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.