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

3.75  ·  Rating details ·  103 ratings  ·  22 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 stic ...more
Hardcover, 194 pages
Published June 1st 2009 by Oxford University Press, USA (first published May 4th 2009)
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Richard Derus
Nov 15, 2011 rated it liked it
Rating: 3.5* of five

This review of a completely bewildering and very important mathematics-related book has been revised and can now be found, feeling itself out of place no doubt among all the lit and smut, at Expendable Mudge Muses Aloud.
William Schram
Jan 22, 2021 rated it really liked it
The Monty Hall Problem refers to a probability puzzle posed in Parade Magazine to Marilyn vos Savant. The Monty Hall Problem explores the titular game from several angles. The best strategy is to switch doors, at least, in the classical variation. The book goes deep into the arguments supporting this strategy.

That isn't all there is to the problem, though. The original column initiated a firestorm of controversy, and vos Savant had to answer it multiple times. Many prominent mathematics instruct
Ed Erwin
Jun 18, 2011 rated it really liked it
Shelves: science, math
When I first encountered the so-called "Monty Hall problem", I refused to believe the correct answer. I wasn't the only one. Some of the best mathematicians got it wrong, too. And like them, I was convinced I was right.

This book proves the correct answer in multiple ways. After the fourth or fifth proof it finally clicked in my head.

After that, the various additional proofs and variations did get boring to me, so I skimmed lots of them. But there's more! Apart from the mathematical problem itsel
Neal Alexander
Apr 06, 2013 rated it really liked it
Symmetry arguments in maths can be misleading. When a magazine published the optimal strategy for the Monty Hall TV game, angry professors wrote in saying it was nonsense, then had to eat humble pie because their intuition had let them down. Now there’s a whole book on the problem, and it starts with convincing explanations of why that strategy really is optimal. In fact the author’s ambition is to use it as a way in to all the main branches of statistics: hence ‘Bayesian Monty’, ‘Monty Meets Sh ...more
Peter Flom
Mar 14, 2013 rated it it was amazing
Shelves: math
The Monty Hall problem is, by far, the most contentious math problem ever. I will attempt to unravel some of its complexity, and I will also review a book about the problem.

Here is how I will proceed:

1. Statement of the Monty Hall Problem and brief notes on history

2. The answer to the Monty Hall Problem

3. Intuitive approaches to the Monty Hall Problem

4. Monte Carlo/computer programming approaches to solving the Monty Hall Problem

5. A formal proof of the solution

6. A book review (beyond what's in
John Petrocelli
Nov 28, 2017 rated it really liked it
Review: A really nice overview of the entire topic, from the mathematical and psychological viewpoints. Certainly not the best writer in the world, but not bad for a mathematician. Cites most, if not all of the important papers published up until the time of publication - very complete. A nice discussion of probability and Bayesian decision making.

Favorite Quote: "All of these questions are answered easily by enumerating the sample space..." (p. 46).
Jan 30, 2021 rated it really liked it
Fun and irreverent, but also a great survey course on topics in probability theory told through analysis of the Monty Hall Dilemma and many variants. The book ends with some fascinating, though potentially skippable discussion of how the problem emerges in psychology and philosophy - often with the author pointing out faulty logic and assumptions made by the untrained academics. It’s not as useful or insightful, but as the author says, food for thought.
Jan 25, 2019 rated it really liked it
For those of you wanting to learn more mathematics than your average school day gives you, or for those of you gripped by interesting statistical problems, this is the book for you!
It's funny, witty, and full of some good math problems that will, as the book warns, "Make you go crazy".
It's overall really good, though you will need background knowledge.
Arlo Linnard
Jan 25, 2021 rated it really liked it
Maths parts were harder to understand, rest was great, really enjoyed it
May 18, 2021 marked it as to-read
Shelves: nonfiction, games, math
As recommended in Gametek. ...more
Maurizio Codogno
Nov 15, 2010 rated it it was amazing
Shelves: matematica, finished
Ricordate il paradosso di Monty Hall? Lo trovate anche su Wikipedia, . Siete concorrenti di uno show, e dovete scegliere una di tre porte, sapendo che dietro una sola di esse c'è un premio: dopo che avete fatto la scelta, il presentatore apre una delle altre due porte - scegliendone una senza premio, e prendendone una a caso se può farlo. A questo punto vi chiede se volete cambiare la vostra scelta. Che fate? La maggior parte delle persone, compresi molti ...more
Dec 30, 2009 rated it liked it
Very novel and interesting book.

