12

What is the fastest possible game that ends in a King vs King endgame? Please post a game and tell me the number of half-moves you've achieved. By some simple logic, I can prove that this number is greater than 32 half-moves. There are 30 pieces to be captured, and the first capture can only be made on the 3rd half-move or later.

An example of such a game could be this:

[FEN "rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1"]
1. e4 d5 2. exd5 c6 3. dxc6 Qa5 4. cxb7 Qxa2
5. bxa8=Q Qxa1 6. Qxa7 Qxb2 7. Qxb8 Qxb1 8. Qh5 Qxc2
9. Qxh7 Qxc1+ 10. Ke2 Qxd2+ 11. Kf3 Qe1 12. Qxh8 Qxf1
13. Qxg7 Qxg1 14. Qxg8 Qxh1 15. Qxf7+ Kd7 16. Qxf8 Qxh2
17. Qxe7+ Kxe7 18. Qxc8 Qxg2+ 19. Ke2 Qxf2+ 20. Kxf2 Kd6
21. Qd7+ Kxd7
1/2-1/2

achieving the result in 42 half-moves.

  • The site that came to my mind for such records is Tim Krabbe's chess records. He has many records there, but I could not find the exact question you have there. – TMM Sep 30 '17 at 23:25
11

This is a famous task, originally tackled by Sam Loyd and only improved a century later. See http://www.chessvariants.com/problems.dir/twokingstask.html, which gives the refinement by Ponzetto:

[FEN "rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1"]
1.e4 d5 2.exd5 Qxd5 3.Bd3 Qxa2 4.Bxh7 Qxb1 5.Bxg8 Qxc2 6.Bxf7+ Kxf7 7.Rxa7 Qxc1 8.Rxb7 Rxh2 9.Rxb8 Rxg2 10.Qxc1 Rxg1+ 11.Rxg1 Rxb8 12.Qxc7 Rxb2 13.Qxc8 Rxd2 14.Qxf8+ Kxf8 15.Rxg7 Rxf2 16.Rxe7 Kxe7 17.Kxf2

For reference, here's the original Loyd solution:

[FEN "rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1"]
1. c4 d5 2. cxd5 Qxd5 3. Qc2 Qxg2 4. Qxc7 Qxg1 5. Qxb7 Qxh2 6. Qxb8 Qe5 7. Qxc8+ Rxc8 8. Rxh7 Qxb2 9. Rxh8 Qxa2 10. Rxg8 Qxd2+ 11. Kxd2 Rxc1 12. Rxg7 Rxb1 13. Rxf7 Rxf1 14. Rxf8+ Kxf8 15. Rxa7 Rxf2 16. Rxe7 Rxe2+ 17. Kxe2 Kxe7

[ ETA: Incidentally, while the linked article leaves it as an open problem, it seems like it would be a very straightforward task to show that 16.5 is optimal; at least at first glance I don't see any lines that have captures by both sides on all four half-moves in moves 2 and 3, which would imply that some form of 'off move' along the lines of White's 3. Bd3 is a strict necessity within the first few moves. ]

  • 1
    I think this is optimal. I said in my post that 33 half-moves was optimal. – ericw31415 Oct 8 '17 at 18:37
9

41 Half moves, not a real game

The first possible capture is indeed on the third half-move. After that, a perfect game would be purely captures. By counting the moves which don't involve a capture, you can show how close to a perfect king v king you got. Giving check is bad, unless the opposing king can take a piece while moving out of check (unlikely, if none of the pieces are moved)

The following is a game I created to challenge this puzzle, and it includes 11 half moves which do not take a piece. The other 30 half moves are all captures. My solution is one half move faster than the OP's proposed solution (42 half moves):

[FEN "rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1"]
1. e4 d5 2. exd5 Qxd5 3. Qh5 Qxg2 4. Qxh7 Qxh2 5. Qxh8 Qxh1 6. Qxg8 Qxg1 7. Qxg7 Qg6 8. Qxf7+ Kd7 9. Qxf8 Qxc2 10. Qxc8+ Kd6 11. Qxb8 Qxb2 12. Qxa8 Qxa2 13. Qxa7 Qxa1 14. Qxb7 Qxb1 15. Qxc7+ Ke6 16. Qxe7+ Kxe7 17. f3 Qxc1+ 18. Kf2 Qxd2+ 19. Be2 Qxe2+ 20. Kg3 Qxf3+ 21. Kxf3

Now in 36 half moves:

[FEN "rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1"]
1. c4 d5 2. cxd5 Qxd5 3. Qc2 Qxa2 4. Qxh7 Qxb2 5. Qxg7 Qxb1 6. Qxg8 Rxh2 7. Rxa7 Rxh1 8. Rxa8 Rxg1 9. Rxb8 Rxg2 10. Rxb7 Rxf2 11. Rxc7 Qxc1+ 12. Kxf2 Qxd2 13. Rxc8+ Kd7 14. Qxf7 Qxe2+ 15. Kg3 Qxf1 16. Qxf1 Kxc8 17. Qxf8+ Kd7 18. Qxe7+ Kxe7

By using the queens and rooks I was able to take pieces from either side of the King. When only using the queen, I had to move the queen across to the other side without giving check, so using rooks aswell removed this problem.

  • Do you think this is the lowest we could go? – ericw31415 Aug 9 '17 at 15:15
  • @ericw31415 I'm not sure. Perhaps I could make it lower By involving the rooks... – Aric Aug 9 '17 at 15:17
  • well, my guess is 36 is pretty close. If every move captured a piece, it would be 30. It seems like if there was a better solution, it would be 35 or maybe 34(though looking at solution doesn't seem like you can be more efficient), given how long it takes to activate pieces. – CognisMantis Aug 9 '17 at 23:20
2

Francois Labelle has studied this as part of the more challenging problem of finding a unique proof game which ends with KvK. His site www.wismuth.com contains a wealth of chess computational results. He has found one proof game leading to KvK in 19.5 moves, and has certainly got all the (non-unique) 16.5 games. A minor point worth noting is that any solution cannot end with a capture of a minor piece, or a forced capture, because there would be a prior dead position.

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