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?

OK, I learned my lesson on infinity, God and the devil made Médecins sans Frontières 20$ richer.
As Charlie, I also didn't get it and looked at the screen untill the screensaver took over.  I think this problem is not a paradox.
The first person must take a finite game.  By choosing Metagame, he defines Metagame to be finite and out of this follows that Metagame is a finite game.  If Metagame was to be infinite, the first person wouldn't be allowed to take it and should have taken chess or something.
And don't you start with an undefined Schrödinger like state of the infinity of Metagame.

Posted by Hugo on 2005-04-12 22:14:16