Preface
I am a lousy poker player. Let me get that out of the way right off the bat. If you are reading this book in the hope that you will learn strategy tips on how to be a better poker player, you are bound to be disappointed. This is not a book on how to use probability to play Texas Hold’em. It is a textbook using Texas Hold’em examples to teach probability.
The other thing I want to state right from the outset is that I in no way intend this book to be an endorsement of gambling. Poker, like all forms of gambling, can be addictive and dangerous. The morality of gambling has been properly questioned by many for a host of reasons, and among them is the fact that many people, especially those who can least afford it, often lose more than they should prudently risk. The rise of online gambling recently, especially among students at colleges and universities, is cause for serious concern. When I have taught my course on poker and probability at UCLA in the past, I have always started out on the first day by lecturing about the dangers of gambling, and my first required readings for the students are handouts on the perils of gambling addiction.
The purpose of this book is not to promote gambling or to teach how to play poker. Instead, my intention is to use students’ natural interest in poker to motivate them to learn important topics in probability. The first few times I taught probability, I was disappointed by many of the examples in the books. They typically involved socks in sock drawers or balls in urns. Most of my students did not even know what an urn was, and certainly were not motivated when informed of its meaning. I thought it would be interesting to try to teach the same topics as those covered in most probability texts using only examples from poker. I was happy to find that students seemed to vastly prefer these examples and that it was hardly a challenge at all to motivate even quite complex subjects using poker. In fact, I needed to look no further than Texas Hold’em, which is currently the most popular poker game, to illustrate all the standard undergraduate probability topics and even some more advanced topics. While some have urged me to discuss other poker games, I have decided instead to stick exclusively to Texas Hold’em examples, for two reasons. The first is that Texas Hold’em is more popular and more commonly televised than other games and hence may be of greater interest to students. The second reason is simply brevity. The purpose of this book is to teach probability, not the rules and intricacies of various poker games, and I found absolutely no reason to search beyond Texas Hold’em to illustrate any probability topic.
The topics covered in this book are similar to those in most undergraduate probability textbooks, with a few exceptions. I have added sections on special topics, including a few specialized poker issues such as the quantification of luck and skill in Texas Hold’em, and some topics typically found in graduate probability texts, such as the ballot theorem and the arcsine law.
I will doubtless be criticized by some of my colleagues for writing this book, because poker is not only perceived as immoral but also as frivolous. While many probabilists and statisticians might feel that probability should be taught using more serious, scientific examples, I disagree. I fully acknowledge the downsides of poker, but poker has its good qualities as well. Texas Hold’em is fun, and its current popularity can be used to attract students and keep them interested. Texas Hold’em involves a blend of luck and skill that may be extremely frustrating at times for players, but can also be wonderfully intriguing, and incidentally is in many ways similar to other pursuits in life that seem to rely on a similar blend of skill and fortune, such as a search for a job or for love. Most importantly, in my opinion, Texas Hold’em is at its heart an intellectual pursuit. Gambling games such as poker have inspired many of the most important ideas in probability theory, including Bayes’s theorem and the laws of large numbers that have found applications in so many scientific disciplines.
Aside from using exclusively Texas Hold’em examples, one other feature that I hope may make this book unique as a probability textbook is that I have tried, wherever possible, to use only real examples—not realistic, but real examples from actual hands of Texas Hold’em shown played in the World Series of Poker or other major tournaments or televised games. The search for these hands was time-consuming but enjoyable, and the use of real examples may help to keep students interested. Sometimes the probability topic discussed is somewhat tangent to the main issue that makes a poker hand interesting, but hopefully readers can look past this. A list of links to some of the hands referred to in this book is at .
When I have taught this course in the past, in addition to homework and exams, I assigned the students two computational projects. On the first project, the students were asked to write a function in R that took various inputs including their cards, the betting before them, their number of chips, the number of players at the table, and the size of the blinds, and then output a bet size of 0 or their number of chips. That is, they had to write a program to fold or go all-in. I would then have their computer programs compete in tournaments that I ran multiple times. For the final project, they were asked to write a Texas Hold’em program in R that could be more complicated, and did not require them to go all-in or fold, but allowed them to bet intermediate amounts. Some students sincerely enjoyed these projects and wrote quite elaborate functions. Several students felt that this was their favorite aspect of the course. I have compiled functions for instructors to use to run these tournaments, as well as some examples of the students’ functions, into a public R package called holdem which may be freely downloaded from and some description is given in Chapter 8 as well.
I have a lot of people to thank. First and foremost, I thank my wife, Jean, not only for supporting me throughout the writing of this book but also for indirectly introducing me to Texas Hold’em by taking me on a surprise trip to Las Vegas for my birthday several years ago. Gamma, Dad, Mom, Randy, Marlena, and Melanie not only gave me endless support but also played tons of cards with me growing up, Aidee’s help made writing the book possible, and Bella gave me inspiration and emotional support. My friend Craig Berger taught me the ins and outs of poker strategy, and David Diez taught me how to make an R package. Keith Wilson and Daniel Lawrence provided numerous stimulating conversations about poker, as did Tom Ferguson, Arnulfo Gonzalez, Reza Gholizadeh, and John Fernandez. I want to thank Jamie Gold, who came and spoke to my class and was extremely nice and entertaining. I am also grateful for the excellent probability texts by Feller (1966, 1967), Billingsley (1990), Pitman (1993), Ross (2009), and Durrett (2010), from which much of the content in this book was taken. My twin children, Gemma and Max, were born while I was writing this book, and provided not only great inspiration but also ample distraction. Any mistakes are their fault!