Author: José de Jesús García Ruvalcaba
Date: 14:22:50 05/21/99
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On May 21, 1999 at 16:03:17, Dann Corbit wrote: >On May 21, 1999 at 15:58:32, Tim Mirabile wrote: >>On May 20, 1999 at 15:24:36, Dann Corbit wrote: >> >>>Which brings up another fascinating idea. If we can come up with a minimal >>>encoding, we can bound the maximum possible number of chess positions. If the >>>claim that all positions can be encoded in 100 bits is true, then there are >>>"only" about 1e30 board positions!! Several orders of magnitude below any limit >>>claimed that I know of. After all, if the mapping really is invertible, we will >>>have a one to one and onto map from a 100 bit binary number to all possible >>>board positions! >> >>A while ago I posted to RGCC about a dozen things to consider when trying to >>decide if a certain random position of pieces/pawns/promoted pawns is legal. >>I'll try to dig it up when I get home. But many of these deal with such >>specific cases its hard to imagine an encoding scheme which can catch them all. >>And some positions could only be tested by doing a retrograde analysis back to >>the opening position; I don't see any way to catch those. >These sort of checks *reduce* the number of legal positions. Any check like >this will lower the estimate when applied. If we can find an encoding scheme >that will cover any contingency (including 'legal positions only' as a subset) >then that number of bits will record them all. Perhaps less bits are needed, >but as long as we have a ceiling, we can say that the number of possible moves >is no more than "x" and possibly much less. Is the discussion about posible moves or about posible positions?
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