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, e.g. suits disregarded or only the colors of interest. For these features, the number of shuffles drops from 3/2 log_2(n) to log_2(n). We derive closed formulae and an asymptotic `rule of thumb' formula which is remarkably accurate.Comment: 27 pages, 5 table