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.