~~Moved from GR--guys, it's nearly over! I'm down to ~20/300! :D~~
Conned Again, Watson: Cautionary Tales of Logic, Math, and Probability
by Colin Bruce
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.