A rule of thumb for riffle shuffling

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 log2n to log2n. We derive closed formulae and an asymptotic "rule of thumb" formula which is remarkably accurate. © Institute of Mathematical Statistics, 2011.