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?
(In reply to hmmm..
agreed, not only does the game not have a defined state, be that infinite/finite, but it also does not specify whether or not the "choosing a finite 2 player game" is the first move in metagame.
also, there aren't any specified rules for deciding who goes first, and considering metagame is completely dependant on this....the paradox is weak. for example. if age (or another relative constant) is used to determine the first player, then the paradox fails after the first chooses to play metagame, as the players are defined and the rules specify the 'first player chooses a finite game', 'second sets up and makes a move'.
regardless, how can one choose to play a game they are already playing?
i don't really care if metagame is finite or infinite...it sounds incredibly boring and stupid. =P
Posted by alex
on 2005-09-20 17:14:48