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Quadibloc wrote:

Also, I'm thinking in terms of digital games like Chess. If one thinks
of an analog game like Billiards, the number of board positions is
infinite.

Unless, of course, the Planck Length (1.61609735×10^-35 meters) is
the quantum of distance and the Planck Time (5.3907205×10^-44 Seconds)
is the quantum of time. If they are, then the number of positions in
Billiards is finite. The smallest difference in starting billiard ball
position that can lead to a difference in ending billiard ball position
that is larger than the resolution of the human eye is far larger than
the Planck Length.

As for a game with infinite variations, the human brain has a large
but finite number of possible states, and thus such a game would
have to map multiple variations to one brain state, and thus the
brain would see those multiple variations as being the same variation.


--
Guy Macon
http://www.guymacon.com/