The Best (and Worst) Ways to Shuffle Cards - Numberphile
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- čas přidán 22. 03. 2015
- 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 ↓↓↓
EXTRAS FROM THIS INTERVIEW -- 1/3: • Shuffling Extra Footag... -- 2/3: • Shuffling Extra Footag... --- 3/3: • Shuffling Extra Footag...
Cards and shuffling videos: bit.ly/Cards_Shuffling
PAPERS
Trailing the Dovetail to its Lair (7 shuffles)): bit.ly/1xU6uPI
Shuffling Cards and Stopping Times: bit.ly/1FR0ca1
Overhand Shuffles: bit.ly/1LNBSuU
Discuss this video on Reddit: redd.it/300rkr
BOOK
Magical Mathematics by Persi Diaconis and On Graham: bit.ly/MagicalMath
COIN TOSSING
• How random is a coin t...
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Unless you are a math guy you can't pull off that hairstyle
Ha 😂
Benjamin Franklin
Larry David
Beethoven is unpleased to disagree with you
Or a crazy scientist
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.
To which methods are you referring?
He's probably talking about the Hindu shuffle
Haha, well I guess you can do 7 riffle shuffles faster than you can do a full minute of smooshing, so there's a small time saving.
But you did say you spent a year learning the riffle... So you make a tiny bit of that time back every time you play a card game and do 7riffles in under a minute.
If you don't want to have wasted that time, you'd better host a few poker nights ;-)
altejoh Einstein is crying now😂😂
@@mythicaldata6297 nope, he's talking about smoosh vs riffle shuffle
"Now, keep going like an idiot"
LOL
6:06 Best moment, hahaha! xD
Yeah I laughed at that. To which, my dog woke up from a nap, looked at me like I'm the worst asshole since Hitler, and went back to sleep.
One day, I am certain I will wake up to those jaws around my neck. I know this from how he stares at me when he eats. I think he's just waiting for me to buy an automated feeder and fill it with a twenty year supply of food and water.
@@since1876 haha!
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.
Jonathan Charles Hold my Beer for a minute
Imagine how much longer it would take with Tarot cards...
@@cameroncoates4863 or with magic the gathering. Funny thing is, you could accidentally shuffle a working Turing machine. (search on CZcams :D)
@@Lukoro1357 wonder how many times you have to shuffle an EDH deck until it's completely randomized
When vampires get bored
did he say "take the top card off" without moving his lips?? 4:36
+ElArboool Eagle Eyes
+ElArboool The Matrix is broken, call Microsoft support...
laught so hard 😂
+ElArboool I think so.
Is He an ALIEN?
I saw that too.
Aha! So my method of shuffling IS a valid method! Always smooshing from now on.
It's valid, but damaging.
I do it and everyone makes fun of me. Little do they know... it's effective.
So is riffling.
Amber Perry No, it's not. It's only damaging when done by people who don't know how to do it.
Riffling is better
I love these kinds of videos. They show more practical and interesting ways to apply math to games and such.
kg583 glad you enjoyed it - more shuffling to come this week!
true mathematician doesn's look for a practical way
AdrenalineL1fe
but we are not all mathematicians, a lot of us are just people who like math. :)
Yes, because pure math is so boring... Wait. Why are you here again?
Raziel Qwazar Because I love math just every other Numberphile subscriber. And when did I say pure math was boring?
Never thought George Washington would teach me how to shuffle cards well. My world is shook.
😂😂
Bruh 💀💀
CZcams is a wild place
:D
Yeah, Hans Zimmer's carreer went odd after retirement
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.
I do this as well.
Ive just done 10 shuffles with 5 riffles each (yeah ik, its a small sample size) and i found the top and bottom most cards in the top or bottom 5 exactly one time each.
@@vanessaxoax7646 bro tell me which is more random?
Overhand 10 times
Riffle 10 times
Smooshing for let's say 30 seconds or less
@@shaniyadav33Answered in the first 1:30 of the video - Riffle 7x is essentially "random" if it's done well, so 10 means you've shuffled three random decks. 30s is barely enough smooshing, and overhand needs about a half-hour of shuffling if you're quick.
I like to cut the deck ~¼-⅓ before shuffling and after a few riffles to bury the top & bottom of the deck, followed by a few more riffles - don't know how it impacts statistical randomness, but I don't see indications of previous hands in the new deck.
Well shuffling shuffling methods while shuffling would be optional.
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.
How come nobody noticed you in these comments? Or even the video isn't popular, that's crazy
Hi presh Talwakar from 6 years hence 🤣
yo presh talwalkar! It seems like it's become a tradition for someone to comment here once a year.
