Riffle seven times and you’ll have a sufficiently random ordering of cards, an ordering that has likely never existed before. In other words, it’s unlikely you’ll ever shuffle two decks the same. //

...what if instead of a standard riffle using a deck roughly split in half, you were to only riffle 1 card at a time?

That is, using a standard deck of 52 cards, in one hand hold 51 cards and in the other hold the remaining single card. Now riffle these together. This is equivalent to taking one card and placing it at random inside of the deck.

So here’s the question:
How many single riffles do you have to do in order to have a completely shuffled deck? //

On average, 236 single card riffles will randomly shuffle a deck of cards. //

Equations are great, but let’s visualize this! Below is the same ordered deck of cards from before, except the K♦ has been highlighted red so we can follow its journey to the top of the deck.

Click the Riffle button to move the top card somewhere else in the deck randomly.