The Best and Worst Ways to Shuffle A Deck of Cards

How many times does a deck of cards need to be shuffled to be mixed up? Discover the answer to the age-old question and learn about the fascinating role of mathematics in card shuffling, with USC Dornsife Mathematics Prof. Jason Fulman.

In his forthcoming book, The Mathematics of Shuffling Cards, Prof. Fulman and his co-author take a deep dive into probability theory, combinatorics, algebra and more while evaluating various card shuffling methods.

Watch as Prof. Fulman demonstrates some of the most common shuffling methods and shares insights into the secrets behind the perfect shuffle.

The USC Dornsife College of Letters, Arts and Sciences is the academic core of the University of Southern California in the heart of Los Angeles. Learn more:

[jarompack]

I very vividly remember a page on my 3rd grade math book from 20 years ago that explained that 7 riffle shuffles was the ideal amount to randomize the deck. I've followed that guidance my whole life.

[yansminikitchen]

Wow! That’s amazing. I never thought of this has something to do with mathematics. Thank you, professor Fulman.

[sdspivey]

Riffle shuffles are not random enough. Cards near the top tend to stay near the top and cards at the bottom tend to stay at the bottom.

A "perfect" riffle will always have the same top and bottom single cards.

[ljohnmiller]

So. How many riffle shuffles would it take to return the cards to where they started - all 52 of them - back into their original order.

[ahall]

I was gonna say this is just a spark notes version of the numberphile video I just watched, and then I saw Persi Diaconis's name on the book

[JamesOGant]

Actually 8 perfect riffle shuffles order the deck back to the start right? That’s a well known card trick. Pile shuffling and riffle shuffling if done a certain way can order the cards and have a memorable number of set of outcomes. I’ve been debating this issue in magic the gathering pages for a little while and years ago when I was in grad school for math I discovered the trick where you write random on the side of a deck of cards and try to perfectly riffle shuffle and it says “random random” if you shuffle once and “random random random random” if you shuffle twice. This is ordering the deck you know depending on how good you are at actually pairing the pairs each time when riffling or doing like a “pharaoh’s shuffle”. There’s like magician pages that show these simple tricks for ordering the cards using what is basically algorithmic pile shuffling… food for thought.

[TheDrAlbee]

The content of the video is interesting, but please stop with the terrible background music.

[davidmiller]

what does he mean by "guessing"?