Our goal in this project is to understand how one can test if a particular dealer's shuffles follow a certain pattern. We have developed a theoretical framework for the same and wish to understand its performance in practice.

Consider a dealer at a casino performing riffle shuffles (a well known style of shuffling which tends to produce the desirable randomness in a few repeats). There are many different riffle shuffles and not all of them have the desirable properties of an unbiased riffle shuffle known as the Gilbert, Shannon, Reeds (GSR) shuffle. We formulate a problem definition for testing whether a certain set of observed shuffles actually follow a certain type of riffle shuffle (for instance, GSR). We then present an algorithm for doing so which we prove succeeds with a large probability in O(n^{3/2}) shuffles where n is the number of cards. We hope to supplement this theory by using it to observe how much bias is present in the shuffles done by people everyday.

Research Areas