Using math to beat the odds

Posted on Wednesday, February 19, 2014

Author: Mike Foster

Pieter Hofstra

Who would take math as an elective?  When the course is Poker 101, taught by uOttawa Associate Professor Pieter Hofstra, the answer is a full house of 200 students.

Hofstra says that his course, entitled Probability and Games of Chance: Poker 101, is not filled with students wanting to get rich quick at the Lac Leamy Casino by using the mathematics behind game theory and probability. Instead, they are often looking to use this math to predict outcomes in legal cases, economics or biology.

We asked Hofstra, a logician at the Faculty of Science’s Department of Math and Statistics who once played poker semi-professionally, for his top tips on how to do the math and not lose your shirt.

Q. Have you ever used mathematics to cash in at the casino or while playing poker?

A. “I used to play a lot of poker. I find that in order to play well, you need to invest enough time. If I play now, it is purely for fun. I’m a bit reserved about telling you how much I have won. It is definitely not millions – a good night would be several thousand dollars. But it is unavoidable that you lose occasionally, especially the game I most like to play, which is Pot Limit Omaha. It is like Texas Hold’em, but played with four hold cards instead of two.”

Q. Do some of your students go to the casino to try their luck?

A. “What I always do at the beginning of the course is give a big disclaimer: this course is not meant to encourage students to go out and gamble. In fact, if I teach them anything, it is that games like roulette and blackjack are not wise from a financial perspective. If you are going to play, you should approach it like going out for dinner or going to the movies. You shouldn’t expect to make money.”

Q. How do you calculate the percentage likelihood of winning a hand of poker?

A. “There is an important concept called expected value. You need to make your best guess as to what is most likely to happen. The formula is the chance of winning the hand, times the money you stand to gain, plus the chance of losing the hand, times negative the money you stand to lose. If that is a positive number, while you are not guaranteed to win, if you were in that same situation thousands and thousands of times, on average you would make a profit.”

Q. What basic mathematics or formulas can help beat the odds in games of chance?

A. “In a game like roulette, you purely use probability theory because you don’t play against other players. You play the numbers. No matter how you divide your money over a roulette table – either putting it all on one number or spreading it out, or some weird combination – in the long run, you lose 2.7%. In blackjack, always stick at 17. (It is always more likely that you will draw a card higher than four and go bust past 21). The more hands you play, the lower the percentage chance you have of coming out ahead. It is something called the law of large numbers. The more you repeat the same thing, the more likely it is to converge to the theoretical outcome, which is financial ruin.”

Q. How can math be used to improve your poker game?

A. “Bayes theorem tells you how to revise your estimates of the likelihood of things happening once new information comes in. This is very relevant to poker. Knowing the math behind the game is one thing, but in practice, people don’t make huge calculations when they make decisions. They go by their intuition. There is this discrepancy between the mathematical theory of decision-making in games and how we really do it. Game theory helps you analyze situations where you need to make a decision but can’t without knowing why every person is doing what. Poker combines game theory, which is the multi-person aspect of decision-making, with probability.”

This popular course has been offered four times since 2011 and is also available in French (Probabilités et jeux de hasard: Poker 101).

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