gotoddgo
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Number of Possible Chess Board positions - 2006/12/04 15:19
I was wondering what mathematical work has been done to calculate the exact number of possible chess board positions that could occur during any game.
Basically at anytime there must be between 2 and 32 peices occupying 1 of 64 tiles. A quick calculation brings this to something like 4 * 10^90 combinations. This number can be reduced because of properties of chess pieces/rules:
Here are the factors I can think of:
1- Both kings must be on the board at all times.
2- Knights, Rooks and Queens of the same colour are indistinguishable.
Only bishops (white and black square identification) and pawns who can only be on sqaures above its rank expanding diagonally - makes pawns partial distinguishable).
3- Starting arrangment restricts movements such that certain peices cannot move beyond certain limits until certain other peices are moved or captured.
4- Pawns can promote to rooks, bishops, knights or queens. (BTW. Is there any use in promoting to Rook or Bishop? Technically its in the rules so it can't be discounted).
5- The king cannot be in check in a situation where it would be impossible to undo any possible move and yet still have the king in check.
Surely someone has done work on this before?.
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