Author: blass uri
Date: 17:49:02 05/21/99
I think that even representing positions when there are 32 pieces on the board is impossible by 100 bits. we have 15^8 options for the pawns. 15 options in every file(choosing the pawns in a file is chossing 2 squares out of 6). 31 bits are not enough to represent 15^8. 17 bits are not enough to represent the bishops on the board(after the choice of the squares for the pawns) (in the worst case we have 32*31*16*15 options to choose squares for the bishops if the squares for the pawns were with the same colour and it is more than 2^17) 10 bits are not enough to represent the kings on the board. 10 bits are not enough to represent the queens on the board. 9 bits are not enough to represent the white rooks on the board. 9 bits are not enough to represent the black rooks on the board. 9 bits are not enough to represent the white knights on the board. 9 bits are not enough to represent the black knights on the board. 31+17+10+10+9+9+9+9=104 bits I remember that I checked random positions with 32 pieces(generated by a computer program) some years ago and I found that most of them are not legal but a small part of them(more than 1/10 of the cases that I checked) are legal and I could generate a game that prove that they are legal. We probably need more than 100 bits only to represent positions with all the pieces on the board and I believe that these is only a small part of the legal chess positions. Uri
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