The Best (and Worst) Ways to Shuffle Cards - Numberphile

Persi Diaconis (Stanford University) on card shuffling. See full description for links to additional videos and detailed papers.
More links & stuff in full description below ↓↓↓

PAPERS

BOOK

COIN TOSSING

NUMBERPHILE

Videos by Brady Haran

[altejoh]

It hurts me that the method of shuffling I took a year to learn and have been using for years is less effective than the one i could do since I was 5.

[slientkillli]

Unless you are a math guy you can't pull off that hairstyle

[xdpptsp]

"Now, keep going like an idiot"
LOL

[ElArboool]

did he say "take the top card off" without moving his lips?? 4:36

[MrNikolidas]

If anyone watches Vsauce, there was a wonderful visual analogy as to how long it would take to shuffle a deck of cards into all of its permutations:

Stand on the equator.
Shuffle a deck of cards once every minute.
After a year has passed, take one step around the equator.
Once you've walked around the earth, take one drop of water out of the ocean. Continue walking one step a year, taking a single drop out of the ocean after every revolution, shuffling the cards once every minute.
Once the oceans of Earth are dry, lay a sheet of paper down on the ground once every revolution.
When the stack of paper reaches the moon, refill the oceans and take the paper down and repeat.
250 more times.

[kg]

I love these kinds of videos. They show more practical and interesting ways to apply math to games and such.

[MindYourDecisions]

Great video! This is the best explanation for why you need "7 shuffles" to randomize a deck. I look forward to more vides on Card Shuffling Week.

[anoukfleur]

Aha! So my method of shuffling IS a valid method! Always smooshing from now on.

[mkaali]

The problem with riffle shuffling is that the order on the bigger scale stays relatively same. The bottom cards stay near the bottom and the top cards stay near the top. They can traverse the deck only very slowly, while the cards towards the middle get more randomness. 7 passes might be enough, but what I like to do is to throw a few of those overhand shuffles (0:36) in there or even just cut the deck at some points to alter the macro scale order more.

[andyhuang]

For anyone wondering what the randomization formula is: For a deck of n cards, the number of riffles needed to sufficiently randomize a deck is the smallest prime number greater than n/10. So 52/10=5.2, and 7 is the next prime number. For numbers that get really close to the next prime (like 49/10=4.9), skipping up another prime (so up to 7 in this example) is best.

[TheGamerSays]

Never thought George Washington would teach me how to shuffle cards well. My world is shook.

[NekuZX]

I was literally just looking for videos on how to shuffle cards. All of the recommendations were about how to shuffle cards in a cool way, but the only video that actually bothered to explain which method is the most random was this one.
Not only I learned what I wanted to learn, but I also got very fascinating facts about random chance!
Thank you very much sir Persi Diaconis.

[shepherdsgamingrun]

Can we request a version of this video using Magic: the Gathering cards? I'm pretty sure I know people who need this video.

[TheMohawkNinja]

This video was perfectly timed. I just started getting back into Magic: The Gathering, and I would always do the "overhand" shuffle. I didn't know that it was so ineffective.

[rogerwilco]

I remember reading in a popular science magazine as a kid 25 years ago about how random the various shuffling methods were. Overhand vs Riffle vs Smooshing shuffles were al mentioned and the conclusion I remember is that the Smooshing shuffle was the most time effective and hardest to mess up. So I've been using it ever since.

[XxearthxX]

its important to cut after each riffle shuffle or the top card is always on top

[zenithquasar]

I love how my smooshing technique turned out to be one of the best ways to do it!

[TheGame]

The numbers when it comes to cards has fascinated me for some time now. Like the fact that if you smoosh the cards properly you will likely have put them in an order that they have never been put in before in the history of cards. That is just mindblowing to me.

[ThisNameIsBanned]

Awesome week, i like this stuff and theres plenty of card games for any range of people that will really enjoy this, even people that normally dont care for math at all, will like to know what method of shuffling is actual usefull.


For me i have some hard times explaining people that pile shuffling isnt randomizing a deck at all, as you can perfectly place the cards at exactly the spot you want it to be, its only really good for counting cards.

[DashRetro]

One weird thing about the riffle shuffle is if you were to "Perfectly" riffle shuffle, as in you split the deck perfectly in half and your riffle perfectly alternates the two sides like a robot, the deck will actually be comepletely back to its starting position after 7 shuffles. This only applies to a 52-card deck, but it's true!