I've been reading this book to our boys (9 and 12), and this is I think the first time they've ever been able to understand why math might be interesting. (Sadly, thanks to our elementary school curriculum from time immemorial, elementary school math is nothing more than arithmetic.)

I stumbled on this book years ago, and I loved it because it was such a beautiful presentation of some rather interesting math--especially for somebody who loved Sherlock Holmes. On a whim, I decided to see if our boys could learn anything from it. I was very surprised to find that my boys seemed to like it, and keep asking for more--they liked it better than the original Sherlock Holmes stories. Apparently this book is good not only for people who like a beautiful presentation of things they already know, but also for people who don't know the stuff yet. ( )

Light probability reading.

Holmes fans will welcome this extension of Holmes' powers into the probabilistic and game-theoretic domain. Sherlock Holmes enters the domain of probability and game theory with panache, tackling well-loved favorites such as the gambler's fallacy, the birthday paradox, the Monty Hall problem, Prisoner's Dilemma, independent versus dependent events, and martingales. Holmes fits well into the paradigm--after all, isn't Holmes' well-loved saying, "Once you have eliminated the impossible, whatever remains, however improbable, must be the truth", just another way of stating conditional probability?

The tales are colourful and entertaining, and the mathematical content is kept at a very low and informal level. The book seeks to provide an intuitive understanding of probability in an entertaining way. Typically, each story contains several instances of the same mathematical fallacy or concept to provide different viewpoints of the problem, and Holmes explicitly points out these connections to Watson (and the reader). Although entertainment is definitely the goal of the stories, rather than rigourous mathematical knowledge, even those who have encountered the material more formally may pick up a new perspective. For example, the rather unintuitive Arrow's Theorem is deftly described, both in terms of aspiring musicians seeking a scholarship and a coin game--with the coin game additionally demonstrating a case with a purely dominant strategy for the second player.

In addition, Bruce provides an afterward that contains notes for each chapter with suggestions for future study for each area described in the chapter.

Purists may take offense: anachronistic ideas and predictions are often used for humour (Holmes and Watson are unable to keep a straight face at the "wild" predictions of heavier-than-air flight and flight to the moon, and Watson ridicules the New Year's predictions of war and the fall of Great Britain as the foremost world power), and Watson takes a buffoon role more suited to Agatha Christie's Hastings than Doyle's slow-but-steady Watson and Holmes is rather more cheerful and vocal; however, anyone expecting a perfect recreation of Doyle's stories are misguided in picking up such a collection in the first place. Those looking for humour and the appearance of old and familiar faces from the Holmes stories (Lestrade, Mycroft, Mrs. Hudson, and more all make an appearance, and old cases are often mentioned in the context of probability and game theory) will find the book all they could wish.

One of the unexpected and pleasing aspects of the stories is the cameo role of (sometimes anachronistic) Victorian period characters such as Lewis Carroll, Lenin, the Baron Munchausen, and more. The book should not be read as a history book--some of the characters and concepts (e.g., the appearance of Carroll, department stores with checkout aisles, game-theoretic reasoning) are pulled out of their time. As one might expect in a comedic Holmes spoof, readers should definitely take the history with a grain of salt, but the book is no less entertaining for a little historical inaccuracy.

Overall, an excellent book, both in terms of entertainment and content. Although the book clearly won't provide a rigourous mathematical look, the reader will come away with an intuitive grasp of some of the favorite probabalistic puzzlers of all time, and readers with all mathematical backgrounds will be diverted and entertained. ( )

The book is a list of biases and fallacies clothed in the English and London universe of 1899-1900. For a 2011 reader, this makes the stories a bit more difficult to follow given the somewhat archaic environment and language.

For instance, the simple Wason Test is described in a convoluted story around some graveyard stones. Bruce explains in the Afterword that the decision was thus made to prevent the reader from distinguishing an abstract Wason test (the odd/even number vs. vowel/consonant cards) from a realistic one (cheating about one's age to drink alcohol). I found this device to be ineffective. In my opinion, you're better off reading about the Wason Test and the Monty Hall problem on Wikipedia than reading Chapter 5 of the book.

That said, there are interesting morsels throughout the book: why buses tend to come in pairs much more often than regularly spaced in time; the minimax method; how to calculate the numbers of wild populations of animals; why picking the shortest checkout line if often a bad idea; why the most common first digit of prices is 1; how self-interest is more effective than altruism for equitable outcomes. ( )