2 questions about chessboard's symmetry

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2 questions about chessboard's symmetry

Postby Jacek » Wed Dec 16, 2015 4:21 pm

Hello everyone,

I would be grateful if you could give me answers to my questions:
1. Can I use only vertical/horizontal symmetry (i.e. restricting king to the a1-d1-d4-a4 square) in the pawnless endgame? I ask this question, because in early work they allowed black king to stay in the a1-h1-e4-d4 trapezium. I wonder what was the reason of that choice.
2. If there are pawns in the endgame, one of them may be put in the a2-d2-d7-a7 rectangle (as Ken Thompson did). Does it mean, that the other pawns can be put only in a2-h2-h7-a7 rectangle instead of whole chessboard?

Thank you in advance.
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Re: 2 questions about chessboard's symmetry

Postby Kirill Kryukov » Sat Jan 16, 2016 2:02 am

Jacek wrote:Hello everyone,

I would be grateful if you could give me answers to my questions:
1. Can I use only vertical/horizontal symmetry (i.e. restricting king to the a1-d1-d4-a4 square) in the pawnless endgame? I ask this question, because in early work they allowed black king to stay in the a1-h1-e4-d4 trapezium. I wonder what was the reason of that choice.


You can, but using diagonal symmetry helps to further reduce the table size, memory requirement and computation time.

Usually white king is restricted to the a1-d4-d1 triangle (or any reflection of it), and black king is allowed anywhere except adjacent to the white king. This seems to be the simplest method. Typically you would precompute all 462 possible unique placements of both kings.

Jacek wrote:2. If there are pawns in the endgame, one of them may be put in the a2-d2-d7-a7 rectangle (as Ken Thompson did). Does it mean, that the other pawns can be put only in a2-h2-h7-a7 rectangle instead of whole chessboard?

Thank you in advance.


The standard approach is to limit the white king to a1-d1-d8-a8 rectangle, and allow pawns anywhere. This is by far easier than trying to restrict the location of one of the pawns.
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