Author: Dann Corbit
Date: 12:24:36 05/20/99
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On May 20, 1999 at 14:13:34, Dann Corbit wrote: [snip] >>The thread about representing positions in the minimum number of bits is also >>about setting an upper bound on the maximum number of chess positions. 160 bits >>is 2^160 or ~= 10^48. >Yes, what a fascinating rejoinder! In this case, if 10^52 is correct, then 173 >bits should be the minimum, since 2^173 = 1.197e52 >If we can encode in less, then the number of board positions is less than we >thought (or we have an error in our thinking and the scheme won't work). 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!
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