Progressive Monty

Abstract 4.1. Proceed at Your Own Risk Version Six: This time we assume there are n identical doors, where n is an integer satisfying n 3. One door conceals a car, the other n 1 doors conceal goats. You choose one of the doors at random but do not open it. Monty then opens a door he knows to conceal a goat, always choosing randomly among the available doors. At this point he gives you the option either of sticking with your original door or switching to one of the remaining doors. You make your decision. Monty now eliminates another goat-concealing door (at random) and once more gives you the choice either of sticking or switching. This process continues until only two doors remain in play. What strategy should you follow to maximize your chances of winning?