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The Mathematics of Games And Gambling: Second Edition. The Anneli Lax New Mathematical Library, by Edward Packel
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The first edition of this book was reprinted eight times! This book introduces and develops some of the important and beautiful elementary mathematics needed for rational analysis of various gambling and game activities. Most of the standard casino games (roulette, , blackjack, keno), some social games (backgammon, poker, bridge) and various other activities (state lotteries, horse racing, etc.) are treated in ways that bring out their mathematical aspects. The mathematics developed ranges from the predictable concepts of probability, expectation, and binomial coefficients to some less well-known ideas of elementary game theory. The Second Edition includes new material on: sports betting and the mathematics behind it; Game theory applied to bluffing in poker and related to the “Texas Holdem phenomenon”: The Nash equilibrium concept and its emergence in the popular culture: Internet links to games and to Java applets for practice and classroom use. The only formal mathematics background the reader needs is some facility with high school algebra. Game-related exercises are included at the end of most chapters for readers interested in working with and expanding ideas treated in the text. Solutions to some of the exercises appear at the end of the book.
- Sales Rank: #356063 in Books
- Brand: Brand: Mathematical Assn of Amer
- Published on: 2006-07-15
- Original language: English
- Number of items: 1
- Dimensions: 8.98" h x .63" w x 5.98" l, .85 pounds
- Binding: Hardcover
- 192 pages
- Used Book in Good Condition
Review
Review of first edition: 'The whole book is written with great urbanity and clarity. It is hard to see how it could be done better or more readably. The main virtue lies in the close and clever interweaving of theory and example.' Mathematical Gazette
Review of first edition: This is an informal, well-written, and witty exposition of the usefulness of mathematics and its analytical processes. The book covers gambling and betting schemes in math in greater detail than do most textbooks on introductory probability. --The Mathematics Teacher
High school students will find this book a good preparion for doing an elementary statistics and probability course at university level. This book is also a good resource for first year university students, in particular in mathematics and statistics, to understand the theories behind the games. --Boris Choy, The Australian Math Teacher
About the Author
Ed Packel} received his BA from Amherst College in 1963 and his PhD from MIT in 1967. He is currently the Volwiler Professor of Mathematics at Lake Forest College, where he has taught mathematics and computer science courses since 1971. Packel's initial work in functional analysis resulted in several research articles and an introductory graduate text. Subsequent research has involved game theory, social choice theory and information-based complexity. He is also heavily involved in using technology, primarily {\it Mathematicas a tool for teaching and research in mathematics.
Most helpful customer reviews
19 of 20 people found the following review helpful.
Excellent, Well-Written Approach to Games and Gambling
By Amazon Customer
As a casual poker player and a sometimes visitor to casinos and race tracks, I wasn't sure what to expect when I picked up this book; however, I found it was just what I needed. Was it a how-to book for Texas Holdem or other specific gambling pursuits? Not at all. But did the book give me ideas on how to improve my poker playing, my understanding of odds and betting strategy in a wide variety of games? Definitely! There's a vast amount of information in a relatively compact book. True it takes a little bit of math background to work through some of the material, but there is enough basic material along with ample references to a relevant bibliography and appropriate web sites so that everyone could learn something from this book. The author is quick to point out his intention of not delving too deeply into some topics, but he does provide abundant resources for the reader who is interested in digging deeper.
The writing style is light and enjoyable. The author even touches on life's lessons and philosophies of life, but most importantly he provides insight into the thought process employed by consistent winners. Along with the number of charts and tables that layout odds, decision trees, and probabilities, there are exercises at the end of each chapter for the reader to increase his understanding of the material presented. It is a book that can be read through from beginning to end or read in sections. The book is certainly digestible for the casual, interested reader, but maybe not all in one meal. Digesting it section by section worked better for me. Again there is a wide range of information on gambling theory with broad application.
The book starts with a brief history of gambling, even referencing some literature in which gambling played a role. The book studies basic theory involved in probability and expectations, permutations, binomial distribution and game theory. There are sections dedicated to various games from dice to poker to backgammon along with applications to more serious topics such as prisoner interrogation, faith beliefs and even war.
In today's age in which people are trying to engage in activities that exercise their minds, this book with its material and exercises provides ideal mind stimulation. It is a broad, educational and entertaining math book.
10 of 10 people found the following review helpful.
For Gamblers Who Would Like to Understand Probability
By calc geek
This is not an academic treatment. There is no calculus; no measure theory foundation. Instead, this delightful read allows the average person with a little high school algebra to study for a few weeks, work the examples, and gain a solid foundation in the theory underlying games of chance. This is the reason for the book's popularity.
Modern college texts require a much higher level of preparation plus about four or five times the effort to assimilate. That's no fun, and truthfully of little value, to the average gambler who just wants to calculate the odds of throwing a 5 at craps. If you can't solve that problem and a hundred others after reading this book, you probably should stop trying.
There is fascinating historical and motivational material woven throughout dozens of examples taken from modern gambling scenarios. The essential combinatorics are developed and the normal distribution is described intuitively as a limit to the binomial. There's even a derivation of the famous gambler's ruin formula -- all without calculus.
A gambler will be more than just sharp after reading this book, he will become dangerous!
19 of 22 people found the following review helpful.
Beginners text
By Harmomelodic
I bought this hoping it would be a sophisticated discussion of probability and game theory as it applies to gambling. Unfortunately it turned out to be an introductory text on probability with some discussion of the history and context of the development of probability theory.
The book uses gambling as its entr� to basic probability theory. Not a bad idea, but the title was clearly ambiguous.
If you are looking for an introductory text, it is probably a 4-4.5 star choice. For my purposes it gets a 2; the historical context was interesting and completely lacking in most texts (otherwise I would have gotten nothing out of it). The writing quality was also very good (easy to read and the explanations were straightforward and complete).
Recommended for beginners, NOT recommended for people looking for more advanced tools to solve more complicated gambling problems. Due to the titles ambiguity, I had to average my rating between the appropriate 'beginner's text' rating of 4-4.5, and the rating of 2 stars I give it for what I was looking for.
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