A mathematical chess problem


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Attila Ba    (2012-08-19 22:28:36)
A mathematical chess problem

ChessPosition (see diagram)

a b c d e f g h

Attila Ba    (2012-08-19 22:30:31)
A mathematical chess problem

White to move. For how many moves can black defer mate?

Attila Ba    (2012-09-24 14:22:50)
A mathematical chess problem

The interesting point is that black can defer mate for so many moves that it makes it practically impossible for chess engines to find the correct move for white. At least Houdini 2.0 can't find the solution and actually values white's position as heavily losing ( -6 pawns or so ).

Sarah Hancock    (2012-10-23 21:11:25)
A mathematical chess problem

24 moves. 1.Bh1 h3 2.Ba8 h4 3.Bh1 h2 4.Ba8 h1Q 5.Bxh1 h3 6.Ba8 h2 7.Bh1 h5 8.Ba8 h1R 9.Bxh1 h4 10.Ba8 h3 11.Bh1 h2 12.Ba8 h1R 13.Bxh1 h6 14.Ba8 h5 15.Bh1 h4 16.Ba8 h3 17.Bh1 h2 18.Ba8 Nb7 19.Bxb7 h1Q 20.Bxh1 Bg2 21.Bxg2 Nf3 22.Bb4 Nxd4 23.Bc6+ Nxc6 24.b3#

Attila Ba    (2012-10-24 08:55:50)
A mathematical chess problem

What makes this problem difficult for an engine is the pawn traffic jam on the h-file. This pushes the solution to an unreachable depth. Once you make the pawn moves for the engine it is suddenly beginning to get what is going on. This is because the engine does not apply logic just brute tree search which becomes exponentially expensive with depth.

Thibault de Vassal    (2012-10-24 12:48:32)
A mathematical chess problem

Nice position indeed...

Attila Ba    (2012-12-11 13:17:43)
A mathematical chess problem

It seems that though some problems are hard for engines there is a hope for improvement. As I mentioned this problem was hopeless for Houdini 2.0 on quite slow tablet PC. Since then I switched to an able laptop and more importantly to the brand new 3.0 version of Houdini. This is 60 ELO points stronger than its predecessore but more importanly it has a tactical mode designed specifically to solve such problems. Surprise surprise in tactical mode Houdini 3.0 can solve this problem in less than a minute (at analysis speed of 4000 kN/sec). Grats to Robert Houdart.

Thibault de Vassal    (2012-12-11 14:30:28)
A mathematical chess problem

That's a very impressive performance for a chess engine!

Wilhelm Schuett    (2012-12-14 20:51:42)
A mathematical chess problem

1.Bh1 h3 2.Ba8 h4 3.Bh1 Bg2 4.Bxg2 hg2 5.Bb4 e1Q 6.b3# or 1.Bh1 h3 2.Ba8 Bg2 3.Bxg2 hg2 4.Bb4 e1Q 5.b3#