Seven Shuffles

How random is a shuffled deck?

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Shuffling is a random walk on the 52! orderings of a deck.
• Riffle shuffles stay far from random, then mix quickly: about seven are needed.
• Rising sequences at most double with each riffle.

Steps

1. A random walk on orderings
2. How many orderings?
3. Watch randomness arrive
4. Rising sequences
5. Overhand shuffles
6. Counting runs