Trinity College Trinity College Digital Repository Faculty Scholarship 4-2019 Progressive Randomization of a Deck of Playing Cards: Experimental Tests and Statistical Analysis of the Riffle Shuffle Mark P. Silverman Trinity College,
[email protected] Follow this and additional works at: https://digitalrepository.trincoll.edu/facpub Part of the Statistics and Probability Commons Open Journal of Statistics, 2019, 9, 268-298 http://www.scirp.org/journal/ojs ISSN Online: 2161-7198 ISSN Print: 2161-718X Progressive Randomization of a Deck of Playing Cards: Experimental Tests and Statistical Analysis of the Riffle Shuffle M. P. Silverman Department of Physics, Trinity College, Hartford, CT, USA How to cite this paper: Silverman, M.P. Abstract (2019) Progressive Randomization of a Deck of Playing Cards: Experimental Tests The question of how many shuffles are required to randomize an initially or- and Statistical Analysis of the Riffle Shuffle. dered deck of cards is a problem that has fascinated mathematicians, scien- Open Journal of Statistics, 9, 268-298. tists, and the general public. The two principal theoretical approaches to the https://doi.org/10.4236/ojs.2019.92020 problem, which differed in how each defined randomness, has led to statisti- Received: March 22, 2019 cally different threshold numbers of shuffles. This paper reports a compre- Accepted: April 25, 2019 hensive experimental analysis of the card randomization problem for the Published: April 28, 2019 purposes of determining 1) which of the two theoretical approaches made the Copyright © 2019 by author(s) and more accurate prediction, 2) whether different statistical tests yield different Scientific Research Publishing Inc.