The notion of expected value is, of course, fundamental material in an introductory statistics course, and finds a place in many “liberal arts mathematics” courses. Leonard Wapner’s *Unexpected Expectations* begins with the basic notion of expectation, but then uses it as a unifying theme for a large collection of mathematical ideas that at first glance, might seem far removed from elementary probability and simple arithmetic.

After a quick exploration of the history of probability, the big idea of expected value is introduced, and then it’s off to a wide range of applications, many of them standard (gambling, insurance, and airline booking among them), but some of them very ambitious for a book aimed at a general audience. These latter examples include Benford’s Law, Parrondo’s Paradox, and some elementary results from game theory. The mathematical arguments are present for those who wish to explore them, but the thrust of the book is to illustrate the myriad of applications of the simple formula for expected value, independent of the mathematical justification that underlies them. At this, *Unexpected Expectations* is a success.

In *The Pea and the Sun*, Wapner took the Banach-Tarski Paradox and brought it to a mainstream audience at a very accessible level. While his subject in this book is not nearly as mathematically complicated, he has done the same thing for mathematical expectation, and the result is an excellent contribution to popular mathematics writing.

Mark Bollman (mbollman@albion.edu) is associate professor of mathematics at Albion College in Michigan. His mathematical interests include number theory, probability, and geometry. His claim to be the only Project NExT fellow (Forest dot, 2002) who has taught both English composition and organic chemistry to college students has not, to his knowledge, been successfully contradicted. If it ever is, he is sure that his experience teaching introductory geology will break the deadlock.