Synopses & Reviews
Mathematicians call it the Monty Hall Problem, and it is one of the most interesting mathematical brain teasers of recent times. Imagine that you face three doors, behind one of which is a prize. You choose one but do not open it. The host--call him 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? In this light-hearted yet ultimately serious book, 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 important, he writes, the problem opens a window on our cognitive difficulties in reasoning about uncertainty.
Review
"...a masterful job of tracing the problem back to its origin...much more comprehensive and wide-ranging than the many articles on the subject that have dribbled out...Rosenhouse offers readers much to think about concerning the perplexing question of whether to stick or switch." -Science
Review
"Excellent survey...If one wants to see "The Full Monty," this is definitely the book to buy. Highly recommended." -- Choice
"Those intrigued by the original Monty Hall problem will find that this book is a superb source of variants of the problem, pays careful attention to the hidden assumptions behind the problems, and is written in a witty accessible style that never lapses into flippancy. This is a model of how to accessibly introduce mathematical material at an elementary level that is not a mere popularization of the material. A virtue of the book is that it goes beyond mere exposition to make some serious contributions to the discussion, including a proof that the strategy of switching at the last minute in the progressive version is uniquely optimal and a discussion of some philosophical treatments on the topic."--Mathematical Reviews
"...a masterful job of tracing the problem back to its origin...much more comprehensive and wide-ranging than the many articles on the subject that have dribbled out...Rosenhouse offers readers much to think about concerning the perplexing question of whether to stick or switch." -Science
"Rosenhouse is both entertaining and precise in his writing. He carefully makes the point that conditional probability is difficult to intuitively process, often because what is being conditioned on is not clear. The book is both informative and an entertaining journey for both those schooled in probability and those with little background in probability."--The American Statistician
"Overall, this book is an excellent example of how a problem that is understandable by all can be used to introduce key concepts in mathematics and probability. If you are already familiar with the problem, this book will make you think more deeply about the nature of chance, and what Rosenhouse describes as "the perils of intuition". If Monty Hall is new to you, then you have a choice: stick or switch? You may be surprised." -- Tom Fanshawe, Lancaster
About the Author
Jason Rosenhouse is an Associate Professor of Mathematics at James Madison University in Virginia.