@@o5-1-formerlycalvinlucien605r55
@@akankshasharma74984r⁵t
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.
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.
6:07 the name of my autobiography
I love how my smooshing technique turned out to be one of the best ways to do it!
I went to go grab a deck of cards while watching this and accidentally dropped two identical decks together all over the floor. What are the chances that I'm an idiot?
Okay, let's start. There's 52 cards. Times 2 decks makes 104 cards. Of course you need to take into consideration the 4 suits and 13 cards per suit, so divide by 4*13. The result needs to be halved, because there's two possibilities of the outcome (you are an idiot or you are not). The result should be the answer :)
Clumsiness isn't really an indicator of stupidity. Granted, the two aren't mutually exclusive, but I wouldn't even say this was an instance of you doing something idiotic, just unfortunate. Now if you did it on purpose, that might be different.
Then again, I consider every human being alive (myself included) to be an idiot, so...
100%
@@Ulkomaalainen take the number of cards in your deck and divide by the number of cards in a deck.
1 in 52
Can we request a version of this video using Magic: the Gathering cards? I'm pretty sure I know people who need this video.
I like what he said at the end. "There is still a trace of the original order, but it diminishes exponentially as you shuffle." Its like mathematical music to my ears.
I agree!
r/iamverysmart
How tidy are those bookshelves!?
sammy0boi well, they don't really reflect randomness, that's for sure ...*or DO they?* woooOOOOooooooOOOOOOoooo
Mathematically speaking...
School library tidy
Beacause he reads them
i guess he is banned from playing in most casinos by now
lol
FIND THIS ONE TRICK THIS MAN USED TO SHUFFLE! *CASINOS HATE HIM!*
This is the guy casinos call to check they are shuffling effectively, and helped design some of the machinery and systems they use to shuffle quickly and efficiently.
Actually, he's not. For multiple reasons.
(1) Card Counting is basically null and void in most CASINO card games due to the use of two 52 card decks (yielding 108! possibilities) and a machine shuffler as well as (2) Poker, Hold'em and other 52 card games are competitive because of probability and card counting. That's how the game works. If you watch a professional "finals" for Tournament, you'll see the screen keeps math stats shown for the viewers as to showcase an average % for a certain turnout, for many pairs of cards -- all of that math is being done by the players at that moment.
So no, he's not banned. He's just able to be very competitive and will find other mathematicians like him.
@@XoIoRouge 108! possibilities? I don't think so... Probably you meant 104! but it should be less - each card is doubled so a lot of the 104! possibilities are identical.
Does this mean Yugi was cheating?
Undead Wizard
So the heart of the cards is just… bad shuffling?
@@Abdega Nah. He didn't just know what was coming. The card that was coming would be exactly the one he needed. It's his magical power to alter fate with the Millenium Puzzle.
He literally was cheating, yes, but not because of poor shuffling.
Stacking, yes.
No.
I mean, he was cheating, but not because of what is in this video
First thought:
I do 8 farros, everyone thinks it‘s fair, i win.
Is it out or in Farros tho?
haha no they don't know what faro is XD
I do in farro, over hand, out farro, riffle.
by table faro
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.
its important to cut after each riffle shuffle or the top card is always on top
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!
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.
All I got from this video is tat I need to "smoosh" my cards
riffle shuffle 7 or 8 times
I guess you weren’t listening very well then
Gotta love a smoosh
Probably faster to riffle seven times than wash the cards for a minute.
*S Q U I S H T H A T C A T*
I use a combination of the first two examples. I wonder what the odds/effectiveness is when you mix those two methods.
my problem with the Riffle is that the bottom/top cards stay on the bottom/top. they just move a few up or down, but stay in the same area of the deck. So i mix both methods, and i feel that gives me the best results.
That’s why I do the overhand shuffle but after I take the first few cards I then go in front and behind, back and forth, so they’re more random
When I riffle, I deliberately stagger the shuffle a bit to avoid this problem. That is, with the top 1/2 of the deck in my left hand, I begin releasing cards a moment *before* I begin releasing the cards in my right, so that ~5 cards from the middle (the bottom of the half-stack in my left hand) end up on the bottom, and the cards that were just after them in the middle (top of the half-stack in my right hand) end up on top. I have no math to prove anything, but I think the "spreading" of the middle cards to the top and the bottom that this produces should outweigh the fact that 2 groups of ~5 cards each move together from the middle to the top/bottom, but are not themselves reordered.
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.
