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The Monty Hall Problem: The Remarkable Story of Math's Most Contentious Brain Teaser [Hardcover]

by Jason Rosenhouse
4.1 out of 5 stars  See all reviews (14 customer reviews)

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Book Description

June 4, 2009 0195367898 978-0195367898 1
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.

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Editorial Reviews


"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.

Product Details

  • Hardcover: 208 pages
  • Publisher: Oxford University Press, USA; 1 edition (June 4, 2009)
  • Language: English
  • ISBN-10: 0195367898
  • ISBN-13: 978-0195367898
  • Product Dimensions: 9.7 x 6.2 x 0.8 inches
  • Shipping Weight: 12 ounces (View shipping rates and policies)
  • Average Customer Review: 4.1 out of 5 stars  See all reviews (14 customer reviews)
  • Amazon Best Sellers Rank: #848,688 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews
77 of 79 people found the following review helpful
5.0 out of 5 stars Don't Stick! Switch! And Why There Is a Difference June 14, 2009
If you are old enough, you remember the sensation that the Rubik's Cube caused all the world over in 1980. No one is still alive that remembers the 1880 fad for the analogous two-dimensional "Fifteen Puzzle", which had fifteen numbered blocks within a four by four container and you were supposed to arrange them numerically. Mechanical puzzles can make storms like these, maybe because you can solve them over and over again, but it isn't often that word puzzles produce such fads. True, the Zebra Puzzle, a reasoning exercise consisting of fifteen seemingly unconnected statements that if regarded together the right way make a logical whole, was popular in 1962. Once you solved it, however, that was that. The Monty Hall Problem entered the public consciousness in 1990 and has been completely solved, but because the solution is so counterintuitive, it is still on the minds of many. One of those minds is that of Jason Rosenhouse, an associate professor of mathematics who has written _The Monty Hall Problem: The Remarkable Story of Math's Most Contentious Brain Teaser_ (Oxford University Press). "My original idea for this book," he writes, was that an entire first course in probability could be based on nothing more than variations of the Monty Hall problem." Indeed, some of the chapters here are full-power mathematics, with unknowns x, y, and z, summation or conditional probability symbols, and complicated equations choked with parentheses within brackets, and more. Math phobics won't get far with such stuff, but there is enough other material here, along with different explanations of the basic puzzle, that will be of interest to anyone who likes recreational mathematics in even the slightest degree. Read more ›
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18 of 19 people found the following review helpful
5.0 out of 5 stars A Detailed Analysis of an Intriguing Brain Teaser September 21, 2009
Believe it or not, this entire book is on the Monty Hall problem! The author, a mathematics professor, has analyzed this fascinating brain teaser from a variety of angles. After discussing the problem's history, he presents various attempts that have been made to understand it. The earlier attempts, including those by Marilyn vos Savant, tend to focus on logical arguments in order to arrive at the correct solution. But in order to solve the problem with mathematical rigour, the author uses some of the tools of his trade such as conditional probability and Bayes' Theorem. But that's not all. He also discusses a series of variants to the problem and proceeds to solve those as well. Finally, psychological and philosophical issues are also presented, partly in an attempt to understand why the human mind has been shown to have so much difficulty in solving this problem. The writing style is clear, friendly and authoritative, although some of the unfortunate editorial errors that the book contains may contribute towards slowing down a reader's attempts at following some of the author's arguments. Regarding accessibility, general readers can learn much from a good part of the main text because of the many clear explanations; however, several sections are fairly heavy with mathematics, a few of which can be rather challenging. Consequently, although anyone with an interest in this problem can benefit greatly from reading this book, math and science buffs are likely to glean the most out of it.
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29 of 34 people found the following review helpful
5.0 out of 5 stars An Important Problem July 6, 2009
Format:Hardcover|Verified Purchase
The "Monty Hall Problem" by Jason Rosenhouse is currently the best coverage of this important problem.

