Author: Russell Reagan
Date: 06:56:26 05/06/02
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On May 06, 2002 at 01:16:41, Uri Blass wrote: >On May 06, 2002 at 00:41:48, Russell Reagan wrote: > >>On May 05, 2002 at 06:54:48, Uri Blass wrote: >> >>>I think that there are only 32 squares and 4 kind of pieces and it means that >>>5^32 is an upper bound for the number of position(a square may be empty) >>> >>>5^32 is only an upper bound and the number of practical positions to analyze may >>>be clearly smaller. >> >> >>443,748,401,247 is the number of positions in the 8-piece (or fewer) endgame >>tablebases for draughts. >> >>That number is extremely close to 441,739,287,424, which is the number of >>possible positions with 8 pieces on the board (32*31*30*29*28*27*26*25) > > >It is not the number of possible positions with 8 pieces on the board. > >choosing 8 different squares in the board can be done in > >32*31*30*29*28*27*25*25/(8*7*6*5*4*3*2) > >After that you need to put in every square a number (1-4) to tell the computer >the kind of piece that is there so you need to multiply that number by 4^8. > >4^8=65536>8*7*6*5*4*3*2=40320 so the number is slightly bigger but your formula >gives bigger numbers for tablebases of more than 8 pieces. > > >Uri I took that original number straight off the Chinook website, so it is an exact value of the number of positions with 8 or fewer pieces. Russell
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