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.

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.

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.

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.