# Shuffling Cards

I get so much poker spam on this site that I figured I may as well post something that's actually relevant to the game... so, here's the Wikipedia entry about shuffling. Since the whole point of shuffling is randomization, how many times do you have to shuffle to get it?

The mathematician and magician Persi Diaconis is an expert on the theory and practice of card shuffling, and an author of a famous paper on the number of shuffles needed to randomize a deck, concluding that it did not start to become random until five good riffle shuffles, and was truly random after seven. (You would need more shuffles if your shuffling technique is poor, of course.) Recently, the work of Trefethen et al. has questioned some of Diaconis' results, concluding that six shuffles is enough. The difference hinges on how each measured the randomness of the deck. Diaconis used a very sensitive test of randomness, and therefore needed to shuffle more. Even more sensitive measures exist and the question of what measure is best for specific card games is still open.

Here is an extremely sensitive test to experiment with. Take a standard deck without the jokers. Divide it into suits with two suits in ascending order from ace to king, and the other two suits in reverse. (Many decks already come ordered this way when new.) Shuffle to your satisfaction. Then go through the deck trying to pull out each suit in the order ace, two, three ... When you reach the top of the deck, start over. How many passes did it take to pull out each suit?

What you are seeing is how many rising sequences are left in each suit. It probably takes more shuffles than you think to both get rid of rising sequences in the suits which were assembled that way, and add them to the ones that were not!

In practice the number of shuffles that you need depends both on how good you are at shuffling, and how good the people playing are at noticing and using non-randomness. 2–4 shuffles is good enough for casual play. But in club play, good bridge players take advantage of non-randomness after 4 shuffles, and top blackjack players literally track aces through the deck.

So play it safe and shuffle seven times!

### Supporters

Email blogmasterofnoneATgmailDOTcom for text link and key word rates.