Author: Dann Corbit
Date: 11:32:55 01/18/02
Go up one level in this thread
On January 18, 2002 at 13:43:58, Sune Fischer wrote: >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.... Uri Blass wrote a program to make an estimate.
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