>Actually that is incorrect as there is no guarantee that every prisoner has been in the room at least once over any amount of time.
IIRC, in the original statement of the problem, there's also a stipulation that, for all prisoners, the king/chooser/whatever will visit them an infinite number of times (so at any time it must be true that each prisoner will be visited [again or for the first time] if the game doesn't terminate).
IIRC, in the original statement of the problem, there's also a stipulation that, for all prisoners, the king/chooser/whatever will visit them an infinite number of times (so at any time it must be true that each prisoner will be visited [again or for the first time] if the game doesn't terminate).