Math in… Card Shuffling

When shuffling a deck of cards, chances are that your go-to method is the riffle shuffle — cutting the deck into two packets and then haphazardly dovetailing those packets together.

This is a fun and fast way to randomize a deck, but how many riffles should you perform so that the deck is random enough?

Mathematicians Dave Bayer and Persi Diaconis showed in 1992 that all possible orderings of a deck of 52 cards start to be about as likely as one another after seven or more shuffles.

The number of shuffles needed to cross that threshold grows with the size of the deck, with eight or more shuffles required to similarly derange a 108-card Uno deck.

These results assume that you don’t always alternate your dovetailing the same way. If you perfectly riffle shuffle a 52-card deck (cutting into two 26-card packets and alternating one card left, one card right) eight times, the deck will end up exactly how it started — not very random at all!