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) log₂ n to log₂ n. We derive closed formulae and an asymptotic “rule of thumb” formula which is remarkably accurate.