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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.

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  • 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
    Commented Sep 30, 2017 at 23:25

3 Answers 3

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14

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. ]

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  • 2
    I think this is optimal. I said in my post that 33 half-moves was optimal.
    – ericw31415
    Commented Oct 8, 2017 at 18:37
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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.

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  • Do you think this is the lowest we could go?
    – ericw31415
    Commented Aug 9, 2017 at 15:15
  • @ericw31415 I'm not sure. Perhaps I could make it lower By involving the rooks...
    – Aric
    Commented Aug 9, 2017 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
    Commented Aug 9, 2017 at 23:20
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Francois Labelle has studied this as part of the more challenging problem of finding a unique proof game which ends with KvK. Labelle's site contains a wealth of computational chess results, including massacre proof games, u.e. proof game problems where nearly all the moves are captures.

He 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.

His Stratgems 58 article on unique bare king proof games is on his site. Here is the full solution, taken from the Die Schwalbe Chess Problem Database.

1.c4 e5 2. Qb3 Qh4 3. Qxb7 Qxh2 4. Qxb8 Qxg1 5. Rxh7 Rxb8 6. Rxg7 Rxb2 7. Rxf7 Rxa2 8. Rxd7 Rxd2 9. Rxa7 Kxd7 10. Rxc7+ Kd6 11. Rxc8 Qxg2 12. Rxf8 Kc5 13. Rxg8 Rxg8 14. Bxg2 Rxg2 15. Nc3 Rxf2 16. Kxf2 Kxc4 17. Kf3 Kxc3 18. Bxd2+ Kxd2 19. Ke4 Kxe2 20. Kxe5

[Title "François Labelle, P0330 StrateGems (58), 6/4/2012"]
[FEN ""]

1. c4 e5 2. Qb3 Qh4 3. Qxb7 Qxh2 4. Qxb8 Qxg1 5. Rxh7 Rxb8 6. Rxg7 Rxb2 7. Rxf7 Rxa2 8. Rxd7 Rxd2 9. Rxa7 Kxd7 10. Rxc7+ Kd6 11. Rxc8 Qxg2 12. Rxf8 Kc5 13. Rxg8 Rxg8 14. Bxg2 Rxg2 15. Nc3 Rxf2 16. Kxf2 Kxc4 17. Kf3 Kxc3 18. Bxd2+ Kxd2 19. Ke4 Kxe2 20. Kxe5
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