How to shuffle cards, and how many times

Split the deck into two roughly equal halves and lay them on the table with their short ends facing each other. Put your thumbs on the inner corners, bend the cards up slightly and let them fall so the corners interlace. Slide the two halves together and you've done one riffle.

Clumps of two or three cards falling together are fine, because real hands don't drop cards one at a time and the math in the 1992 paper assumes they won't. Most people who struggle are holding too many cards or pushing too hard. Practice with half a deck in each hand and go slowly.

The flashy finish where the cards arch up and snap back is called a bridge. It looks good and does nothing for the mix, so leave it out while you're learning, and bend the cards as little as you can, because bent cards stay bent.

Hold the deck on its long edge in one hand and use the other hand to pull small packets off the back and drop them in front. It's the shuffle most people pick up as kids, because you can do it standing up with no table.

It mixes badly because every packet stays in order and most cards end up near the neighbors they started with. Work by Jason Fulman and Persi Diaconis, reported by Hackaday, puts a full mix at about 10,000 to 11,000 overhand shuffles. Use it to loosen the cards up, then riffle.

A cut lifts the top part of the deck and puts it underneath, so the cards stay in the same circular order and only the starting point moves. It adds no mix at all.

People cut for a different reason: it stops a dealer from knowing or arranging what's on top, and it keeps the bottom card out of sight.

In a home game the dealer offers the cut to the player on the right. That player lifts a chunk and the dealer completes it, with nobody looking at the bottom card. Casino dealers put the deck on a plastic cut card, which stays underneath for the same reason.

The first card can be any of 52, the next any of the 51 left, and so on down to the last one. Multiply them all together and you get 52 factorial, written 52!, which is about 8.07 x 10⁶⁷. The first three cards alone can come out 52 x 51 x 50 = 132,600 ways.

That number has 68 digits, shown in full on this page. If all 8 billion people on Earth had shuffled one deck every second for the 13.8 billion years since the Big Bang, that would be about 3.5 x 10²⁷ decks, which is less than one in 10⁴⁰ of the possible orders.

Yes, and it works better than it looks. Poker players call it a wash, and researchers call it smooshing: spread the deck face down and push the cards around with both hands.

Fulman and Diaconis found that 30 to 60 seconds of it randomizes the cards, which makes it the easiest way to break up a new deck when nobody at the table can riffle yet.

Keep the cards face down and keep them moving. Two people can wash at once if you want it done faster, and a wash followed by a few riffles is a good habit for any new deck.