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The Monty Hall Problem: The Remarkable Story of Math's Most Contentious Brain Teaser
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.
on our cognitive difficulties in reasoning about uncertainty.
208 pages, Hardcover
First published May 4, 2009
17 people are currently reading
182 people want to read
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Displaying 1 - 22 of 22 reviews
April 19, 2013
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.
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.
January 23, 2021
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 instructors and teachers doubted vos Savant and her rationalization of the problem. So the book also takes its time in examining the Cognitive Dissonance that comes with this problem.
The book doesn't take too long to read. It does go into the pure mathematics behind a lot of the reasoning, and you will find mention of Bayes' Rule and other classic probability problems. For example, the book discusses the Birthday Problem.
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 instructors and teachers doubted vos Savant and her rationalization of the problem. So the book also takes its time in examining the Cognitive Dissonance that comes with this problem.
The book doesn't take too long to read. It does go into the pure mathematics behind a lot of the reasoning, and you will find mention of Bayes' Rule and other classic probability problems. For example, the book discusses the Birthday Problem.
March 1, 2016
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 itself, there are many interesting things to talk about, such as the psychology of why people are so likely to get the wrong answer and how they react when told they are wrong. Then it lead off into an equally interesting philosophical discussion of what does probability really mean? If the long-term probabilities say that one answer is correct in multiple repetitions of a given situation, does that mean it is also the best answer in a single instance? (The author thinks "yes", and I do, too, but it is an interesting debate.)
Though the math involved is never more complicated than addition, subtraction, multiplication and division, there are lots and lots of symbols to content with. But the first few chapters are light on symbols, and you can probably get a good bit of worth out of reading just those if you want.
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 itself, there are many interesting things to talk about, such as the psychology of why people are so likely to get the wrong answer and how they react when told they are wrong. Then it lead off into an equally interesting philosophical discussion of what does probability really mean? If the long-term probabilities say that one answer is correct in multiple repetitions of a given situation, does that mean it is also the best answer in a single instance? (The author thinks "yes", and I do, too, but it is an interesting debate.)
Though the math involved is never more complicated than addition, subtraction, multiplication and division, there are lots and lots of symbols to content with. But the first few chapters are light on symbols, and you can probably get a good bit of worth out of reading just those if you want.
April 6, 2013
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 Shannon’ and so on. And there a few more general insights along the way, eg that frequentism bars irrational numbers from being probabilities (obvious once pointed out) and that, empirically, people better judge the success of different strategies if they’re couched in terms of numbers - - say, 1000 attempts - - rather than probabilities, which I imagine could be important for Bayesian prior elicitation.
March 14, 2013
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 the diary already)
I'll mention right up front that the book was sent to me by Oxford University Press, it's called the Monty Hall Problem, the author is Jason Rosenhouse, and I liked it a lot. If you like this article, I think you'll like the book
Statement of the Monty Hall problem
You are on a game show. You are presented with three doors. Behind one of them is a car, behind the other two are goats. You get to choose a door. But before you open it, the host (Monty Hall), who knows where the car is, opens one of the other doors. He always opens a door with a goat. If both of the unchosen doors have goats, he picks one at random. The car was placed randomly, with 1/3 chance for each door.
You are then offered a chance to change doors, or stick with your choice.
What should you do?
Brief history of the Monty Hall problem
This problem has been around a while, but it got famous when Marilyn vos Savant (self billed as the person with the world's highest IQ) wrote about it in Parade magazine. She got it right, although her explanation wasn't 100% on the money. She then got tons of mail. Angry letters saying how stupid she was, bemoaning the state of education, and so on. Some came from mathematicians, and some of the most vituperative ones were from mathematicians. They were all wrong.
The solution to the Monty Hall problem
You should switch. If you switch, you have 2/3 chance of winning the car. If you stick, you have 1/3 chance.
This is counter-intuitive to nearly everyone. Even one of the greatest mathematicians (Paul Erdos) got it wrong. But, I guarantee you, the solution is correct.
