The Monty Hall problem is not a probability puzzle* (It's a challenge in mathematical modelling)

Abstract

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, ‘Do you want to pick door No. 2?’ Is it to your advantage to switch your choice?The answer is ‘yes’ but the literature offers many reasons why this is the correct answer. This article argues that the most common reasoning found in introductory statistics texts, depending on making a number of ‘obvious’ or ‘natural’ assumptions and then computing a conditional probability, is a classical example of solution driven science. The best reason to switch is to be found in von Neumann's minimax theorem from game theory, rather than in Bayes’ theorem.