the bishop enters this diagonal at h5, g4 or e2.) And it’s at this point that the knight must perform a second two-step dance, this time from e6 to c5 to e4, relinquishing control of g7, retaining control of g5, and gaining control of g3. This needs to be done after the bishop is established on the d1-h5 diagonal, and before Black’s king can escape the new triangle via g5 while the knight is at c5 en route to e4.
20… Kg3 21. Nc5 Kg2?
Kh4! is preferable since it is further from h1 and thus likely to delay checkmate.
22… Kh3 23. Kf4 Kg2
23… Kh4! was also possible but would not have allowed the Black king to escape since White controls g4, g5 and h5. However, 24. Bg4?? in reply would give stalemate. After 23 … Kh4 24 Kf5 Kh3 25 Kg5 Kg2 26 Kg4 Kh2 27 Bf1 Kg1 28 Bh3 Kh1 29 Kg3 Kg1, Black’s king is confined to just two squares - g1 and h1 - and ready for White’s final mating sequence.
24. Kg4 Kh2 25. Bf1
The bishop occupies the innermost diagonal, f1-h3, but is unprotected until 26 Bh3.
25… Kg1 26. Bh3 Kh1 27. Kg3 Kg1
The king now has only two squares he can shuttle between - g1 and h1 - and it’s time for the checkmating combination to begin, with the knight’s third and final two-step dance from e4 to c3 to e2.
28. Nc3 Kh1 29. Bg2+ Kg1 30. Ne2# 1-0
Usually, as in this game, the bishop delivers the “assist” (in football terms) and the knight scores; but occasionally (as in the variation introduced by Diagram 8) you will find it’s the other way round.
I paraphrase what I said earlier: practise, practise, practise. Set up random starting positions, so that you get used to placing the knight on the appropriate square (c2, b6, f7 or g3), and the bishop on the appropriate diagonal (b1-h7, a7-g1, a2-g8 or b8-h2). And avoid drawing through the 50-move rule, threefold or fivefold repetition of position, or stalemate.
Now we are in a position to answer more fully your unspoken question: what if Black’s king fails to head for one of his safe corners and says to himself: “I’m doomed anyway; so let me do something my opponent won’t be expecting, and see if he can cope with it.” (I bow to the great Aron Nimzowitsch, who correctly perceived that every piece and pawn has its own personality; and this Machiavellian pivot is just what we might expect from a king.)
Suppose Black moves Kb5?, suddenly deciding to head to the “wrong” corner (from his point of view), i.e. a8, being one of the two killing corners where White proposes to mate him (the other is h1)? The same principles apply: confine the Black king behind (in this case) diagonal a2-g8, and gradually push him closer to the a8 corner. I try to show here how the game could have gone from this point (Lichess):
As you can see, Black’s attempt to make a mad dash for the killing corner leads him to be mated in 19 moves, instead of the 30 moves needed had he defended correctly.
This ending appears complicated, and I suspect that this article was easier to write than it is to read. But you are sure to master the technique with practice against a computer or a friend, and with occasional reference to this article and to videos on YouTube. You need to bear in mind that with pawns off the board there is no natural direction of play, and you need to be able to win the ending from literally any legal position: which means randomising the starting position frequently when practising, however you choose to do this. Good luck!