Intuitive approaches to the solution
The 100 doors approach to the MHP
This one apparently convinces a lot of people. It didn't help me, but maybe it will help you.
Suppose there are 100 doors, and Monty reveals 98 of them. Would you switch?
The added information approach to the MHP - where does the information go?
It's clear that when Monty opens a door, he gives you added information. But what information? In this, the classic version, he cannot tell you anything about your door, only the other two. Your door stays at 1/3, but all of the other 2/3 is now in one door. On the other hand, in an alternative version, where Monty does not know where the car is, he might give you information about your door. If he shows a car, it tells you your door has a goat.
Monte Carlo computer methods to solving the Monty Hall problem
Statisticians use the term "Monte Carlo" methods for simulations that use random numbers to generate answers. Often, this is done on computer. Many people have programmed the problem, and they *all* get the answer that swapping is good, and all are at close to 2/3 vs. 1/3 ... as close as can be expected. People have also done this using playing cards and simulating by hand. They take 2 red aces (goats) 1 black ace (car) and then have pairs of people be Monty and the contestant. This also gives the answer that swapping is right.
Formal proof of the solution to the Monty Hall problem
Here I rely heavily on the book (I rely on the book everywhere, but more so here); again, it's The Monty Hall Problem by Jason Rosenhouse.
First, we need to define a sample space. Whenever you do an "experiment" broadly defined, the sample space is everything that could happen.
if you flip one coin, the sample space is {H, T}
if you flip two coins the sample space is {HH, HT, TH, TT}
if you flip one coin and roll one die, the sample space is
{H1, H2, H3, H4, H5, H6
T1, T2, T3, T4, T5, T6}
the various outcomes do not have to be equally weighted. If you ask two liberals who they voted for, and use Mc, Ob and Ot for McCain, Obama, Other, then the sample space is {McMc, McOb, McOt,
ObMc, ObOb, ObOt,
OtMc, OtOb, OtOt}
but I know which one I'd bet on happening! :-)
in the Monty Hall problem, three things happen: You choose a door, Monty opens a door, and the car is behind a door. We can represent each of these with A, B, and C for the doors. So, if you choose door A, Monty opens door B and the car is behind door C, we would write {A, B, C}
The sample space in the classic Monty Hall problem is
{ABC, ACB, ABA, ACA,
BAC, BCA, BAB, BCB,
CAB, CBA, CAC, CBC}
We can make things a little simpler by assuming you choose door A to start with. Now the sample space is
{ABC, ACB, ABA, ACA}
Note that some triples are impossible. e.g AAB is impossible, because Monty never opens your door, and ABB is impossible because Monty never opens the door with the car.
Remember that the four outcomes do not need to be equally likely; in fact, here, they are not.
We are told that the car is equally likely for the car to be behind any door. The location of the car is the third item in the triple, so this means
P(ABC) = P(ACB) = P(ABA) + P(ACA)
each being 1/3. Note that there are TWO ways for the car to be behind door A. But the total probability for door A is 1/3.
We are also told that, when Monty can open either door, he chooses at random so:
P(ABA) = P(ACA)
and, since the total is 1/3, each of these is 1/6.
OK, so we have
P(ABC) = 1/3
P(ACB) = 1/3
P(ABA) = 1/6
P(ACA) = 1/6
when do you win by switching? In the first two cases, total probability 2/3. When do you win by sticking? In the last two cases, total probability = 1/3.
Alternatively, we could look at the sample space after Monty opens a door. Say he opens door B. Since he does this half the time, we halve the sample space, but we have to double the probabilities associated with the outcomes. The sample space is now
{ABC, ABA}
P(ABC) = 1/3*2 = 2/3
P(ABA) = 1/6*2 = 1/3
you win more often by switching.
