I seem to remember from way back in high school that the number of potential moves by the third set of moves is on the order of billions of legal moves. I am also pretty sure that it is not exponential but a factoral growth. I don't think that it is possible to determine every possible game.
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Not to mention all of the repeating- non-ending games Shadow p.s. i wonder if there is a "irrational" game....one that goes on to infinity but never repeats itself.....I would imagine not as there are only a finite number of possibilities for peices to exist on the board it was an interesting thought whie it lasted.... I have recieved a lot of personal mail stating that the game is a draw if such and such happens....i was ignoring this when i wrote the post....it takes all the fun out of thinking about the problem... Shadow
p.s. I'm also referring to perfectly logical entities playing who aren't out to win the game...just play and play and play and aplay and play and aplay ......