dpalmer

Of course not, but it doesn't matter. If N knows what he or she draws, then the only reason to continue the game is if he or she draws not-M. Calling STOP at this point would ensure a loss. Continuing gives a chance of victory and a chance of loss. So clearly it's better to allow another round. This logic continues until k=n, at which point whoever draws next wins.

Oh, I was assuming that the choice was only secret for D, but N knows what he or she draws. Those are two different games.