Most two person games are finite; for example, chess has rules that don't allow an infinite game, and tic-tac-toe obviously ends after at most 9 plays.

Let's define a new two person game: the "Metagame". The first player first picks any two person finite game (e.g., chess or tic-tac-toe). Then, the second player sets up the board (or whatever is needed) and makes the first move in that game, and the Metagame winner will be whoever wins that game.

The question: is Metagame finite or infinite?

(In reply to No paradox by David Shin)

The paradox as I see it is that, if we start by claiming that Metagame is infinite, there is NO scenario in which two people can play Metagame in such a way that the game proves to be infinite. 

Posted by Bryan on 2005-04-13 17:09:38