Author: Chris Welty
Date: 11:45:46 03/04/05
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Your idea of restricting the allowed sets of pieces on the board is brilliant, because most of the legal positions in chess have really silly combinations of pieces. Generally you need to use the maximum length of the encoding rather than the average length. If you know enough about the encoding to calculate the average length you know enough to calculate the exact number of positions and can encode the positions by giving each position a number. I tried it with a slightly different restriction: Each side may have no more than 7 officers (officer=Q/R/B/N). An upper bound on the number of positions with this restriction is 2.3754e+043 and it can therefore be encoded in 144.091 bits. Probably this can be reduced by another 1-2 bits by someone really determined. Is a 7-officer maximum realistic in actual games?
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