Customer Reviews

The Mathematics of Games And Gambling: Second Edition. The Anneli Lax New Mathematical Library

5 star:		(4)
4 star:		(1)
3 star:		(1)
2 star:		(0)
1 star:		(0)

 

 

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.

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!

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 entré 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.

This book would be an ideal text for what would no doubt be a popular special topics course in game theory applied to gambling. While gambling has always been a popular recreation among humans, it is now probably more popular than ever. With state sponsored lotteries now almost universal, new gambling casinos being built everywhere and the rise of internet gambling, it is now easier than ever to do battle with the odds as declared by the gambling gods. Although the chances of winning the battle rarely change. When I was a math professor decades ago, being asked a question about gambling was a regular event.
Packel begins with a discussion of the basics of probabilities and mathematical expectation, explanations of the basics of counting and then analyzes some familiar games such as backgammon, craps and chuck-a-luck. The coverage then moves on to elementary game theory as expressed in zero-sum games and the now classic prisoner's dilemma situation. The explanations are detailed and complete, exercises appear at the ends of the chapters and solutions to some of them are included in an appendix.
Game theory may be unique in that it is a topic that people find interesting and the mathematics is not very difficult. With a bit of explanation, relative novices can understand it. Therefore, this book falls into an unusual niche, it is a book containing mathematics and mathematical formulas that can be considered popular mathematics. A lot of people would be a lot wealthier if they read material like this before they spent their gambling dollars.

Though this is a somewhat short book, the topics and methods covered are amazingly precise in their rendition of key points found in the calculations of various games. The text will grant a superb base from which even the best protégés of mathematical analysis may expand their knowledge from.

This book is pretty good if you are new to probability theory. I like the book because it provides easy examples to help understand some of the basic theories in probability. The first chapter covers a small history about the beginning of probability and gambling. I like the chart it provides of the first origins of certain games such as poker, craps, and even the lottery. It also talks about the three types of gamblers there are casual, compulsive, and professional gamblers. The second chapter talks about finite probabilities and expected value. Examples used to define finite probabilities games such as rolling a die, drawing cards, or even the roulette wheel. These probabilities are simply found by taking the desired outcome(s) over all the possible outcomes. Determining odds is also explained in this chapter. Odds can be found by taking the probability of event E over 1 minus the probability of event E. The third chapter is about certain games that played based on the outcome of dice. Some examples are backgammon, craps, and the chuck-a-luck game. The book gives strategies based on determining the probability of a certain dice roll outcome and how it applies to winning or losing depending on the game's rules.
The fourth chapter is about the difference between permutations and combinations. Also explains the use of factorials and the n choose r notation in this chapter. Games using these concepts are poker, bridge, and keno. The book offers a pretty good betting strategy when it comes to poker. The fifth chapter talks about the binomial distribution, some general betting strategies, and talks about blackjack could be a favorable game to the player if you could count cards. The sixth chapter talks elementary game theory. The only thing I found interesting in this chapter is the Nash Equilibrium or also called the prisoner's dilemma. The final chapter has some pretty interesting topics. First topic is about bluffing in the game of Texas Holdem. The book gives some pretty nice formulas to determine when to bluff or not. Next topic was about horse race betting which talked about some observations and strategies behind it. Lastly it talks about probability and expected value behind certain lottery tickets which is pretty interesting. In a nutshell, this book would be pretty good to take a certain topic in probability theory like combinations or finite probability and use the game examples behind it to explain its meaning.