Author: Uri Blass
Date: 02:07:02 01/30/02
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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)... > > > >> >>>Second, you simply store the index into the ordered list of positions. >> >>With all its associated data. >> >>>But you totally ignore how you are going to turn that "index" into a real >>>position? Or how you are going to turn a real position into that index? >> >>You take the position you are interested, and create all of its reflections (it >>can be hundreds). > > >How can there be more than 8 "reflections"? you can find symmetry along thhe >vertical center, horizontal center, and the two diagonals. and side to move that make 16 "reflections" based on the definition of having practically the same position(this is not the definition of Les). b1 a2 a7 b8 g1 h2 h7 g8 are symmetric when there are no pawns and in all of these cases you can change the side to move. Uri
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