Author: Reinhard Scharnagl
Date: 02:52:18 03/03/05
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On March 03, 2005 at 05:18:27, Reinhard Scharnagl wrote: >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- Hi Dieter, I have to correct myself. When I try to make a calculation: Pawn constellations at 8 files: 15^8 placing white w Bishop in average: 8 placing white b Bishop in average: 8 placing black w Bishop in average: 7 placing black b Bishop in average: 7 placing 2 white Knights: 28*27/2 placing 2 black Knights: 26*25/2 placing 2 white Rooks: 24*23/2 placing 2 black Rooks: 22*21/2 placing white Queen: 20 placing black Queen: 19 placing white King: 18 placing black King: 17 side to move 2 e.p. is possible or not 2 affected e.p. file 8 castling rights (s+w) 4*4 -------------------------------------------- estimated possibilities (2^11)*(15^8)*(7^2)*28!/16! this is meaning about 101.5 bits. Reinhard.
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