whoever needs to use the bathroom first loses, or if you die of thirst or hunger, that could also disqualify one from such a theoretically limitless dilemma.

Alternately, if you have a mathematical way to measure boredom, and also introduce a rule that the person to truly become bored with the game first (or more bored, measured quantitatively somehow) would actually win automatically after a draw… or the game could just be determined by some arbitrary momentary measure of chaotic systems outside the game that the players can’t see or affect, and then giving the win to one of the players based on some hidden scoring matrix of outside variables probing purely environmental or coincidental variables, to generate an arbitrary-enough-seeming-to-the-players (though not likely enough for the mathematicians) winner, in the event of a repeated draws which outnumber the lower of the two single largest numbers that each player could think of, probed proper to match before each challenge, unbeknownst to the players, that way they cannot strategize to give a dishonest answer to affect play somehow towards their advantage (by saying a lower number than the highest possible [countable-to-by-this-person] number that they had ever actually been taught to count up to)