Book review of the Monty Hall Problem by Jason Rosenhouse
This is one diary and the book is 200 pages. So, what else is in the book? There's considerable detail about the origins of the problem and the huge outcry when vos Savant published the right answer. There's extensive coverage of a lot of variations of the Monty Hall game (e.g. different probabilities, more doors etc). Much more important, though, this is a (mostly successful) attempt to teach a course in probability theory through the use of the MH problem.
Who should read the book?
I think it has a couple audiences. First, if you are taking a formal probability course at university, this could be a good backup to your text. OTOH, if you are *teaching* such a course, you could use this as a main text (I've never seen a probability text that is this much fun to read). A course based on this book would cover a lot of the ground of a one-semester intro to probability course.
Among the general population, I think this book could be read in two ways: First, you could read chapters 1, 2, 6, 7, and 8, and either skip 3, 4, and 5 or skim them. (Chapter 4, in particular, will be heavy going). Second, if you want to learn probability theory, you could read the whole book. In this case, you'll want to read it more like a text book.
Speaking of chapters, here's the table of contents:
1. Ancestral Monty
2. Classical Monty
3. Bayesian Monty
4. Progressive Monty
5. Miscellaneous Monty
6. Cognitive Monty
7. Philosophical Monty
8. Final Monty
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 the diary already)
I'll mention right up front that the book was sent to me by Oxford University Press, it's called the Monty Hall Problem, the author is Jason Rosenhouse, and I liked it a lot. If you like this article, I think you'll like the book
Statement of the Monty Hall problem
You are on a game show. You are presented with three doors. Behind one of them is a car, behind the other two are goats. You get to choose a door. But before you open it, the host (Monty Hall), who knows where the car is, opens one of the other doors. He always opens a door with a goat. If both of the unchosen doors have goats, he picks one at random. The car was placed randomly, with 1/3 chance for each door.
You are then offered a chance to change doors, or stick with your choice.
What should you do?
Brief history of the Monty Hall problem
This problem has been around a while, but it got famous when Marilyn vos Savant (self billed as the person with the world's highest IQ) wrote about it in Parade magazine. She got it right, although her explanation wasn't 100% on the money. She then got tons of mail. Angry letters saying how stupid she was, bemoaning the state of education, and so on. Some came from mathematicians, and some of the most vituperative ones were from mathematicians. They were all wrong.
The solution to the Monty Hall problem
You should switch. If you switch, you have 2/3 chance of winning the car. If you stick, you have 1/3 chance.
This is counter-intuitive to nearly everyone. Even one of the greatest mathematicians (Paul Erdos) got it wrong. But, I guarantee you, the solution is correct.
Intuitive approaches to the solution
The 100 doors approach to the MHP
This one apparently convinces a lot of people. It didn't help me, but maybe it will help you.
Suppose there are 100 doors, and Monty reveals 98 of them. Would you switch?
The added information approach to the MHP - where does the information go?
It's clear that when Monty opens a door, he gives you added information. But what information? In this, the classic version, he cannot tell you anything about your door, only the other two. Your door stays at 1/3, but all of the other 2/3 is now in one door. On the other hand, in an alternative version, where Monty does not know where the car is, he might give you information about your door. If he shows a car, it tells you your door has a goat.
Monte Carlo computer methods to solving the Monty Hall problem
Statisticians use the term "Monte Carlo" methods for simulations that use random numbers to generate answers. Often, this is done on computer. Many people have programmed the problem, and they *all* get the answer that swapping is good, and all are at close to 2/3 vs. 1/3 ... as close as can be expected. People have also done this using playing cards and simulating by hand. They take 2 red aces (goats) 1 black ace (car) and then have pairs of people be Monty and the contestant. This also gives the answer that swapping is right.
Formal proof of the solution to the Monty Hall problem
Here I rely heavily on the book (I rely on the book everywhere, but more so here); again, it's The Monty Hall Problem by Jason Rosenhouse.
