777JILI How to Shuffle Cards: A Riffle Shuffle in Four Steps

To learn how to shuffle cards by hand, you only need a deck, a flat surface and the riffle: cut, interlace, repeat. This 777JILI page gives the steps first and then the numbers from the Bayer and Diaconis paper on the riffle shuffle, because the number of passes matters as much as the move itself. It sits in the poker games cluster because every card page here assumes a deck mixed before the deal.

How to shuffle cards by hand: the riffle in four steps

Bayer and Diaconis call the riffle, or dovetail, shuffle the most commonly used method for shuffling cards. Their one-line description is that the deck is cut about in half and the two halves are riffled together. Turned into hand steps:

1. Hold the deck face down and cut it into two packets of similar size.
2. Riffle the packets together so cards from both interlace.
3. Square the deck and repeat the riffle.
4. Finish with one cut.

The fourth step is borrowed from the Massachusetts rules of Casino War, whose manual shuffle ends with a cut so the top card cannot be identified if it was exposed during the earlier steps.

What one riffle does to a deck you can check

Check it yourself in two moves:

1. Take a deck in new order, face down, and riffle it once.
2. Turn it over and look for the two packets.

The paper’s Figure 1 shows the effect on 13 cards: the two packets can still be identified in the shuffled deck as two distinct rising sequences of face values. After one pass, the cards from your left packet still appear in their old relative order, and so do the cards from the right packet.

That leftover pattern is why one pass is not a mix, and the table in the next section shows how many passes the paper’s measure needs.

How many times to shuffle cards: the paper’s figures for 52

Bayer and Diaconis measure how mixed a deck is with a total variation distance. In plain words, it compares the deck’s chance of each possible order with the case where every order is equally likely: 1.000 is the largest value in the paper’s table, and the number shrinks as the deck mixes. Their Table 1 for 52 cards reads:

The paper’s text says the distance stays essentially at its maximum up to 5 shuffles and then falls by a factor of 2 each time. It also gives (3/2) log2 52 = 8.55 as the number of shuffles to compare. The pages this site read do not contain the words seven shuffles; seven is a reading of the table. The figures were read by hand from scanned pages, so check them against Table 1 in the paper.

How the count changes with deck size

The paper’s Table 4 gives (3/2) log2 n for other deck sizes. The count rises slowly, not in step with the cards:

Manual shuffle steps at a casino table

The Massachusetts Casino War rules name five steps for a dealer’s manual shuffle. When a card game reaches a table, what a tie means in a push and what a split in blackjack involves both start from a deck mixed this way.

1. The plug inserts unused cards from behind the cut card into the cards in the discard tray.
2. The riffle divides the cards into two piles and interlaces them.
3. The turn divides the shoe into two stacks and rotates one stack 180 degrees before riffling them together.
4. The strip, also called running cuts, should not occur before at least two riffles have taken place.
5. The cut is the final step before the cards go back into the shoe.

Shuffle problems and fixes