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?

This game seems that it can be played infinitely or finitely, depending on the moves made in the game.  Just as chess could be infinite, if there is no stale mate, Kings could just move back and forwards forever.

Posted by Chris, Phd on 2005-11-27 22:29:16