Author: Sune Fischer
Date: 10:43:58 01/18/02
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On January 18, 2002 at 12:50:43, Chris Hull wrote: > >I haven't looked at the estimates in a while but the last ones I recall were on >th order of 10^65 unique positions. Basically, a very large number. > >Chris 10^65 for the number of positions? That seems high to me. A very high upper limit with all 32 pieces on the board is: 64!/(64 - 32)! = 5*10^53 with only 31 pieces the number is even _less_: 64!/(64 - 31)! = 1.4*10^52 If we add these all the way down to two pieces, we still won't get much higher than 10^53. It is possible to get much lower upper limits: *) bishops can only go to 32 squares at most *) there are 8 pawns and 2 knights and 2 rooks, so thats a factor 8!*2!*2! less. *) if the white king has all 64 squares, then the black king can at most have 60 *) the pawns can at most see 48 squares, not 64. and there will be many more illegal positions.... -S.
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