Author: Robert Hyatt
Date: 08:12:28 05/05/01
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On May 05, 2001 at 05:45:06, Dan Andersson wrote: >Even without the 50-move rule the game is finite. The permutations on a chess >board have a finite limit, even the permutation of strings of positions i.e. >moves are finite. The point that play can continue forever is of no consequence. > >Regards Dan Andersson Then let's define "finite" and "infinite". If the game of chess is such that you can say the game can't last more than N moves, then it is finite. If the game can continue _forever_ without ending, then it is obviously infinite. By the current rules of the game, the latter is true since the 50 move rule and three-fold repetition rules are not absolute, but optional for either player to claim. Note that if we factor in the 50-move rule, you can't use the number of permutations of the pieces on the squares as that would be incorrect. A single position is not just the combination of pieces on specific squares, it must include that info _plus_ all the moves made to reach this position, since the 50-move rule and repetition would depend on the history of that position, not just on the position. With the 50-move rule changed to mandatory, the game is _still_ essentially infinite since each position would have a _huge_ number of different ways it could have been reached without violating the 50-move or repetition rules.
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