### DIMACS - RUTGERS EXPERIMENTAL MATHEMATICS SEMINAR

Sponsored by the Rutgers University Department of Mathematics and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

**Co-organizers:**
**Doron Zeilberger**, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu
**Nathan Fox**, Rutgers University, fox {at} math [dot] rutgers [dot] edu)

Title:Shuffling Large Decks of Cards and The Bernoulli-Laplace Urn Model

Speaker: **Evita Nestoridi**, Princeton University

Date: Thursday, April 6, 2017 5:00pm

Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

In board games, in Casino games with multiple decks and cryptography, one is sometimes faced with the practical problem: how can a human (as opposed to the computer) shuffle big decks of cards. One natural procedure (used by casinos) is to break the deck into several reasonable size piles, shuffle each thoroughly, assemble, do some simple deterministic thing (like a cut) and repeat. G. White and I introduce variations of the classical Bernoulli-Laplace urn model (the first Markov chain!) involving swaps of big groups of balls. A coupling argument and spherical function theory allow the original problem to be solved.

See: http://www.math.rutgers.edu/~nhf12/expmath/