Dave Roberts;
mathematics professor and mystifyingly savvy card player

The Best Poker Players Must Be Mathematicians

The final hand of an all-night poker game comes to a tense conclusion as the two weary competitors size up the current bet—and each other.

Player A calls Player B’s bet with a smile. “You’re bluffing.”

“How did you know, how could you know?” the loser wails.

It’s all about game theory, says UMM mathematics professor Dave Roberts. His submitted paper on game theory came about not as a result of his own interest in the topic, but because one of his senior seminar students, Stacy Nordgren, chose this subject for her project. To successfully advise Nordgren, Roberts needed to learn a little something more about game theory. A surprise awaited him in the research.

“There were old game theory papers written back in 1965 that raised a problem but didn’t solve it,” Roberts explains. “I realized I could solve the problem and wrote a 30-page paper doing just that.”

In the games Roberts studies, each player has a number of strategies at their disposal.

“Some strategies should be rejected as bad. The others should be mixed with certain probabilities in a way that includes bluffing. You really need to mix strategies to play optimally,” he says. “My paper is concerned with how many strategies to reject and how many to keep in the mix. I saw this in a purely mathematical context.”

Arithmetic geometry is Roberts’ own research area of choice. He strives to combine numbers, polynomials and matrices in a way that is both elementary and sophisticated.

“I want my work to connect with the big guys in math but also to be accessible to undergrads,” Roberts says. His soon-to-be published paper on arithmetic geometry, also 30 pages, fits that ongoing goal but it was a long wait to get it to print.

“It took 16 months for the editors to get back to me on a decision, but the news was good.” he recalls. “The referee had only good things to say, including that the paper was ‘extremely well written.’ I was very pleased.”

Roberts notes that while his research area is not a perfect match for undergraduate research, he still spends plenty of time with students working on their senior seminar presentations. Helping students with their own research allows him to branch out and gain some knowledge in areas beyond his field.

“For example, one senior sem student, Susie Hanson, was working with fractals,” says Roberts. “In the process of helping her, I learned a lot about the topic myself and I was able to use that in my Math Perspectives course. Delving into math areas beyond my main research broadens me as well as the students.”

Anyone for a hand of poker?