Poker News / Short-Stacked Shamus / 27 January 2012 / Leave a Comment

Since I began teaching my "Poker in American Film and Culture" class I've come to find out about other college-level courses being taught which highlight poker. One such course has been taught by Professor Bruce McCullough at Drexel University in Philadelphia. I spoke with Bruce recently about his course, an honors class titled "Probability, Poker and Decisions."

An Entrance to Poker

Short-Stacked Shamus: In what department are you at Drexel? And what is your academic background?

Bruce McCullough: I'm in the Business School in the Decision Sciences Department. I earned a degree in economics from Georgetown University after which I worked for a consulting firm for a couple years. Then I went to graduate school at the University of Texas at Austin where I got a Ph.D. in economics. I'm an econometrician by training, which is sort of like applied statistics for economics.

SSS: So how did you get interested in poker?

BM: Well, I was invited to an investment house a few years ago to give a talk on the accuracy of statistical software. As it turns out many software packages have inaccuracies in them -- for example, Microsoft Excel has lots of errors in it -- and so I was there to talk about that. When I was getting the tour, the guide stopped and pointed at a door and said, "In there is our poker room." And I laughed, because I thought she was joking. But she opened the door and I entered and sure enough there were several felt covered tables.

SSS: How about that?

BM: So I looked at the room. I had read books on the mathematics of finance and I know something about financial econometrics. And suddenly as I looked at the poker tables and realized where I was, I saw the connection: poker is just trading off risk and reward on the fly.

So I thought about it a little more and I started doing the probability calculations in my head and I realized I could calculate the probability of winning poker hands. And I saw the game theoretic aspects of it right away, too, so in the space of about thirty seconds I figured out that I had spent my entire graduate career preparing to play poker, and I didn't even know it!

SSS: Ha! So you began to play soon after that?

BM: Right. I went home and did a Google search and the book by Bill Chen and Jerrod Ankenman had just come out, The Mathematics of Poker. I read that book and it was off to the races. I found out how to get some money into an online poker account and started playing penny poker and enjoying it quite a bit.

The Decision to Teach Poker

SSS: How did you come to teach your "Probability, Poker, and Decisions" course?

BM: I was teaching an undergraduate statistics class which has a probability section in it. One of the students during the class asked me how to calculate probabilities for poker hands, and I said I didn't think it would be of interest to everyone, but I'd be happy to explain it after class. So after class four or five students stayed around and for the next few meetings we got together after class and I showed them the basics.

Now one of these students was an honors student and he asked me whether I would be interested in teaching an honors course on math and poker, and I said sure. So he did all of the paperwork and I got to design and teach the class.

SSS: That's terrific. And when was the first time you taught it?

BM: I've only taught it once, in 2010. It was a lot of fun because I had to systematize everything I'd learned and make it intelligible to people who didn't know a lot of math. And I had to come up with a lot of outside readings to try to make it germane to them.

SSS: The syllabus looks very interesting.

BM: Yes, we start with the basic probability calculations, counting methods, and so on. Then we do expected value and Bayes theorem. Then we proceed through odds, outs, implied odds, and David Sklansky's Fundamental Theorem of Poker. Then I introduce them to limit poker calculations and we talk about deciding whether to call, raise, or fold and the math of sucking out.

Following that we go over some utility theory because, of course, this is a business school and all of this has to be directly applicable to business. So we do the expected utility theory and then introduce the standard paradoxes from that and then move into prospect theory and show the heuristics and biases that occur naturally in a decision-making context. Then I relate these biases to poker.

SSS: I do see a few familiar names on your syllabus among the readings.

BM: Right, Barry Tannenbaum and Rachel Croson had a couple of nice little articles in Card Player on prospect theory. Then after we do limit hold'em we move on to no-limit, because that's what everyone wants to play. So we do the no-limit calculations for fold equity, implied odds, semi-bluffing, the gap concept, and so on.

Some "Hands-On" Experience

SSS: So you have a semester's worth of interesting lectures and discussions, and I see you have a paper and a couple of exams.

BM: Yes, and another interesting thing I was able to do -- this was before Black Friday -- was to have someone set up for me my own weekly tournament on Full Tilt Poker. I think it was every Tuesday night at 10 o'clock, we had a mandatory limit hold'em tournament.

SSS: That's excellent. I also have my "Poker in American Film & Culture" class play some poker early in the semester, primarily to get the students familiar with the rules and different games (draw, stud, and hold'em).

