Author: KarinsDad
Date: 09:49:59 05/21/99
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On May 20, 1999 at 15:24:36, Dann Corbit wrote: >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! Dann, Where did you come up with this 100 bit possibility? It seems extremely unlikely that this is true for 2 reasons. One, is that the 10^30 board positions is many many magnitudes lower than even the most aggressive minimum number of positions estimate that I have ever read. Secondly, after spending many hours on attempting to decrease the minimum even to 160 bits, I cannot even fathom a paradigm shift (such as a compression scheme after getting to the 170+ bit range) that would enable someone to decrease the documented minimum (of approximately 173 bits) by over 40%. This seems absurd to me. Is this just a computer chess urban myth? KarinsDad :)
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