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>"Most two person games are finite"</i>

We are all assuming that the definition of an infinite game is a game that goes on for an infinite number of moves.  (and I also believe this is probably the best definition).   Call this "infinite duration."

But what about a game that might have an infinite variety of the type of moves available yet the game will end after a finite number of moves?  Might not such a game be considered to have "infinite variety"?

An argument could be made that in the game of Metagame, Player 2 can choose from an infinite number of finite games to play.  By the "infinite variety" definition, then, Metagame would be infinite.

Posted by Larry on 2005-04-13 05:28:18