No. 002 THU 01 OCT 2026

A deck of cards needs about seven shuffles to become random.

The riffle shuffle

In 1992, mathematicians Dave Bayer and Persi Diaconis worked out how quickly riffle shuffling mixes a 52-card deck. Order does not fade gradually. It survives the first few shuffles remarkably well, then collapses around the seventh — the point at which the deck becomes reasonably close to random. Extra shuffles after that change very little.

Why it’s interesting

Fig. 002 Fifty-two cards, seven riffles — one ring per shuffle. The black line follows a single card.

The longer version

Their paper, "Trailing the Dovetail Shuffle to its Lair", used a model of the riffle shuffle in which the deck is cut roughly in half and the two packets drop together card by card. Measured this way, the distance from a truly random deck stays high for five or six shuffles and then falls off a cliff.

This sudden drop is called a cutoff, and it turns up in many other mixing processes. The practical upshot became a familiar rule of thumb at card tables: shuffle seven times.

A deck of cards needs about seven shuffles to become random.

Why it’s interesting

The longer version

See how we got here

Sources