Author: J. Wesley Cleveland
Date: 22:26:16 05/20/99
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On May 20, 1999 at 23:41:03, Timothy J. Frohlick wrote: >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! > > >1,000,000,000,000,000,000,000,000,000,000 board positions. There are >31,536,000,000 seconds in a millenium. That is 31,709,791,983,760,000,000 >positions per second. I think that we'll find Martians before that happens. With alpha-beta, we may need to look at about the square root of that number or 10^15 poaitions. At the 200,000,000 positions/second claimed for Deep Blue, it would take only about 2 months. I think, though, that 10^40 is closer to the true number of positions, which would take a couple millenia.
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