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?

I don't understand what the the paradox would be.

Once the first player has picked a game, it proceeds like whatever finite game was chosen.  The total play is only one more step (the choosing of the game) than the number of steps (moves) in the chosen finite game.  And 1 plus any finite number is still a finite number.

It certainly sounds to me that the Metagame is finite.  Am I missing something?

Posted by Charlie on 2005-04-12 20:49:38