The Annals of Applied Probability

Trailing the Dovetail Shuffle to its Lair

Dave Bayer and Persi Diaconis

Full-text: Open access

Abstract

We analyze the most commonly used method for shuffling cards. The main result is a simple expression for the chance of any arrangement after any number of shuffles. This is used to give sharp bounds on the approach to randomness: $\frac{3}{2} \log_2 n + \theta$ shuffles are necessary and sufficient to mix up $n$ cards. Key ingredients are the analysis of a card trick and the determination of the idempotents of a natural commutative subalgebra in the symmetric group algebra.

Article information

Source
Ann. Appl. Probab. Volume 2, Number 2 (1992), 294-313.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aoap/1177005705

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aoap/1177005705

Mathematical Reviews number (MathSciNet)
MR1161056

Zentralblatt MATH identifier
0757.60003

Subjects
Primary: 20B30: Symmetric groups
Secondary: 60B15: Probability measures on groups or semigroups, Fourier transforms, factorization 60C05: Combinatorial probability 60F99: None of the above, but in this section

Keywords
Card shuffling symmetric group algebra total variation distance

Citation

Bayer, Dave; Diaconis, Persi. Trailing the Dovetail Shuffle to its Lair. The Annals of Applied Probability 2 (1992), no. 2, 294--313. doi:10.1214/aoap/1177005705. http://projecteuclid.org/euclid.aoap/1177005705.


Export citation