He covers the version of the problem as it was made famous in Parade by vos Savant, and also it numerous variations and generalizations, its history, its occurrence in various fields (psychology, philosophy, quantum theory), and he gives a rather extensive bibliography which will be of great use to the serious student. The depth of coverage varies depending on the topic. For example, the classical analysis is satisfyingly extensive, while the fringe areas (quantum Monty Hall, for example) are just touched upon, and then references are given in the bibliography.

The chatty tone of the text is such that it probably should be categorized as a "mathematics for entertainment" book. And as such, Rosenhouse has allowed himself literary license that one might not normally expect in a math book. For example, we have to wait to until page 42 before "probability basics" are actually discussed . Douglas Adams allusions aside, it might have been better to have given at least the classical definition of probability somewhat earlier. The definition is further developed in pages 84 - 88 when he excellently discusses the classical, frequentist, and Bayesian concepts of probability. This section I consider one of the best in the book.

Rosenhouse states that the book should be within the reach of any undergraduate math major. This is probably overkill. If you know what a binomial coefficient is and what it is used for, know the classical definition of a probability in terms of a sample space, and know how to sum simple series, then you should have no difficulties.
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2 of 2 people found the following review helpful
THE MONTY HALL PROBLEM: THE REMARKABLE STORY OF MATH'S MOST CONTENTIOUS BRAIN TEASER follows one of the most interesting mathematical brain teasers of modern times, and uses a surprising minimum of math concepts in the process. Any interested in puzzle challenges - which ranges from college-level libraries strong in math to general-interest holdings - will find this a lively review of basic math problems and philosophy alike.
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Most Recent Customer Reviews
3.0 out of 5 stars beware of typos in kindle version
The book is fine but the kindle version is plagued with typos - this is not how the new book should look like. Read more
Published 4 months ago by Amazon Customer
5.0 out of 5 stars Picking th Right Door
Probability can be one of the most counter-intuitive concepts our brains struggle with. This book by mathematician Jason Rosenhouse explores one of the most famous brain twisters... Read more
Published 5 months ago by JonK
5.0 out of 5 stars Monty an intellectual pleasure
Rosenhouse is great!
This approach helps you to grasp the whole problem even if you are
Not a mathematician. Read more
Published 13 months ago by Dr. Fenyvesi Tamás
4.0 out of 5 stars Variants for the enthusiastic reader
This book is not aimed at someone with a casual interest in the basic version of the problem. The mathematician author has clearly enjoyed examining and explaining numerous... Read more
Published 20 months ago by David J. Aldous
3.0 out of 5 stars Flawed
I applaud the support for Marilyn (page 29) against the attack on her by Morgan, Chaganty, Dahiya, and Doviak (MCDD) in 1991. Read more
Published on February 17, 2011 by John Garst
5.0 out of 5 stars monty-hall: a review
monty-hall is a great probability problem, this book does a good job at reviewing it, describing it and relating its history and other details
Published on January 22, 2010 by Howard W. Andrews
2.0 out of 5 stars Brain Tease or Brain Torture
Full disclosure up front: I have not read the book, but have a point to make about the way it is being presented here. Read more
Published on December 21, 2009 by Drew Keeling
1.0 out of 5 stars What
I cannot believe there is a book on this
"People feel strongly that the answer the mathematicians have worked out is wrong" (because it is)
On your first choice your... Read more
Published on December 17, 2009 by David Burke
5.0 out of 5 stars I Never Had a Clue
Jason Rosenhouse's witty and most enlightening perspective into the otherwise dry field of mathematical probability will help even the novice (for example, me) get a better... Read more
Published on September 19, 2009 by Larry Underwood
5.0 out of 5 stars Rosenhouse could have reached for the AK 47 but instead he wrote a...
Jason Rosenhouse has written what is a witty and informative book on the remarkable Monty Hall problem. Read more
Published on July 28, 2009 by Peter Haggstrom
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