A rule of thumb for riffle shuffling

Sami Assaf, Persi Diaconis, K. Soundararajan

Type: Article

Publication Date: 2011-06-01

Citations: 25

DOI: https://doi.org/10.1214/10-aap701

Abstract

We study how many riffle shuffles are required to mix n cards if only certain features of the deck are of interest, for example, suits disregarded or only the colors of interest. For these features the number of shuffles drops from (3/2) log2 n to log2 n. We derive closed formulae and an asymptotic "rule of thumb" formula which is remarkably accurate.

Locations

arXiv (Cornell University) - View - PDF
DataCite API - View
The Annals of Applied Probability - View - PDF

Similar Works

Action	Title	Year	Authors
+	The cutoff phenomenon for randomized riffle shuffles	2007	Guan‐Yu Chen Laurent Saloff‐Coste
+	HOW MANY TIMES SHOULD YOU SHUFFLE A DECK OF CARDS?1	1998	Brad Mann
+	Information Loss in Riffle Shuffling	2002	Dudley Stark Ayalvadi Ganesh Neil O’Connell
+ PDF Chat	Trailing the Dovetail Shuffle to its Lair	1992	Dave Bayer Persi Diaconis
+ PDF Chat	Matching Adjacent Cards	2024	Kent E. Morrison
+	Riffle shuffles of a deck with repeated cards	2009	Sami Assaf Persi Diaconis K. Soundararajan
+ PDF Chat	Riffle shuffles of a deck with repeated cards	2009	Sami Assaf Persi Diaconis K. Soundararajan
+	How Many Shuffles to Mix a Deck?	1995	Joseph B. Keller
+	A Shuffle that Mixes Sets of any Fixed Size much Faster than it Mixes the Whole Deck	2004	Robin Pemantle
+	A Better Way to Deal the Cards	2010	Mark Conger Jason Howald
+	Shuffling cards for blackjack, bridge, and other card games	2006	Mark Conger Divakar Viswanath
+ PDF Chat	Riffle shuffles of decks with repeated cards	2006	Mark Conger Divakar Viswanath
+	A Random Card Shuffling Process	2022	Joel Brewster Lewis Mehr Rai
+	How,when and how much a card deck is well shuffled?	2014	Benjamin Isac Fargion
+ PDF Chat	On the rate of mixing for $p$-shuffles	2000	Steven P. Lalley
+ PDF Chat	Cutoff in total variation for the shelf shuffle	2024	Andrea Ottolini R.-X. Chen
+	Persi Diaconis und Jason Fulman: The mathematics of shuffling cards. (Providence, RI: American Mathematical Society (AMS) 2023, 346 Seiten, ISBN: 978-1-4704-6303-8/pbk; 978-1-4704-7290-0/ebook)	2024	Dominik Schmid
+ PDF Chat	Card shuffling and Diophantine approximation	2008	Omer Angel Yuval Peres David B. Wilson
+	Cutoff for biased transpositions	2017	Megan Bernstein Nayantara Bhatnagar Igor Pak
+	Riffle shuffles with biased cuts	2011	Sami Assaf Persi Diaconis K. Soundararajan

Works That Cite This (21)

Action	Title	Year	Authors
+ PDF Chat	Lumpings of Algebraic Markov Chains Arise from Subquotients	2018	C. Y. Amy Pang
+	A Random Walk in Representations	2014	Shanshan Ding
+	Carries, shuffling, and symmetric functions	2009	Persi Diaconis Jason Fulman
+ PDF Chat	Functions of random walks on hyperplane arrangements	2010	Christos A. Athanasiadis Persi Diaconis
+ PDF Chat	An analytical model of information dissemination for a gossip-based protocol	2009	Rena Bakhshi Daniela Gavidia Wan Fokkink Maarten van Steen
+ PDF Chat	Hopf algebras and Markov chains: two examples and a theory	2013	Persi Diaconis C. Y. Amy Pang Arun Ram
+	Coupling for features of random walks	2019	Graham White
+	Random walks on hyperplane arrangements and stopping times	2016	Evita Nestoridi
+ PDF Chat	Riffle shuffles with biased cuts	2012	Sami Assaf Persi Diaconis K. Soundararajan
+ PDF Chat	Riffle shuffles of a deck with repeated cards	2009	Sami Assaf Persi Diaconis K. Soundararajan

Works Cited by This (31)

Action	Title	Year	Authors
+	New Mathematical Diversions from "Scientific American"	1975	Martin Gardner
+	Martin Gardner's new mathematical diversions from "Scientific American"	1969	Martin Gardner
+	Linear Representations of Finite Groups	1977	Jean-Pierre Serre
+	Group representations in probability and statistics	1988	Persi Diaconis
+	Shuffling cards for blackjack, bridge, and other card games	2006	Mark Conger Divakar Viswanath
+ PDF Chat	Normal Approximations for Descents and Inversions of Permutations of Multisets	2007	Mark Conger Divakar Viswanath
+ PDF Chat	None	2002	Jason Fulman
+ PDF Chat	Functions of random walks on hyperplane arrangements	2010	Christos A. Athanasiadis Persi Diaconis
+	On Choosing and Bounding Probability Metrics	2002	Alison L. Gibbs Francis Edward Su
+ PDF Chat	Total variation cutoff in birth-and-death chains	2008	Jian Ding Eyal Lubetzky Yuval Peres