Download this article
 Download this article For screen
For printing
Recent Issues

Volume 17
Issue 4, 543–722
Issue 3, 363–541
Issue 2, 183–362
Issue 1, 1–182

Volume 16, 5 issues

Volume 15, 5 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 8 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN 1944-4184 (online)
ISSN 1944-4176 (print)
 
Author index
To appear
 
Other MSP journals
An absorbing version of the top-to-random shuffle

Joel Brewster Lewis and Mehr Rai

Vol. 17 (2024), No. 4, 603–632
Abstract

Consider a randomly shuffled deck of 2n cards with n red cards and n black cards. We study the average number of moves it takes to go from a randomly shuffled deck to a deck that alternates in color by performing the following move: if the top card and the bottom card of the deck differ in color, place the top card at the bottom of the deck; otherwise, insert the top card randomly in the deck. We use tools from combinatorics, probability, and linear algebra to study this process.

Keywords
finite Markov chain, absorbing Markov chain, card shuffling, top-to-random shuffle
Mathematical Subject Classification
Primary: 60C05, 60J10
Secondary: 05A05
Milestones
Received: 16 June 2022
Revised: 2 May 2023
Accepted: 4 May 2023
Published: 2 October 2024

Communicated by Jonathon Peterson
Authors
Joel Brewster Lewis
Department of Mathematics
George Washington University
Washington, DC
United States
Mehr Rai
Department of Mathematics
Aalto University
FI-00076 Aalto
Finland