I was a scholar in the Illinois Geometry Lab, conducting research under the guidance of Professor A.J. Hildebrand. With three other students, we studied and extended a three-player mathematical poker model proposed by John Nash and Lloyd Shapley, who derived optimal probabilistic strategies for each of the players.

 

We met two times per week to investigate extensions and variations of the model, and to familiarize ourselves with the relevant literature on the mathematics of poker. We first reproduced the three-player five-round game discussed in the

paper using Mathematica, and then extended the model in several directions, including two-player version and three-player three-round and four-round versions. For each game, I helped derive formulas for expected profits for each player.

 

This research led to poster presentations at the 2017 Undergraduate Mathematics Symposium at UIC and the 2018 Nebraska Conference for Undergraduate Women in Mathematics. I really enjoyed this experience. I found

it rewarding to read literature and learn about the methodologies others used in their research, as they can give me guidance and stimulate new thoughts in my research. It is also rewarding to work in a collaborative setting. I learned that there is always something I can learn from others, and in return, there is always something I can contribute to the group.

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Poster