Markov Chains, Random Walks, and Card Shuffling

Outlaw, Nolan

Markov Chains, Random Walks, and Card Shuffling

Files

Outlaw_ecu_0600O_11494.pdf (1.47 MB)

Date

2016

Authors

Outlaw, Nolan

Publisher

East Carolina University

Abstract

A common question in the study of random processes pertains to card shuffling. Whether or not a deck of cards is random can have huge implications on any game being played with those particular cards. This thesis explores the question of randomness by using techniques established through analysis of Markov chains, random walks, computer simulations, and some basic shuffling models. Ultimately, the aim is to explore the cutoff phenomenon, which asserts that at some point during the shuffling process there is a sharp decline in the shuffled deck's distance from random.