This is the clearest and most interesting explanation of the Monty Hall Problem I have ever seen:

What is the Monty Hall Problem? It is basically a game show with 3 doors. Behind one of the doors is a car, while behind the other two doors are two goats. Most people will want to get the car of course.

The player gets a chance to choose one of the doors. Then, the host will open a door which contains a goat. Now, the player is allowed two choices: either stick to his original choice, or switch to the other unopened door. Which choice is better?

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.

I do feel the need to point out that Monty Hall didn’t play any games like the one of the Monty Hall puzzle. The basic format of Let’s Make A Deal is to give a contestant one of a set of choices to make, and then to force them to double-guess themselves, yes, but picking what’s behind a rejected door just, as best I can determine, never been played. Typically it’d be along the lines of, keep what’s behind the door you selected or have the contents of this envelope, or whatever it is the keys which Carol Merrill is holding will open up — all cases where your knowledge of what’s behind the doors doesn’t help any, because they weren’t part of the original setup.

Thanks for your comment! Yes indeed, the theoretical Monty Hall is quite different from the actual Monty Hall game.
Reminds me of the quote, “In theory there is no difference between theory and practice. In practice there is.”

I do feel the need to point out that Monty Hall didn’t play any games like the one of the Monty Hall puzzle. The basic format of Let’s Make A Deal is to give a contestant one of a set of choices to make, and then to force them to double-guess themselves, yes, but picking what’s behind a rejected door just, as best I can determine, never been played. Typically it’d be along the lines of, keep what’s behind the door you selected or have the contents of this envelope, or whatever it is the keys which Carol Merrill is holding will open up — all cases where your knowledge of what’s behind the doors doesn’t help any, because they weren’t part of the original setup.

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Thanks for your comment! Yes indeed, the theoretical Monty Hall is quite different from the actual Monty Hall game.

Reminds me of the quote, “In theory there is no difference between theory and practice. In practice there is.”

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