Author: Sune Fischer
Date: 13:26:06 01/18/02
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On January 18, 2002 at 15:12:07, Dann Corbit wrote: >Here is the numeric output of Uri's program: >3.70106301211527e+046 > >Which would indicate (if I interpret it correctly) that there are _at most_ >3.7e46 distinct positions in chess. That number is still on the large side, a simple calculation can bring it under 10^43. 32 pieces on the board: (64*(64 - 4)*62!)/((62 - 30)!*(8!*2!*2!*2*2)^2)= 1.1*10^42 The factors are: white king 64 squares black king 64-4 squares (if white king in corner) rest of the pieces: 62!/(62-30)! white pawns can cycle: 8! white knights can cycle: 2! white rooks can cycle: 2! white's white squared bishop half the board 2 white's black squared bishop half the board 2 square the last few factors since those are identical for black Now realize that the white pawns can only move from rank 2 to 6, this is another huge factor that is not included in the above. Okay, now we shoud add the number of positions with 31 pieces and 30 and ... down to the two kings. Each of those elements in the sum will be orders of magnitudes smaller than the number above (right?), so they can be ignored. I'm sure it could be proven to be less than 10^35 if one did more of those considerations;) >This indicates that a chess position could be encoded in at most 155 bits (if we >were clever enough). > >Even at that, it's quite a pile of board positions. and then think of the number of possible games! ;) -S.
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