Author: Dann Corbit
Date: 11:35:56 01/29/02
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On January 29, 2002 at 14:11:47, Uri Blass wrote: [snip] >>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. > >If this is his point then he is wrong. > >The number of reflection of the same position is only 4 so the total number of >classes of 4 positions is only 1/4 of the number of positions and it cannot be >less than 2^81. I was unclear. You should read his document. It also included all motions of the sliding piece to the winning position. Be aware that this system does not produce a sure best move. It could be thought of as producing a winning bound. If you look at the list of positions Les posted, all 44 of them were generated by a single position. I suppose if you read the document: ftp://cap.connx.com/pub/les/cp.doc it will be immediately clear to you. It could also be used to produce alpha/beta bounds for moves that are analyzed. Again, it might not produce the best possible move. But it could produce a bound that you know it cannot be worse than that. So, in a sense, it could also be used to create an inexact information database for move choices. You would get similar compressions for arbitrary positions at the beginning of a game.
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