Arthur Benjamin from Harvey Mudd College presents the Kirwan Undergraduate Lecture.

Arthur Benjamin, the Smallwood Family Professor of Mathematics at Harvey Mudd College, gave the 2025 William E. Kirwan Distinguished Undergraduate Lecture on April 8. His lecture, “Solving the Race in Backgammon,” highlighted his research on perhaps the oldest game that is still played today.

Backgammon is a game that combines luck with skill, where two players take turns rolling dice and decide how to move their checkers in the best possible way. It is the ultimate math game, where players who possess a little bit of mathematical knowledge can have a big advantage over their opponents. Players also have the opportunity to double the stakes of a game using something called the doubling cube, which, when used optimally, leads to players winning more in the long run. Optimal use of the doubling cube relies on a player's ability to estimate their winning chances at any stage of the game.

When played to completion, every game of backgammon eventually becomes a race, where each player attempts to remove all of their checkers before their opponent does. The goal of Benjamin’s research is to be able to determine the optimal doubling cube action for any racing position and approximate the game-winning chances for both sides. By calculating the effective pip count for both players and identifying the positions' variance types, Benjamin arrives at a reasonably simple method for achieving this, which is demonstrably superior to other popular methods.

Outside of the classroom, Benjamin is a professional magician and one of the world’s fastest mental calculators. In 2020, he applied his talents to the game of backgammon and won the American Backgammon Tour and was elected to the American Backgammon Hall of Fame. He is one of 15 backgammon grandmasters in the United States.

Benjamin has been honored by the Mathematical Association of America for his teaching and writing, and is a recent winner of the Communications Award from the Joint Policy Board of Mathematics. He has given 3 TED talks that have been viewed over 50 million times and written several books and created numerous video courses that share the beauty and magic of mathematics.