>  Mass and energy is quantized, and thus there's only a finite number of
> ways the balls can act. It doesn't matter how many possibilities there 
> are,
> they are still finite.

Down at that level of detail, when stuff collides there is some random noise 
due to the unpredictability of where sub-atomic particles will be and at 
what velocity.  Unless you can predict that (currently I believe it is 
thought to be impossible) then you have no chance of exactly predicting the 
outcome of a collision between two balls.  The best bet you have will be to 
say that within a certain percentage confidence the ball will be in a 
certain range of positions, and as there are more collisions and the game 
goes on, the range of the expected position will grow exponentially.  It 
probably means that even with perfect knowledge of the starting positions, 
after 10 shots with multiple collisions the best you could say is that 
you're 99% sure the balls will be on the table :-)

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