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  • Print publication year: 2012
  • Online publication date: April 2013

32 - The Monty Hall Problem, Reconsidered

from VI - Cards and Probability


In its classical form, the Monty Hall Problem (MHP) is the following:

Version 1. (Classic Monty) You are a player on a game show and are shown three identical doors. Behind one is a car, behind the other two are goats. Monty Hall, the host of the show, asks you to choose one of the doors. You do so, but you do not open your chosen door. Monty, who knows where the car is, now opens one of the doors. He chooses his door in accordance with the following rules:

Monty always opens a door that conceals a goat.

Monty never opens the door you initially chose.

If Monty can open more than one door without violating rules one and two, then he chooses his door randomly.

After Monty opens his door, he gives you the choice of sticking with your original choice or switching to the other unopened door. What should you do to maximize your chances of winning the car?

In the entire annals of mathematics, you would be hard-pressed to find a problem that arouses the passions like the MHP. It has a history going back at least to 1959, when Martin Gardner introduced a version of it in Scientific American [4, 5]. When statistician Fred Moseteller included it in his 1965 anthology of probability problems [9], he remarked that it attracted far more mail than any other problem.