A former Harvard professor of decision science and game theory draws on those disciplines in this review of controversial strategic decisions of World War II. Allied leaders--although outstanding in many ways--sometimes botched what now is termed meta-decision making or deciding how to decide. Operation Jubilee, a single-division raid on Dieppe, France, in August 1942, for example, illustrated the pitfalls of groupthink. In the Allied invasion of North Africa three months later, American and British leaders fell victim to the planning fallacy: having unrealistically rosy expectations of an easy victory. In Sicily in the summer of 1943, they violated the millennia-old principle of command unity--now re-endorsed and elaborated on by modern theorists. Had Allied strategists understood the game theory of bluffing, they might well in January 1944 not have landed two-plus divisions at Anzio in Italy.