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Sunday, November 08, 2009

The Monty Hall Problem


To a mathematician, it's obvious. To everyone else, it's just plain wrong. Imagine that you face three doors, behind one of which is a prize. You choose one but do not open it. The host - Monty Hall - opens a different door, always choosing one he knows to be empty. Left with two doors, will you do better by sticking with your first choice, or by switching to the other remaining door?

Jason Rosenhouse explores the history of this fascinating puzzle. Using a minimum of mathematics (and none at all for much of the book), he shows how the problem has fascinated philosophers, psychologists, and many others, and examines the many variations that have appeared over the years. As Rosenhouse demonstrates, the Monty Hall Problem illuminates fundamental mathematical issues and has abiding philosophical implications. Perhaps most importantly, the problem opens a window on our cognitive difficulties in reasoning about uncertainty.