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?

Let's define a new two person game: the "Metagame".

However, it we insist that a game must be either finite or infinite, the definition of Metagame has not defined a game.  This is just like the Russell paradox: "The collection of all sets that do not contain themselves" does not define a set.

Posted by Richard on 2005-04-12 23:28:06