Author: blass uri
Date: 16:30:50 04/22/00
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On April 22, 2000 at 17:41:35, Heiner Marxen wrote: >On April 22, 2000 at 14:47:08, Tom Kerrigan wrote: > >>On April 22, 2000 at 13:28:39, KarinsDad wrote: >> >>>On April 22, 2000 at 13:25:03, Tom Kerrigan wrote: >>> >>>[snip] >>>> >>>>Notice my idea was to use Huffman encoding for the bitboard, and not the pieces. >>>> >>>>-Tom >>> >>> >>>How so? Please elaborate. >>> >>>KarinsDad :) >> >>I doubt it would be possible to do a very good job compressing the pieces (4 >>bits ea.) themselves, but I think the bitboard should be fairly compressable. I >>suspect that most bitboards have strings of 0's scattered throughout them. > >If you mean that bitboard which distinguishes empty from nonempty positions, >then no: try to do the math yourself (at first I did not believe it myself): >there are at least 2 and at most 32 of the 64 bits set to "non-empty". >Sum choose(2,64) upto choose(32,64) and compare to 2^64, and you will see, >that you need a little bit more than 63 bits to code all possibilities, >regardless of how clever you do it. > >Heiner You are right if you assume that all the location configurations of 2-32 pieces are legal and have the same probability but not all the location configurations of 2-32 pieces are legal For example: If there are 32 pieces you must have at least 2 of them in every file because there is one white pawn and one black pawns in every file. If there are 31 pieces you must have at least 2 of them in at least 6 files. There are many configurations with probability 0 and I think that you can save at least one bit even if you assume that all the legal configurations have the same probability. Uri
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