First, we need to define a sample space. Whenever you do an "experiment" broadly defined, the sample space is everything that could happen.
if you flip one coin, the sample space is {H, T}
if you flip two coins the sample space is {HH, HT, TH, TT}
if you flip one coin and roll one die, the sample space is
{H1, H2, H3, H4, H5, H6
T1, T2, T3, T4, T5, T6}
the various outcomes do not have to be equally weighted. If you ask two liberals who they voted for, and use Mc, Ob and Ot for McCain, Obama, Other, then the sample space is {McMc, McOb, McOt,
ObMc, ObOb, ObOt,
OtMc, OtOb, OtOt}
but I know which one I'd bet on happening! :-)
in the Monty Hall problem, three things happen: You choose a door, Monty opens a door, and the car is behind a door. We can represent each of these with A, B, and C for the doors. So, if you choose door A, Monty opens door B and the car is behind door C, we would write {A, B, C}
The sample space in the classic Monty Hall problem is
{ABC, ACB, ABA, ACA,
BAC, BCA, BAB, BCB,
CAB, CBA, CAC, CBC}
We can make things a little simpler by assuming you choose door A to start with. Now the sample space is
{ABC, ACB, ABA, ACA}
Note that some triples are impossible. e.g AAB is impossible, because Monty never opens your door, and ABB is impossible because Monty never opens the door with the car.
Remember that the four outcomes do not need to be equally likely; in fact, here, they are not.
We are told that the car is equally likely for the car to be behind any door. The location of the car is the third item in the triple, so this means
P(ABC) = P(ACB) = P(ABA) + P(ACA)
each being 1/3. Note that there are TWO ways for the car to be behind door A. But the total probability for door A is 1/3.
We are also told that, when Monty can open either door, he chooses at random so:
P(ABA) = P(ACA)
and, since the total is 1/3, each of these is 1/6.
OK, so we have
P(ABC) = 1/3
P(ACB) = 1/3
P(ABA) = 1/6
P(ACA) = 1/6
when do you win by switching? In the first two cases, total probability 2/3. When do you win by sticking? In the last two cases, total probability = 1/3.
Alternatively, we could look at the sample space after Monty opens a door. Say he opens door B. Since he does this half the time, we halve the sample space, but we have to double the probabilities associated with the outcomes. The sample space is now
{ABC, ABA}
P(ABC) = 1/3*2 = 2/3
P(ABA) = 1/6*2 = 1/3
you win more often by switching.
Book review of the Monty Hall Problem by Jason Rosenhouse
This is one diary and the book is 200 pages. So, what else is in the book? There's considerable detail about the origins of the problem and the huge outcry when vos Savant published the right answer. There's extensive coverage of a lot of variations of the Monty Hall game (e.g. different probabilities, more doors etc). Much more important, though, this is a (mostly successful) attempt to teach a course in probability theory through the use of the MH problem.
Who should read the book?
I think it has a couple audiences. First, if you are taking a formal probability course at university, this could be a good backup to your text. OTOH, if you are *teaching* such a course, you could use this as a main text (I've never seen a probability text that is this much fun to read). A course based on this book would cover a lot of the ground of a one-semester intro to probability course.
Among the general population, I think this book could be read in two ways: First, you could read chapters 1, 2, 6, 7, and 8, and either skip 3, 4, and 5 or skim them. (Chapter 4, in particular, will be heavy going). Second, if you want to learn probability theory, you could read the whole book. In this case, you'll want to read it more like a text book.
Speaking of chapters, here's the table of contents:
1. Ancestral Monty
2. Classical Monty
3. Bayesian Monty
4. Progressive Monty
5. Miscellaneous Monty
6. Cognitive Monty
7. Philosophical Monty
8. Final Monty
November 29, 2017
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).
Favorite Quote: "All of these questions are answered easily by enumerating the sample space..." (p. 46).
January 31, 2021
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.
January 25, 2019
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.
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.
January 25, 2021
Maths parts were harder to understand, rest was great, really enjoyed it
to-read-later
May 19, 2021As recommended in Gametek.
