Prize insights in probability, and one goat of a recycled error: Jason Rosenhouse's The Monty Hall Problem

TL;DR

This paper reviews Jason Rosenhouse's analysis of the Monty Hall problem, exploring its probability, variations, and philosophical implications, while also identifying a subtle error in the original reasoning.

Contribution

It provides a Bayesian perspective on Rosenhouse's work, clarifies the problem's nuances, and discusses its broader implications and an unnoticed mistake.

Findings

Bayesian analysis clarifies optimal strategies

Variations of the problem reveal different insights

Identification of an inadvertent error in the original analysis

Abstract

The Monty Hall problem is the TV game scenario where you, the contestant, are presented with three doors, with a car hidden behind one and goats hidden behind the other two. After you select a door, the host (Monty Hall) opens a second door to reveal a goat. You are then invited to stay with your original choice of door, or to switch to the remaining unopened door, and claim whatever you find behind it. Assuming your objective is to win the car, is your best strategy to stay or switch, or does it not matter? Jason Rosenhouse has provided the definitive analysis of this game, along with several intriguing variations, and discusses some of its psychological and philosophical implications. This extended review examines several themes from the book in some detail from a Bayesian perspective, and points out one apparently inadvertent error.