"Let's Make a Deal," with its popular host Monty Hall, was a staple of 1970s game shows, with squirming contestants trying to guess which of three doors concealed the grand prize. The contestant chooses a door, but does not open it. Monty opens a different door, always empty. The contestant faces a choice: stick with his original door or switch to the remaining door?

This mindbender is known as "the Monty Hall Problem," the subject of Jason Rosenhouse's witty new book. Rosenhouse, associate professor of mathematics at James Madison University, examines the problem from multiple angles, lucidly explaining why, though counterintuitive, the best choice is to switch doors.

//The Monty Hall Problem// is sure to elicit emotional responses — as the conundrum itself has for years among mathematicians, philosophers, physicists, and others. Rosenhouse acknowledges the provocative nature of the problem and faces it head on, thoroughly and convincingly explaining the math and logic of the problem and addressing several variations.

Although Rosenhouse's enthusiasm for the subject is infectious, readers whose education ended with Math 101 may find much of this book beyond reach, as it is thick with equations. But for those who aren't arithmophobes, //The Monty Hall Problem// is delightfully challenging.

Reviewed by Kelli Christiansen