November 15, 2010
Ricordate il paradosso di Monty Hall? Lo trovate anche su Wikipedia, http://it.wikipedia.org/wiki/Problema... . 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 matematici, dicono che è indifferente cambiare o mantenere la scelta iniziale: e invece no, conviene di gran lunga cambiare scelta! La cosa è così controintuitiva, e soprattutto dipende così sottilmente dalle ipotesi fatte, che l'autore di questo libro - scherzando ma non troppo - dice che si potrebbe fare un corso di calcolo delle probabilità solo basandosi sulle varianti del paradosso! In effetti il libro l'ha scritto, anche se fortunatamente per noi lettori il testo non è troppo pieno di formule e cerca sempre di dare una spiegazione qualitativa prima che quantitativa. Non solo il paradosso è controintuitivo, ma è anche molto sensibile alla sua formulazione: basta cambiare appena il testo, e la risposta cambia. Rosenhouse parte dalla storia del paradosso - un problema equivalente apparve nel 1959 nella rubrica tenuta da Martin Gardner sullo Scientific American; racconta la sua esplosione negli anni '90 e mostra una serie di varianti, ciascuna delle quali ha una risposta leggermente diversa. Infine dà un'occhiata a come il paradosso viene studiato in psicologia... e persino nella meccanica quantistica!
Diciamo che se non vi viene il mal di testa a star dietro a tutte le minuzie possibili, alla fine della lettura avrete imparato due cose: a non fidarvi del vostro buon senso, e a stare molto attenti al calcolo delle probabilità!
Diciamo che se non vi viene il mal di testa a star dietro a tutte le minuzie possibili, alla fine della lettura avrete imparato due cose: a non fidarvi del vostro buon senso, e a stare molto attenti al calcolo delle probabilità!
January 31, 2010
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 opening an incorrect door, Monty gives you the option of either switching to the other unopened door or sticking with your original choice. You then receive what is behind the door you choose. What should you do?"
Hint: Most people, including some very intelligent people, including many mathematicians do not get the correct answer. It is most definitely NOT intuitive!
The book answers the basic question with explanations early on and the rest of the book is dedicated to variations and even psychological and philosophical discussions concerning the problem.
There were a few pages consisting mostly of long equations. I skimmed those :-)
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 opening an incorrect door, Monty gives you the option of either switching to the other unopened door or sticking with your original choice. You then receive what is behind the door you choose. What should you do?"
Hint: Most people, including some very intelligent people, including many mathematicians do not get the correct answer. It is most definitely NOT intuitive!
The book answers the basic question with explanations early on and the rest of the book is dedicated to variations and even psychological and philosophical discussions concerning the problem.
There were a few pages consisting mostly of long equations. I skimmed those :-)
March 29, 2014
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't hesitate to use math to explicate a solution (a positive for me, as I am well-acquainted with the level of mathematical sophistication presented here). I definitely recommend if you like logic or mathematical puzzles, and even if you don't, I still recommend it (it is possible to skip the mathematical justifications).
The book is clear, and doesn't hesitate to use math to explicate a solution (a positive for me, as I am well-acquainted with the level of mathematical sophistication presented here). I definitely recommend if you like logic or mathematical puzzles, and even if you don't, I still recommend it (it is possible to skip the mathematical justifications).
June 25, 2010
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 sabe sua posição e intui a dos outros. Para quem curte matemática, probabilidade e ciências cognitivas é uma ótima pedida.
July 8, 2010
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 for humans and why do we have such difficulty with almost trivial probability problems?
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 for humans and why do we have such difficulty with almost trivial probability problems?
November 16, 2009
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.
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.
February 29, 2012
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.
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.
March 24, 2010
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.
February 7, 2013
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.
August 19, 2013
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.
February 15, 2012
An interesting topic, accurately introduced and explained, but this is really an essay stretched to book length.
June 20, 2010
Fun, readable introduction to statistics.
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