Love videos like this.
***** cheers
likes of the reply received is just the half of that of the comment.... it stops me from giving like to any of the two....
same here, aced my probability courses because i find it so intuitive.
Frosty hat are. The uses of Bluetooth elephane
Am I the only one that didn't get how 200 pokes turns into about 7 shuffles? I also saw 3/2 log_2(52) = 8.55 shuffles but that wasn't talked about either...
Love this guy. Math prof and magician, one of the best combos there is.
At 5:27 he does his famous "Matrix Hands" maneuver. Love the old-school New York accent too!
"Keep going, like an idiot", is maybe the best line I've ever heard on Numberphile!
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.
Wow, I explained all the article about card shuffling for a math class (France). I would have never hoped to see the author explain himself his theory. Thank you Numberphile.
I get overwhelmed listening to this but I love it. I am of the simple peasant among a family of science, medicine and engineering and those with this kind of talent take my breath away, like when seeing a rainbow or a lightening strike for the first time. Thank you for the videos
3:20 + '..and if you have a really good memory' you get thrown out of the Casino.
For cards I don’t want to damage, I do the pile shuffle in 7-8 piles, followed by several rough overhead shuffles.
This week it happened that I played a lot of card games and was thinking about the math behind shuffling... was on my mind to make a research and WALLA! Numberphile delivers!
that's a pretty complex bit of mathematics to explain so clearly in such a short amount of time. Brilliant stuff!
"Keep going, like an idiot"
-induction in a nutshell
Oh my goodness. THE Persi Diaconis? The man who traveled with, was taught by, lived with, and consistently impressed Dai Vernon?
Brady, you've got to ask him about more than shuffles. This man knows more about magic than anyone you'll ever meet.
I KNOW! I could talk to this guy for hours if I knew him.
Though I must admit I probably wouldn't be able to teach barely anything to this guy *'cause he's a fricking GENIUS*
Alex Obviously false, if one ever meets PD. Possibly he knows more than anyone ELSE you’ll ever meet.
Yes. The same PD. See the Ricky Jay biopic Deceptive Practice.
In some card games, you DONT want a completely shuffled deck. Dutch 'kingen' comes to mind, where you are supposed to only split the deck 2 times, then deal again. This distributes each play of four cards of (mostly) the same color to all players, so no player ends up with most of one color.
This is already one of my favourite people featured on Numberphile
4:36 wtf
yep
You never heard of ventriloquism?
i m laughing so hard
do you know what adr is?
Illuminati confirmed
I prefer the Hindu (overhand) shuffle. When you do it real fast, the mechanistic and casual feel to it just makes it look cool.
It's also very easy to do controls in Hindu
So you are a cheater, unless you shuffle 10,000 times.
A way that casinos shuffle a deck of cards is: shuffle, strip, then shuffle again. Stripping is basically take 10-15 cards off the top of the deck, put them on the table, take 10-15 cards off the top of the deck, put them on top of the cards on the table, and repeat until no more cards in your hand. This way, you're moving groups of cards around before shuffling again, making it much more effective.
Also, you need much more space to "smoosh" (or wash) the cards. You have to be able to be sure the cards on top can mix with cards all the way on the bottom.
That slow motion looks so cool!
This is such a cool video. Love the breakdown. Always preferred a true breakdown of a concept rather than a loose explanation :D
1/52 I GUESSED THE TOP CARD, I swear that's probably a one time thing
I alternate between the overhand shuffle and the riffle shuffle. Usually about 3 complete overhand, 1 riffle, then repeat 3 or 4 times.
as a computer science student and a poker player i found this extremely interesting :) keep it up!
I'm surprised he didn't mention this fact: the riffle shuffle doesn't mix up the cards as much as you'd think. If you have a 52-pack in store bought order, and you complete 8 perfect riffle shuffles (or 8 perfect out-faro shuffles) then the pack will be restored to its original order! Very hard to do, though some expert card handlers can do it.
7j557j7j5 That's interesting. I've known that eight perfect riffle shuffles bring the cards back in order but I've never known that there are people who can actually do it.
anticorncob6 There are no people who have done perfect riffle shuffles three times in a row. I'm not sure if even two times. It is kinda Holy Grail for sleight of hand artists, but anyone who has tried it has had to give up, it's too inconsistent. Out-faro shuffles however are easier, and with moderate amount of practice, I managed to do a couple of perfect faro shuffles.
