Four shuffles suffice

It takes a while to shuffle a deck of cards seven times, but it is well known that that is how many riffle shuffles it takes to fully randomize a deck of 52 standard playing cards. This was shown in 1992 by Bayer and Diaconis.

As it turns out, however, for some games fewer than seven shuffles suffice. In their paper “A Rule of Thumb for Riffle Shuffling” Assaf, Diaconis, and Soundararajan prove that if some features of the cards are not relavant to the game, then seven may not be needed. In blackjack, for instance, only the values of the cards are important, not the suits. In this case four shuffles will do.

[via Math in the News]