Author: Dann Corbit
Date: 13:03:17 05/21/99
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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.
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