# Luck, Logic and White Lies:

The Mathematics of Games

*by Jörg Bewersdorff*

A.K.Peters 2005 xvii + 486 pages

This is a new edition and translation into English of the German
original published in 2001. The preface contains a brief discussion of
the role of uncertainty in games, which leads to a division of games
into three main types: games of chance, in which chance is more
influential than decisions of the players; games whose uncertainty
rests on the large number of possible moves, called combinatorial
games; and strategic games, where uncertainty arises primarily from
the fact that not all players have the same information about the
current state of the game. Some games fall clearly into one of these
categories (roulette, chess, rock-paper-scissors), but most combine
features of two or all three. The book is divided into three parts,
according to these game types, and each part into some 15 chapters,
each devoted to a single problem, usually a game. The chapters are
each introduced by an interesting question, for example: “It is hardly
to be expected that in 37 spins of the roulette wheel, all 37 numbers
will appear exactly once. How many different numbers will appear on
average?” Among the games discussed, in addition to those already
mentioned, are dice, lotteries, poker, backgammon, Risk, Monopoly,
snakes and ladders, blackjack, chess, nim, go, and baccarat.

The aim is to introduce the mathematics that will allow analysis of
the problem or game. This is done in gentle stages, from chapter
to chapter, so as to reach as broad an audience as possible. The
opening chapters introduce the basic concepts of elementary probability,
building from there to random variables, Markov chains
and some statistics by the end of Part I. In Parts II and III we find
discussions of strategy, the minimax theorem, algorithms, the halting
problem, Gödel’s Incompleteness Theorem, complexity theory, and
linear optimization. Anyone who likes games and has a taste for
analytical thinking will enjoy this book, and for those who wish
to go deeper there are plenty of suggestions for further reading.

Peter Fillmore, Dalhousie University, Halifax, NS

*CMS Notes*, published by the Canadian Mathematical Society, **37 (4)** (May 2005), p.9.