How to win at Jenga: Trine student presents game theory research at online conference

How would you like a guaranteed win at Jenga?

Caleb Aukeman, a Trine University mechanical engineering and mathematics major from Winona Lake, Indiana, recently conducted a presentation at an online game theory conference showing how a modified version of Jenga will always be won by the second player.

Though it may not help you keep those wood blocks from tumbling the next time you play, Aukeman’s presentation earned positive feedback from the 55 who attended from around the world.

Undergraduate participation

Sprouts, held April 12, is an annual online conference covering combinatorial game theory, which is the mathematical study of turn-based games such as chess where random and hidden and elements are not involved.

The conference is targeted toward undergraduate students. In addition to Aukeman, three other Trine students attended along with Michael Smith, assistant professor of mathematics.

Aukeman’s research built on a version of Jenga outlined in others’ research that only allows players to move blocks of their own color.

He first heard of the conference in the Combinatorial Game Theory class taught by Smith. He researched impartial Jenga, in which all moves are available to both players, as part of the first class project.

Aukeman learned that partizan Jenga, which limits certain moves to certain players, had not been studied.

“I became even more interested in presenting when I first began Project 2 for the class,” Aukeman said. “Prof. Smith encouraged me that my topic would be perfect to present at Sprouts.”

Working with Prof. Smith, Aukeman was able to prove mathematically that there is a series of moves the second player can follow in combinatorial partizan Jenga that allows them to always beat the first player.

He also proved that a starting setup of alternating rows of block colors is always won by the second player if the number of those rows is equal; otherwise the player with the most rows will win.

He overcame nerves and some technical difficulties to present his research at the conference.

“Overall, it was a good experience, and I am really glad that I got to do it,” he said. “I received really positive feedback on my figures for my presentation. They also seemed to like the notation that I created.”