Author: Reinhard Scharnagl
Date: 02:18:27 03/03/05
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On March 03, 2005 at 04:57:19, Dieter Buerssner wrote: >On March 03, 2005 at 02:39:16, Reinhard Scharnagl wrote: > >>there might be possibilities to store chess positions in some few less bits if >>always THE COMPLETE PIECESET is used for both sides. But I hardly could imagine >>that 100 bits should be sufficient even then. > >Only little more than 100 bits will be needed for positions with all pieces on >the board. On each file, there will be 2 pawns. There are only 10 possible pp >configurations. Of these we can count 2 twice for a possible ep-target, so we >have 12. There are less than 4096 KK-configurations including castling rights (I >forgot the actual number). So only 14 pieces are missing. Even if I don't use >the fact, that both bishops will have different square color, I get: > > 2*12^8*4096*46!/(32!*2*2*2*2*2*2) = ~2^110 > >46!/32! is for the 14 remaining pieces on 46 remaining squares. Six times the >factor 2 is for the indistinguishable pieces. Factor 2 at the start for side to >move. I doubt, that this can be reduced by many orders of magnitude. 100 bits >might be possible. Hi Dieter, in each file there will be 15 possible valid pP configurations, not only 10: 01: -p----P- 02: -p---P-- 03: -p--P--- 04: -p-P---- 05: -pP----- 06: --p---P- 07: --p--P-- 08: --p-P--- 09: --pP---- 10: ---p--P- 11: ---p-P-- 12: ---pP--- 13: ----p-P- 14: ----pP-- 15: -----pP- Reinhard.
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