28 May 2017

Bishop and Knight Checkmate

Forcing checkmate with a bishop and knight requires piece coordination and foresight. It is the most difficult of the elementary checkmates. I remember being on the weaker side in a game on the Internet Chess Club in the late 1990s. I told my opponent, "I think this is a draw." He was convinced that it was a win, but he tried to checkmate me in the wrong corner. The game was drawn by the fifty-move rule. After the game, I looked it up. He was right and I was wrong.

Shortly after that game, I learned the checkmate through study of several key positions in Bruce Pandolfini, Pandolfini's Endgame Course (1988). Occasionally, in blitz games or against Chessmaster, I would underpromote a pawn so that I could execute this checkmate. Those instances were usually simple, as only a few moves were needed for checkmate.

I required students to demonstrate it for the Rook Award when I first created my youth chess awards. When I was teaching it regularly, I could perform it reasonably fast, but not easily. Ten years ago, however, I was persuaded by Jeremy Silman to drop it from my awards. It is excluded from Silman's Complete Endgame Course (2007) because it almost never occurs in actual play. In its place in my awards are the Philidor and Lucena rook endgame positions. There should be no question that rook endgames occur frequently and are of immense practical value. The Philidor and Lucena positions also are easier to teach.

Last year in a blitz game at the Spokane Chess Club, I underpromoted and then struggled to execute the checkmate. It had been several years since I practiced this checkmate regularly and my skills had atrophied. Success came well after the fifty-move mark. Last week, I tried the checkmate using Chess.com's "Drills" feature. Again, I struggled. To repair my deficiency, I went to YouTube and watched a video by NM Elliott Neff and another by IM Daniel Rensch. Both of these videos are excellent. After watching these videos, I succeeded with the drill quickly and easily. But, the next morning, I struggled again. Something about the knight's W pattern eluded me. Had I been more attentive during the last two minutes of Neff's video, I might have understood it better.

White to move
The W

Through the past few days, I have watched eight or ten videos, reread the relevant portions of Pandolfini's Endgame Course, and read the bishop and knight section of Karsten Muller and Frank Lamprecht, Fundamental Chess Endings (2001). I also have played out dozens of positions against Stockfish on my iPad. I have been in the diagram position above in game after game. I have played this position so often that my hand is learning the moves.

Transition to the Lock

For many years, I have had a vague memory of Pandolfini's Endgame 22, "Transition to the Lock".

White to move

1.Bg5 Ke8 2.Ng6

2.Ke6 is an easier system to remember.

2...Kf7 3.Ne5+ Ke8 4.Kc7

Black to move

When I was failing, I was always aiming at this position, but the bishop and knight swapped places in my memory. As a consequence, Black was able to shuffle the king between e7 and e8 and White failed to make progress. With these two minor pieces in their correct positions, the finish is easy.

4...Kf8 5.Kd7 Kg8 6.Ke8?!

6.Bh6 was the correct move.

6...Kg7 7.Ke7 Kg8

White to move

8.Bh6 Kh7 9.Bf8 Kh8 10.Kf7 Kh7

White to move

11.Nd7 Kh8 12.Bg7+ Kh7 13.Nf6#.

The Drill

Chess.com's drill employs the position that tablebases have identified as the one requiring the most moves to checkmate. This position is among those listed in the appendix in Fundamental Chess Endings. The engine Chess.com uses is less accurate than Stockfish on my iPad, or so it seems. With optimal play on both sides, this position leads to checkmate in 33 moves. Neither I nor the computer played the best moves.

There are three steps in the process:

1) centralize and drive the king to the edge,
2) drive the king from wrong corner to right corner,
3) checkmate.

White to move

Among the videos that I watched this week, some were better than others. One that is okay, but not to be recommended, is Kevin's from thechesswebsite.com. Through the first phase, he keeps repeating, "it doesn't matter," or similar phrases. I disagree. While slight inaccuracies in the first phase will not be the determining factor in success or failure, they can add up. When you have 50 moves to execute a checkmate that requires 33, an inaccuracy that requires four or five moves to correct can be repeated twice. The third time could be fatal. The inaccuracies through the first eleven moves here, however, add only one or two moves each to the final solution. Had the computer been more stubborn, however, checkmate might have occurred on move 40.

Stripes,J -- Computer
Chess.com, 26.05.2017

1.Ka7 Kd8 2.Bg6 Kc7 3.Nf3 Kc6 4.Bd3

Better is either 4.Be4+ or 4.Ka6.

4...Kc5 5.Kb7 Kd6 6.Kb6 Ke7

6...Kd5 resists longer.

7.Kc6 Kf6

7...Ke6 resists longer.


8.Kd6 is better. Centralization is a good general concept, but should not supplant concrete analysis.


8...Ke7 is more stubborn.

9.Ke5 Ke7



10.Bc4 is more accurate.



11.Kf6 Kg8

White to move

Black's king is on the edge and seeking refuge in the corner where checkmate is impossible without a dark-squared bishop. White's king is optimally placed, as is White's bishop. The knight must go to f7 to evict the king. In Neff's video, the knight gets to f7 via g5. Objectively, there is no difference between g5 and d5, but as a practical matter, it is worth remembering that the knight wants to be on the center square that is two spaces diagonally from the wrong corner. In some cases, the knight might take up this position before the bishop is posted on its ideal diagonal.

12.Ne5 Kh8 13.Nf7+ Kg8 14.Bg6

Here, in his video, Kevin states that the bishop "improves its position" ("Chess Endgames -- Bishop and Knight, Part 1"). Nonsense. The point of the bishop's move is to lose a tempo without altering the position.

14...Kf8 15.Bh7 Ke8

We have reached the position with the colored W near the top of this post. The letter W highlights the route the knight will take through the course of the second phase. Rensch offers a useful principle, "lead with the knight, follow with the king."

16.Ne5 Kd8 17.Ke6 Kc7

White to move

This was the point where I failed on the second day, earlier this week. As panic set in, I struggled to find a route to Pandolfini's position (after move 4 in "Transition to the Lock"). But, there is another lock available.

18.Nd7 Kb7

White to move


This move completes the lock by covering the squares highlighted in yellow.

19...Kc6 20.Bc4 Kc7 21.Bd5

21.Bb5 pursues Pandolfini's "transition to the lock", which also works.

21...Kd8 22.Kd6

Black to move

We have a sitiuation identical in all its particulars to one that existed two squares to the right after evicting Black's king from the wrong corner. Here, the same maneuver as before drives the king back in the direction we wish.

22...Ke8 23.Be6

Losing a tempo.

23...Kd8 24.Bf7

Denying Black's return to the e-file.

24...Kc8 25.Nc5

The knight reaches the third point of the W. White repeats the process--knight moves, king follows, bishop either loses a tempo or cuts off the escape.

25...Kd8 26.Nb7+ Kc8 27.Kc6 Kb8 28.Kb6 Kc8 29.Be6+ Kb8

White to move

Now, the third and final phase. It is checkmate in four. White's only difficulty is easily solved. The knight must check the king on g8 without blocking the bishop's control of the long diagonal. Two squares are available: d7 and a6. However, d7 would allow the king to return to c8. If we had this position with Black to move, then the bishop could check first and the knight deliver checkmate from d7.

30.Nc5 Ka8 31.Bd7 Kb8 32.Na6+ Ka8 33.Bc6# 1–0

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