Joni Hanski Sorry Joni, but you are quite mistaken. There are plenty of cardists who can do a perfect riffle. For anyone who knows how to handle cards, it's not particularly difficult with a bit of practice. It's about 20% technique and 80% card quality. Some of my friends can do endless perfect riffles, I can usually do about 5 or 6 perfect riffles consecutively. For more info google "Joe Barry", he is known for developing one of the common perfect riffle techniques.
Note: For beginners, it's *much* easier to learn the faro shuffle (compared to perfect riffle).
so in 8 shuffles where does the first card go? does it stay where it is (which is one definition of a perfect shuffle, but seems to me to be bogus), or does it move through the deck? If it moves through the deck 52 is not factorable by 2 alone, so I don't see how that would work after the 6th shuffle (it goes 2, 4, 8, 16, 32, then (I think) 12, 24, 48, 44 which is not 1.
So this 8 riffles only works if you assume you are never moving the first card (i.e. you always shuffle the same way)- is that right?
ed simnett Yes, the 8 riffles will need the top card to stay on top for each shuffle. The top card never moves. Also known as an "out-faro shuffle".
4:37 He shows off his ventriloquist skills. Cool video though! 10/10 would watch again.
Brilliant professor! Absolutely brilliant!
There is also the table shuffling method where you make 4+ piles of cards on the table randomly from the top. I do that plus a few overhand shuffles while cycling my deck in dominion
But if you alternate Overhand and Riffle it's better, because in the Riffle, you pick the top cards, if you alternate, you're picking up ''random place cards'' Is my theory true?
You get more variety more quickly from doing both, so yes you are correct.
This is how it is done as a casino dealer (sans shuffle machine). Wash (smoosh) > riffle > overhand > riffle x2
In the poking method, it seems like poking the top card anywhere *above* the King of Hearts doesn't accomplish anything. Wouldn't it be just as random, and faster, to always poke the top card somewhere below the King of Hearts? Or, equivalently, to randomly poke each card in the deck into a *new* pile, which begins empty and gradually fills with cards in a random order? That would give you a fully shuffled deck in exactly 52 pokes (though, like the longer poking method, it depends on a truly random poke).
Sure, but one problem is that by randomly placing it anywhere you make it harder to trace the path. If I knew the order the cards were in, and watched you do it your way, I would then also know the order the newly shuffled deck was in.
I thought about this too. I think it might not be complete random. Take the first card for example, in a complete random deck, it has 1/52 chance of being on top. With the new pile method, the first card has 1*1/2*2/3*3/4.....*51/52 chance of being on top. Is this logic correct?
edit: nvm, that's still 1/52
Matthew Baker You're wrong.
Draw out all possibilities. In iteration 1, you have only 1 possibility, the first card being on top.
Second iteration you have two possibilities, it on top once.
Third iteration, there's 6 possibility (for each possibility in iteration 2, you can place the new card on top, in the middle, or underneath),and it's on top twice.
Or the options are...
iter 1 - A
iter 2 - AB, BA
iter 3 - CAB, ACB, ABC, CBA, BCA, BAC
Meaning in iter 3, there's a 1/3 chance of it being on top.
seigeengine I think you are recounting. order of AB and BA was already determined in iter 2. So you are doing 1/2*2/3 in iter 3, which is counting the 1/2 twice. Therefore by iter 52, the chance is 1*1/2*2/3*3/4.....*51/52=1/52 chance of being on top
edit: i think we are on the same page now. I think you replied to my previous version.
Matthew Baker I am not "recounting" anything.
There is one possible outcome after we move the first card.
There are two possible outcomes after we move the second card.
When we move the third card, there are three places we can put it, on top, in the middle, or on the bottom, but there are two possibilities for how the cards can be ordered, either they're in AB or BA format before we move the third card, so there's 2*3 possible orderings of the new deck at this point.
You might try to say "well the deck is already either in AB or BA format, so the other possibility isn't relevant!" But it is, because we don't know whether it's in AB or BA format. If it was in BA format, the probability of A being on top is already zero, if it's in AB format, the probability of A being on top after we move the next card is 2/3, because there's only 1 in 3 chances it'll go on top, or 1*(1-1/3).
The math you're trying to use is wrong. The correct math is....
1 * (1-1/2) * (1-1/3) * ... * (1-1/52)
I've learned to riffle the cards and then raise roughly third of the deck from the middle to top after each riffle (which is pretty simple to do simply by pinching from the sides of the deck and pulling the middle part away) before halving the deck again for the next riffle. I think that it improves the changes that the top and the bottom of the deck get mixed during the suffle, but I have no mathematical explanation if it really matters.
I really love your videos! Makes me want to play card games.
