Author: KarinsDad
Date: 16:10:21 06/28/99
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On June 28, 1999 at 18:39:34, Randall Shane wrote: >I hope somebody knows the answer to this -- or can point me where to look. > >Like KarinsDad (and others), I'm trying to come up with an mimimal encoding >method for chess positions. What's the best known upper limit on the number of >unique positions (counting e.p., side-to-move, and castling status)? > >I figured out/proved for myself a upper bound of 2**151 -- and I think 2**149 >can be proved as well. There's an enumeration/encoding method associated with >it, but it's uglier than sin. How far off of 'best known' is that? > >Thanks! Wow!!! You are doing well. Out of 351 different types of piece/pawn possibilities (with maximum promotions) in my schema, I currently have 68 (about 20%) which have a range of 161 to 164 bits required and I have spent a LOT of time on this. Note: All of the 161 to 164 bit positions have anywhere from 0 to 9 pawns remaining on the board and most of the rest of the pawns are promoted to unknown other pieces. For example, with 0 pawns remaining on the board, you could have a maximum of 12 promotions and still have 28 non-pawn pieces (and the problem here is that pawns compress down smaller than non-pawns). So, I cannot even get down to 160 bits consistently. My hat is off to you if you have taken into consideration all pawn promotion possibilities and still have gotten down to 151 bits. KarinsDad :) PS. I used a spreadsheet to verify my data. I just cannot seem to drop that extra 4 bits (or lose a piece off the board :) ).
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