24

If a King, Knight, and Bishop are pitted against the opposing King, is it possible to force checkmate? I find it very hard to do, enough so that I'm not sure whether there's a clean method.

31

Yes, mate can be forced in 33 moves from nearly any position, according to Wikipedia.

See the standard "w" maneuver cited in that article.

22

Yes it is possible to force mate. There's a phenomenal video explaining the process on chessvideos.tv.

If you want to practice the endgame, you can do so on the same site as well.

8

Yes, it can be done. The standard position is to force the enemy king into a corner of the same color as the bishop. Then there are four squares (the corner, the diagonal, and two lateral) squares that need to be attacked.

The bishop attacks the corner and diagonal squares, the king guards one of the lateral squares, and the knight the other one.

[FEN "8/5N2/8/5K2/8/5Bk1/8/8 w - - 0 1"]
[White "K + B + N vs K"]
[Black "White to play and win"]
[Result "1-0"]

1. Ne5 Kh3 2. Kf4 Kh4 3. Ng6+ Kh3 4. Bd5 Kh2 5. Kf3 Kg1 6. Ke2 Kh2 
7. Kf2 Kh3 8. Be6+ Kh2 9. Bg4 {A waiting move to transfer a move to Black, so that the knight will arrive at its destination while giving check.} Kh1 10. Nh4 {The knight starts its journey to f1.} Kh2 11. Nf3+ Kh1 12. Nd2 Kh2 
13. Nf1+ {The all-important destination-check.} Kh1 14. Bf3# {Note: White's bishop can be anywhere on the c8-h3 diagonal (except h3) before this move, and anywhere on the long diagonal to give mate.} 1-0 
  • Diagram oh so welcome. This would really make this question and answer incredibly more useful (tell me if you'd rather have me post it). – Nikana Reklawyks Nov 27 '12 at 5:02
  • 1
    @NikanaReklawyks feel free to edit the posts and add a replayer yourself, or add a new answer drawing from the other answers! (see also the FAQ section about editing.) – Andrew Dec 3 '12 at 17:16
  • @NikanaReklawyks I added a diagram and variation for your convenience. – jaxter Sep 28 '16 at 4:17
4

Yes it is. Check out this video!

http://www.youtube.com/watch?v=r3EqM17jvOc

The general rule is to get the opponent king in the same corner as your bishop. Use the knight and king to control the squares of opposite color to the color your bishop controls. Then, drive the opponent king to one of the two corners with the correct color!

4

While it's possible to force this mate, before you go getting interested in it, take a look at these facts:

  1. It's a very rare ending. Most GM's never see one.
  2. There are only 263 such endgames in my database of 1,172,256 games in which at least one player was at least 2450 ELO. That's only 1 such endgame in nearly 4,500 games.
  3. Of the 263 games, 24 (9%) were drawn because the player with the pieces couldn't force mate.
  4. Only 31 were forced mates, in which the player with the bare king forced the opponent to complete the mate. In the 232 other games, the one with the bare king graciously resigned first.

Some interesting character stories in this rarified drama:

  • Two Super-GM's with ELO over 2700 couldn't force the mate:

    • Ruslan Ponomariov (vs Daryatkin in 2004, in a blitz game)
    • Alexander Moiseenkko (vs Drozdowski in 2013, also in a blitz game)
  • The highest-ranked GM to fail in a standard-time-controls game was Kiril Georgiev, vs Julio Granda Zuniga in 2009, in Pamplona. Other 2600-level GM's to fail were Socko and Motylev (standard) and Sethuraman (blitz).

Of those who forced their opponent to complete the mate in the hopes of getting a draw, Alexander Morozevich holds the record with three attempts; he failed twice (his opponents Ivanchuk and Malakhov were up to the task and duly mated him in front of spectators), and gave up once when he saw it was going to happen when playing against Tal Shaked in the Under 20 World Championship, 1997.

Interestingly, Drozdowski has also seen this ending three times, once in the aforementioned draw against Moiseenko, once as the probable winner (his opponent Viktor Erdos resigned first, in the European Championship in 2012), and once as the loser, against Lukasz Licznerski in 2014. Entertainingly, Licznerski was the underdog by 130 ELO, with a rating of only 2344, and could pull this off!

So, learn it if you want; it may just come up once in your life. But you'll see way more games with equally-matched numbers of minor pieces, and like B v N or R+B v R+N.

  • 3
    Actual occurrence over the board can be a misleading statistic. K+R v K or K+Q v K is rare because people resign when that's about to happen. – Noam D. Elkies Feb 13 '17 at 3:41
  • @NoamD.Elkies It depends on the level of the players and the speed of the game, but generally I agree. – jaxter Feb 14 '17 at 7:24
  • Hoping Ivanchuk doesn't know it (Morozevich) is bordering on idiocy. – TheMathemagician Feb 24 '17 at 16:57
4

[Edited] The winning plan is to force the king into either of the corners which have the same colour as your bishop.

This is done in a few steps.

  1. Force the king to one side of the board so he is stuck on either the a/h file or 1st/8th rank
  2. Use the W manoeuvre to force the king to the corner of your bishop, then use the motif of knight check on (e.g. Na3+ to hit b1) then mate with your king on b3, knight covering b1 and Bishop mates on the long diagonal (e.g. Bg7#).

I have put a detailed review of each step of the ending on my website.

1

It is possible, but hard.

Memorizing it doesn't help (it rarely occurs over the board). But, if you try to do it own your own, it will help you with learning how to make better use of minor pieces in the end game.

If you can confine the king to a corner of the same colour as the bishop, then it is over (try it!).

The method most people know is composed of two parts: (i) confine his king to some corner, and (ii) force it to a corner of correct colour (colour of your bishop). Part (ii) is is called the W technique in the lore. Part (i) is easy; part (ii) is not. I recommend against memorizing part (ii).

But being able to do part (i) is a must. Practice it if you cannot do it. If you are good at it, in some positions, you will be able to directly confine the opponent king to a 'right' corner - something that memorizing people cannot. Once you can do part (i) easily, may be just see the 'W technique' more to enjoy than to memorize. It is basically repeatedly forcing the king to move one square closer to the right corner (you fix that corner this time). This is done with a knight maneuver basically. You can then try to do it on your own. Whether you can recreate it or not doesn't matter.

(Note: if you are doing it on your own, it may go beyond the allowed 50 moves and lead to a draw. Don't worry about that. Once you can do it on your own, practice that ending with a friend and try to achieve that mate quicker. )

-1

Yes, it is possible, and any basic chess manual will demonstrate the method. As mentioned above, the king must be driven into a corner the color of your bishop. To those who say it occurs too rarely to bother to learn, I might mention that I was able to steer a rated game into such an ending, knowing that with my understanding of how to do it I could force mate, which I was able to do well within the allotted 50 moves.

-8

It is not always possible , I try out everything possible in maximum cases I found it written as possible but then I started playing obtaining that position with chess grandmaster , it doesn't let his game defeated by any cost , then I tried grandmaster with various softwares and finally game draw .

  • 6
    It is actually always possible, except when the defender can take one of the pieces. Can you give an example of a position you think is a draw? – Dag Oskar Madsen Jan 20 '14 at 10:55
  • 1
    What do you mean by a "chess grandmaster"? A software or a human GM? – JiK Jan 20 '14 at 15:48

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