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download beyond counting grosjean pdfTributes to the International Conference on Gambling and Risk-Taking
My field is applied probability, a branch of mathematics. One of the applications
that has most interested me over the years has been gambling. When probability was
first studied in the 17th and early 18th centuries by Fermat, Pascal, Huygens, Montmort,
Bernoulli, and De Moivre, gambling was its principal application, with application to
actuarial science still in its infancy. Today, gambling plays a less central role in applied
probability. The result is that there are few mathematicians working exclusively in this area. There are some, like me, who contribAnother reason to attend the ute occasionally.
As one might expect, there are also few, if any, mathematics
conferences, albeit a less
conferences devoted to gambling. Nevertheless, there is a triennial
important one, is that they interdisciplinary conference that always has a number of sessions
are entertaining. At what concerned with mathematical topics. I am referring to the Intermathematics conference could national Conferences on Gambling and Risk Taking organized by
Eadington and the Institute for the Study of Gambling and
one hear a presentation by Bill
Commercial Gaming at the University of Nevada, Reno. I have
Bishop Arnold Snyder of the attended nine of the last ten such conferences and have co-edited
First Church of Blackjack? Or one of its proceedings volumes, Optimal Play.
have I kept coming back to these conferences after more
a mathematical talk by Peter A. thanWhy
25 years? There are several good reasons. One is that they
Griffin done entirely in his best bring together people that one might not otherwise meet. In my
Dr. Strangelove imitation? case, I met Edward O. Thorp, author of Beat the Dealer, at the
5th conference (1981); J. Laurie Snell (1925--2011), who solved
the game of baccarat chemin de fer, at the 6th conference (1984);
Thomas Cover (1938--2012), well known for his universal portfolio, at the 7th conference (1987); Jerome H. Klotz (1934--2006), a former statistics professor of mine, at the
9th conference (1994); Robert C. Hannum, coauthor of Practical Casino Math, at the
10th conference (1997); and James Grosjean, author of Beyond Counting, at the 12th
conference (2003), just to name a few of the mathematically inclined attendees.
At all of the more recent conferences, there has been a reception for authors promoting their recently published books. It was at such a reception at the 12th conference
(2003) that I resolved that a book on probability and gambling at the level of Richard
A. Epstein’s classic The Theory of Gambling and Statistical Logic needed to be written for the present generation. I was confident that a 400-page book could be ready in
three years, in time for the next conference. Seven years later, my monograph/textbook
The Doctrine of Chances: Probabilistic Aspects of Gambling, at over 800 pages, was
published. The book was an attempt to document the state of the art of the subject as of
2010, restricted only by the constraint that it be presentable at the undergraduate level
(i.e., that it not be too technical).
At the 5th conference in 1981, I met Peter A. Griffin (1937--1998) and at the 6th in
1984, I met Russell T. Barnhart (1926--2003). I kept in touch with Griffin, author of The
Theory of Blackjack, and Barnhart, one of the few historians in the world whose focus
was the history of gambling, until their deaths, and I dedicated my book to their memories as a way of acknowledging the major influence they had on it.
Another reason to attend the conferences is to learn of new research. Many of the
papers presented at the conferences, and particularly many of the ones published in
UNLV Gaming Research & Review Journal ♦ Volume 16 Issue 2
the proceedings volumes Finding the Edge: Mathematical Analysis of Casino Games
and Optimal Play: Mathematical Studies of Games and Gambling, both co-edited by
Bill Eadington, were cited in my book. These include 10 articles in Finding the Edge,
perhaps the most influential of which (for me) was Donald E. Catlin’s “Using overall
expected return per dollar risked to determine strategy decisions in gambling games,”
and 16 articles in Optimal Play, perhaps the most important of which (for my book) was
Chris and Tom Ferguson’s “The endgame in poker,” a game-theoretic study of poker.
In particular, nearly half of the articles in these two volumes were deemed significant
enough to be cited in a basic textbook on the subject.
The more important point is that new mathematical research is being done on the
topic of gambling, and the subject is evolving. I can also acknowledge that, at least a few
times, when the call for papers arrived from Bill Eadington, I started thinking about what
I could speak on and went on to write a research paper that might not have been written
were it not for that motivation. My work on Oscar’s system (“Analysis of a gambling
system” in Finding the Edge) is an example of that.
Another reason to attend the conferences, albeit a less important one, is that they are
entertaining. At what mathematics conference could one hear a presentation by Bishop
Arnold Snyder of the First Church of Blackjack? Or a mathematical talk by Peter A.
Griffin done entirely in his best Dr. Strangelove imitation?
Finally, in the volume Optimal Play, one of the papers, Richard A. Epstein’s “Parrondo’s principle: An overview,” first introduced me to this intriguing topic, which has been
the focus of my research for the past four years. In summary, I can say categorically that
Bill Eadington’s International Conferences on Gambling and Risk Taking have played an
important role in my own career and, more importantly, in the continued development of
mathematical research on gambling. Of course, my field is only one of numerous subject
areas addressed by the conferences, so one can only speculate on the number of gambling scholars who owe a debt of gratitude to Bill Eadington for his foresight in initiating
this conference series in 1974 and his career-long efforts on its behalf.
Stewart N. Ethier, Ph.D.
Department of Mathematics, University of Utah
UNLV Gaming Research & Review Journal ♦ Volume 16 Issue 2