The
Mathematics of Games and Gambling
Edward Packel
Publisher: Mathematical
Association of America (2006)
Details: 174 pages, Hardcover
Edition: 2 Series: The Anneli
Lax New Mathematical Library 28
Price: $44.00
ISBN: 0883856468
Category: Monograph
Topics: Game Theory, Mathematics for
the General Reader, Probability Theory
This book is in the MAA's basic library list.
MAA Review
[Reviewed by Sarah Boslaugh, on 08/21/2006]
It's often said that you have the same chance of
winning the lottery, whether or not you buy a ticket. While that statement is
not absolutely true, the infinitesimal probability of winning is close enough
to zero to dissuade anyone who understands the concept of expectation
from playing the state-run lotteries. However, the general public has not yet
caught on: in weeks when the jackpot offered is unusually high, so many New
Yorkers travel to Connecticut to buy Powerball tickets that Metro-North (a
local commuter rail line) distributes fliers indicating at which train stops
the tickets (not available in New York State) can be purchased.
If some of those eager Powerball players invested
their money in Edward Packel's The Mathematics of Games and Gambling,
the money they would save by forgoing such loser's bets would soon cover the
purchase price of the book. Not that I have anything against gambling per se,
but some of the earlier research into statistics was conducted in support of
gambling, and the current popular interest in poker and other games of chance
provides an excellent teaching opportunity to introduce elementary concepts of
probability.
Consider the case of the Chevalier de MŽrŽ, who
thought that because he prospered by making bets at even odds that he would
roll at least one six in four rolls of the dice, he should do equally well
betting that he would roll two or more double sixes in twenty-four rolls of two
dice. In fact, the first bet is a consistent winner and the second is a
consistent loser, and in their efforts to explain why this was so, the
mathematicians Blaise Pascal, and Pierre de Fermat developed the concepts of
binomial probability and what is now known as "Pascal's Triangle". To
his credit, Packel notes although Pascal and Fermat brought this knowledge to
the Western world, the triangle was known earlier in both China and Persia,
where it is known as the "Khayyam triangle" after the Persian poet
and astronomer Omar Khayyam. Inclusion of such information is a significant
strength of Packel's book: the mathematical content is embedded in a social and
cultural context which makes it enjoyable reading even for individuals who have
no vested interest in either mathematics or gambling. The first chapter, which
combines a discussion of Girolamo Cardano and Fyodor Dostoyesvsky, should win
over the most right-brained English major.
The Mathematics of
Games and Gambling is suitable for many different audiences. Those
who have a recreational interest in mathematics will enjoy reading it because
of the clear explanations of the mathematics behind many popular games of
chance, and those explanations require only a knowledge of high school
mathematics. Beginning students of probability will appreciate this book for
the same reason: Packel's exposition of basic probability is clearer than that
contained in some textbooks. It would be an ideal textbook or supplement in
courses for mathematics for non-majors. And those who are truly interested in
gambling should buy a copy in order to understand how to optimize their
winnings, or at least lose their money more slowly. In fact, I'm beginning to
think of Packel as an ambassador to the non-mathematical majority,
demonstrating to them that mathematics can be useful and entertaining, and that
mathematicians can be literate and articulate.
Edward W. Packel is
currently the Volwiler Professor of Mathematics at Lake Forest College in
suburban Chicago, where he has taught mathematics and computer science courses
since 1971. Packel received his BA from Amherst College in 1963 and his PhD
from MIT in 1967. His research interests include game theory and social choice
theory, functional analysis, information-based complexity, and the use of
technology such as Mathematica in teaching mathematics. Professor Packel
maintains a website at http://math.lfc.edu/packel/.
Sarah Boslaugh, PhD, MPH, is a Performance Analyst for BJC HealthCare in Saint Louis, Missouri. She published An Intermediate Guide to SPSS Programming with Sage in 2005 and is currently editing The Encyclopedia of Epidemiology for Sage (forthcoming, 2007) and writing Secondary Data Sources for Public Health (forthcoming, 2007) for Cambridge University Press.