This assumes Ballmer is cheating, rather than just behaving adversarially but within the rules. If we accept cheating is allowed, we can also potentially accep

This assumes Ballmer is cheating, rather than just behaving adversarially but within the rules. If we accept cheating is allowed, we can also potentially accept other 'cheating' scenarios where the player repeatedly punches Ballmer in the face until he discloses the number, thus winning. Or where the player just refuses to pay at the end. IMO the problem is only interesting if we assume any form of cheating isn't allowed.