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?

Chess is defined as finite because there are rules in place which don't allow for infinite loops, like two kings trying to capture each other.

For the Metagame to be defined as finite, it, too, must have similar rules which don't allow for an infinite loop in play (otherwise, as was shown in other reponses, the game can be infinite, just as chess can be infinite.)

I don't know what the rules would be to disallow the infinite loop in the metagame, but knowing that they exist would be enough to determine that it is finite.

Posted by Erik O. on 2005-04-13 15:24:40