BM: It worked really well the first several weeks, although after we moved to no-limit hold'em in the class people became less interested in playing limit hold'em -- I wasn't able to change the parameters of the tournament.

SSS: To me it makes perfect sense to have them play in a course about decision-making and probability. That's a great idea to make that part of the class.

BM: Oh, it certainly was. I played, too, the first couple of times, but it wasn't really that fair. I think the first two times I won and the third time I finished second. So I quit playing but I would watch the tournaments after that. In fact we had a great discussion in class about the tournament in which I managed to finish second, because I had not previously had any heads-up experience against an aggressive player. And the person who beat me played very aggressively, so I knew he was raising with crap but I couldn't call him!

SSS: Right!

BM: So we had a great discussion in class about that and in fact I brought in an article about Jerry Yang's win in the 2007 WSOP Main Event in which the author describes how Yang was bluffing one-third of the time. I asked the students what one thing really stood out to them from that article, and it wasn't that Yang wasn't a professional or anything else, but the fact that he bluffed a third of the time.

SSS: It was his strategy, not his story, that stood out.

BM: Right. And when we got to the game theory part of the course, I showed them that in that setting the game theory optimal bluffing ratio is one-third!

SSS: Wow. That's definitely a memorable example, too.

BM: Yes, the game theory part of the course is just fascinating.

SSS: It seems to me that unlike my class -- which is more focused on history, literature, and film and not so much on learning how to play poker -- students taking your course really do come away with a better understanding of how to play the game.

BM: Depending upon where the student starts, yes. And, of course, I tell them as well that beyond just learning the math of the game it also takes patience and discipline to win.

Not Just a "Poker Class"

SSS: Let me ask you one more question about teaching a college course in which poker is part of the class. Since I began teaching my course, I've been asked quite often about teaching a "poker class" in college. What do you say when people have asked you about teaching poker in college?

BM: Well, I don't really call it a "poker class." This is a course in decision-making. And we do all the usual decision-making stuff that you would find in many other decision-making classes. We do utility theory, prospect theory, decision trees, Bayes theorem, and so on. It just so happens that the examples that I use to illustrate the concepts are all from poker.

My next step, when I teach the class again, will be to place a business application at the end to illustrate each concept. So when we do decision trees or game theory or other topics, we'll talk about them in limit hold'em but then we'll also be talking about them in business. I've taught this as a special topics honor class, but if this is going to be a regular class in a business school, it really has to be about business, too.

That said, the course is very rigorous. We do lots and lots of math. And the students are all interested in the topic to begin with and willing to work hard because they want to learn the material.

A Probability-Studying Poker Player in Havana

SSS: You recommended a film to me a while back, Havana (1990), as one I should consider for my class. As you know the film is set on the eve of the Castro revolution in Cuba at the end of 1958 and stars Robert Redford as a poker player, Jack Weil.

I wrote about the film on the Epic Poker blog this week and talked about how it uses poker to help convey ideas both about Redford's character and American identity. One thing I didn't mention in the column was a kind of interesting moment near the end of the film. A character is in Jack's apartment and finds a couple of books. [A screenshot showing the books appears above.]

BM: Right, we see in his flat he has a couple of books, one titled Laws of Probability and another called A Theory of Numbers.

SSS: Are those actual books?

BM: Yes, they are actual titles. There are a thousand books called A Theory of Numbers, really, but looking at the books one can tell they are graduate-level textbooks from the 1940s or 1950s. And those can't be read by a layman. They can't be read by someone without extensive training in mathematics.

SSS: So it isn't just a random detail in the film. Those books tell us he's more than just an average poker player.

BM: Right, Jack Weil is some sort of autodidact to have taught himself enough math to have mastered these books. If you can imagine somebody with a modern-day ability to play poker going back forty years and playing then, he would clean up! And so that's kind of what Jack Weil was doing, using all of this cutting edge probability and number theory to be a better poker player. The stuff we take for granted now, he was doing back in the 1950s!

SSS: That moment makes me think a little of the shot in The Cincinnati Kid when we see Eric preparing for his big match with the Man by doing some math exercises, calculating percentages. Not exactly graduate-level work, but just something to keep his mind limber before he plays. So it's a little similar in Havana, but those books are doing more than just suggesting that Jack is an analytically-minded person. Rather he is someone highly unique in that late 1950s world.

BM: Yes, he's extraordinary.

SSS: Well, thanks very much for taking the time to talk about your not-so-ordinary course!

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