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 re: Possible paradox by David Shin)

If Metagame is finite, it can be picked as a possible game to play from Metagame. Player 1 picks it, and then Player 2 picks it, infinitely many times, but this conclusion means that Metagame is infinite.

If Metagame is infinite, it can't be picked as a possible game. Only finite games can be picked in Metagame, and then whatever game is chosen is finite, and that means Metagame is infinite as well.

Assuming both possibilities proves that the other one is true.

Posted by Gamer on 2005-04-12 21:17:16