Isn't this analogous to a "guess a number" game? You have a stack of cards that range from 2 to Ace. If I were to play this game I would not start talking to a guy who has a King on his forehead. I would go to a 5-7 and then determine where I ranked, if I felt I were below 5-7, then I know I am in 2-4 or if I were above them, 8-K. It would seem it would only take only a few more iterations to figure out which status I have.