[rc5] Chess - Many possible boards

Tobias Bergmann bergmats at trick.informatik.uni-stuttgart.de
Thu Oct 30 18:45:57 EST 1997


Something about the problem of saving a list of all possible boards:

Background:
One piece has 64 possible positions on the board. Two pieces have 64*63
possible positions. So 32 pieces have 64*63*...*33 (<- yes it is a 33)
possible positions. With that in mind the upper limit of all possible
boards is:

 32
 ---
 \     64!
  |  -------   = 497275065157795229721406525452498161822005325091061504
 /   (64-i)! 
 ---           
 i=1

This is about 2^178!
Of course there are some boards that aren't possible (e.g. a pawn has no
chance to get to the first row!) but there are quite *enough* possible
constellations!!!
Does someone have a better guess about the total number of boards we
have
 to evaluate?

BTW we could compress this list (there are many redundancies in there
because
 successive boards have most of the pieces/positions in common) but I
don't
expect this method to reduce the data so much that it would fit into any
*real world* storage system.
Some comments?


Tobias

------
Tobias Bergmann             | email:
"In a world without fences  | bergmats at trick.informatik.uni-stuttgart.de
     who needs gates?"      |
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