Classical Monty

Abstract We begin with some terminological ground rules. The host of our hypothetical game show shall always be referred to as “Monty.” We will use the second person in describing the game-show contestant. That is, we will phrase things as if you, the reader, are playing the game. A door will be said to be “correct” if it conceals the car and “incorrect” or “empty” if it conceals a goat. When we speak of being presented with identical doors, you should interpret that to mean that each of the doors has an equal probability of being correct. Your goal in every case is to maximize your chances of winning the car. If it is said that Monty makes a decision at random, that means he chooses from among his possibilities with equal probability.