In a nutshell:

"You are shown three identical doors. Behind one of them is a car. The other two conceal goats. You are asked to choose, but not open, one of the doors. After doing so, Monty, who knows where the car is, opens one of the two remaining doors. He always opens a door he knows to be incorrect, and randomly chooses which door to open when he has more than one option (which happens on those occasions where your initial choice conceals the car). After openi
Mar 26, 2014 rated it it was amazing  ·  review of another edition
I don't ever seem to be disappointed by Jason Rosenhouse's books, and this book heartily lives up to that standard. Dr. Rosenhouse does a great job of explaining the possible solutions to the Monty Hall problem and looking at why we poor humans are so bad at getting the solution. He also takes us through a bunch of variations of the Monty Hall problem, which if the original didn't trip you up, you are almost assuredly going to be tripped up by one variation or other.

The book is clear, and doesn'
Feb 20, 2010 rated it it was amazing
Shelves: ciências
Um livro intrigante sobre um problema aparentemente simples que gerou polêmicas e mais polêmicas. Alguns momentos de muita matemática que um leitor desavisado perde o controle de seu cérebro que devem ser superados para chegar no excelente capítulo sobre as questões cognitivas ou o porque nossa mente não é capaz de fazer boas análises de probabilidade e risco. As variantes do problema são interessantes principalmente a que entra dois jogadores pois parece muito o mercado de ações que cada um sab ...more
May 15, 2009 rated it really liked it
Shelves: nonfiction
I have been fascinated by the Monty Hall problem ever since I first read about it in the late 1980's. Like the author, I started a file folder with notes about it, never even contemplated publishing what I had gathered. It was agood thing, too, because this author has done a much better job then I ever could have done.

While the analysis of the problem itself is fascinating, the research into why we have such difficulty understanding the problem is even more so. Why is it so counter-intuitive fo
Chris Moyer
Dec 22, 2011 rated it really liked it
A fun, quick read (if you are a math genius or willing to skim some of the denser bits.)

I really enjoyed 2/3s of the chapters. The endless variations and calculations got a bit boring after a while, though. It was great to get to the psychology and philosophy chapters which really brought a neat take to the topic.

I just read a whole book on one brain teaser/math problem... I'm quite ageek.
Oct 14, 2009 rated it liked it
Shelves: nonfiction
This is probably the best book you'll ever read about the Monty Hall problem. :) Its a very well written book, Jason Rosenhouse is an engaging writer, but there's only so many different ways you can analyze the Monty Hall problem before the book gets tedious.

If you like math/science nonfiction at all, I guarantee you'll like some of this book. But by the end, you'll know more than you probably wanted to about the Monty Hall problem.

With that caveat, I recommend it.
Jerry Smith
Interesting as an explanation of the Monty Hall problem itself, especially the account of the early disputes as the the correct solutions. However Rosenhouse is true to his word that he loves math and when his narrative gets into the (for me anyway) more esoteric matters of prbablility generally he lost my interest completely and therefore the book ended up unfinished.
David Daniele
Sep 19, 2012 rated it really liked it
Great book especially if you enjoy statistics and game shows. Towards the end of the book the math gets very heavy and dry to prepare yourself for that. I've had the pleasure of having Dr. Rosenhouse for multiple math classes at JMU and his humor definitely shows throughout the book. Overall, an enjoyable read and I highly recommend it to any math/stat person especially. ...more
Kiên Trần
Aug 18, 2013 rated it it was amazing
Shelves: stats
just like most anybody else, I came to the wrong answer which the odd is 50/50 when first encountering this subtle probability interpretation called Monty Hall Problem. And this book is a must-read related directly to those variations which provides us a full ideas in this issue.
Feb 14, 2012 rated it liked it
An interesting topic, accurately introduced and explained, but this is really an essay stretched to book length.
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