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 When I first encountered the so-called "Monty Hall problem", I refused to believe the correct answer. 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?

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## Gambler’s Ruin | Math in the Spotlight

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. Mar 14, Peter Flom 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. A formal proof of the solution 6. A book review beyond what's in The Monty Hall problem is, by far, the most contentious math problem ever.

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.

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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. 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 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. 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 doors approach to the MHP This one apparently convinces a lot of people.

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It didn't help me, but maybe it will help you. Suppose there are 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. 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.

## Download The Monty Hall Problem: The Remarkable Story Of Math\'s Most Contentious Brain Teaser

Often, this is done on computer. 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.

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First, we need to define a sample space. Whenever you do an "experiment" broadly defined, the sample space is everything that could happen. We can represent each of these with A, B, and C for the doors. 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. Note that there are TWO ways for the car to be behind door A.

When do you win by sticking? 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. 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. 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. 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.