Author: Uri Blass
Date: 01:57:47 01/30/02
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On January 30, 2002 at 01:56:33, Dann Corbit wrote: >On January 30, 2002 at 00:03:19, Robert Hyatt wrote: >>On January 29, 2002 at 13:58:20, Dann Corbit wrote: >>>No. His notion is that if you mirror using every symmetry, the total number of >>>those positions (including ALL reflections) would be less than 2^81 in that >>>category. >> >>OK. You are a math guy. If you allow for 8 symmetries, which is false for >>positions with pawns, you reduce the number of bits by a factor of 8, which >>is 3 bits. That is the mistake that is being made here, unless I misunderstand >>something seriously. IE for king vs king, allowing _all_ possible permutations >>even with two kings on one square, you get 64^2 positions, which is >>2^12. If you take into account 8 symmetries, you reduce that to 2^9 positions, >>not 2^(12/8)... > >Let's suppose that you need 170 bits to encode a chess position. Now, with that >position [for instance], you may have automatically stored 50 permutation of it. > The net number of bits needed to store each of those 50 positions is 170/50 = >3.4 bits. you said those positions (including ALL reflections) would be less than 2^81 in that category. Based on the same wrong logic in this case you can say that those positions(including ALL reflections) would be less than 2^3.4 in that category. It is clearly wrong. <snipped> >>How can there be more than 8 "reflections"? you can find symmetry along thhe >>vertical center, horizontal center, and the two diagonals. > >Well, they are actually more than just reflections. They are not the same position and I do not see how the fact that there are a lot of positions that you can get the same position from them help you practically to generate smaller tablebases. I am sure that it may be possible to compress the data of tablebases but the information does not tell me how to do it. Uri
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