Undergraduate Research & Scholarships

AJ Grover L&S Math & Physical Sciences

Simulated Shuffle Sequences: GSR and Others

I’m looking to investigate the question: how does the randomness of a deck of cards change as a result of various shuffling techniques applied in sequence? To answer this question, I plan to build upon the work of Bayer and Diaconis in their paper “Trailing the Dovetail Shuffle to its Layer” by creating Python-simulated models of different card shuffling techniques, including the Gilbert-Shannon-Reeds model of a riffle shuffle, the box, the cut, and others. I will then test the randomness of the deck (via a distance metric such as KL Divergence or Total Variation Distance on the distribution of cards) after various sequences of said simulated shuffles. Although there is a vast literature on card randomization and shuffling in probability theory, this project will fill a gap by exploring the evolution of randomness and distance through simulation over sequences of shuffles, neither of which have been studied in as much detail.


Message To Sponsor

Thank you so much for funding my research project this summer! Without your support, I wouldn't have the ability to dedicate my summer to this project. To have the opportunity to further my research without having to worry about the financial cost of not pursuing other opportunities is a position I'm extraordinarily lucky to be in. Thank you again for making it possible.
Major: Applied Math, Data Science, Computer Science
Mentor: Steven N. Evans
Sponsor: Anselm MPS Fund
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