I am fascinated by this often heard reference to the number of particles in the universe.
So like how many and how is this determined ?
+Susan Bruce They get people who are on Work for the Dole to count them.
Kutulue Yeah and community service reformers they specialize in counting Dark matter particles.
It'll always be an estimate.
yes like my electricity bill
Which helped this guy make a little bit more cents :D
I'd also like to hear about the math behind pile shuffling. In particular, I always make the number of piles a prime number (either 5 or 7 usually). Many people don't believe that makes a difference. Are they right?
Also, what about non-standard card decks? 5 card draw is often played with 32 cards, whereas trading card games often use decks of 60-90 cards that almost always contain multiples of the same card (and where these multiples "bunching up" is often a problem), but maybe only half those cards are actually drawn overthe course of the game.
+Ann O. Nymus I'm pretty sure pile shuffling isn't shuffling at all, it's deterministic. There's no variance in how you split the halfs, or how many cards you drop when riffling. Cards bunching up isn't a problem, it's pretty likely to happen when you have actual randomness and multiple copies of the cards.
Theres a slide in this video that says log2(n) * (3/2) gives you approximately the number of shuffles. 52 cards = 8.55 shuffle, 60 cards gives you 8.86, 90 gives you 9.73.
+vuvuzelaelaela You're right. While pile shuffling can mix things up quite well, it is not a truly random method.
It's been a long time since I played any of the trading card games but I remember that, due to pile shuffling lacking true randomization, the tournament rules usually allowed it as part of the shuffling process but not as the final method employed.
You're right, of course. In retrospect, that should have been obvious to me.
+vuvuzelaelaela The benefit to pile shuffling, at least to my understanding, is that it breaks up pre-existing clumps in the deck, and is much less wear and tear on the cards (which is important for games with special cards, or trading card games where an individual card's value can be extremely high).
For instance, let's take a game with a standard deck of cards. Each player draws one card from the deck on their turn, then if they have at least 4 cards of the same suit, they discard those cards and score a point. After the deck runs out, the discard pile is reshuffled and the game continues. Now, while doing several riffle shuffles is sufficient to randomize them, let's say you're not willing to bend your cards that way. Chances are, most other methods of shuffling are going to be insufficient to break apart the clumps in the discard pile that form from people discarding similar cards in groups of 4. A pile shuffle, followed by normal shuffling, is going to be enough to break up those clumps, assuming you do it with at least 4 piles. Some normal shuffling after to actually randomize the cards may end up with more clumps forming, but now that the clumps that were created deliberately are broken up, it doesn't matter so much.
Use the plastic card protectors, and shuffle properly. Breaking up "pre-existing clumps" isn't shuffling, it's making a deck homogeneous. You're supposed to be making the deck random.
As someone who likes card plays and plays quite some with friends (Doppelkopf), this is very interesting. We usually use the overhand shuffle for it is predominant in Germany, I suppose. I always thought the way of shuffling does not significantly influence the cards' distribution -- my eyes were opened. Riffle shuffle then from now on!
Thanks Numberphile for the great videos on game theory! It is a very interesting field of mathematics.
Finally a video that validates my shuffle method. I alternate riffle shuffles, and overhand shuffles (I consider overhand shuffles as a cut) then I repeat that sequence 13 times and I leave the last cut for an opponent.
"And then, keep going like an idiot..."
My favorite line of this video :P
Could you do something comparing the futility of pile shuffling vs. riffle shuffling?
Pile "shuffling" isn't futile, but it isn't shuffling either; it is stacking the deck.
If the cards are sticky and clumping a lot, piling before or after riffles or mashes/washes can help.
Just wanted to learn how to shuffle cards l, now I'm majoring in mathematics and trying to understand the cardinality of the set of rational numbers
Penn Jillette mentioned Persi Diaconis on an episode of "Fool Us" in reference to shuffling decks. Nice to see him speak.
What about pile shuffling? Mtg players want to know.
No way a Magic player is ever going to 'smoosh' shuffle his deck.
@@jeffreymackay4343 if they're in sleeves, you can take half in each hand, hold them loosely, and push the two piles together. the edges of the sleeves create a taper to let them smoothly merge
@@ENCHANTMEN_ I think he means the one where you throw them all in a pile and wave them around, which would ruin your deck in a hurry
I double sleeve and I wouldn't dare smoosh shuffle haha.
I use the overhand shuffle with a twist, instead of always inserting a number of cards on top of the newly formed deck I alternate between adding on top and adding to the bottom. This way each card can easily end up on the other side of the deck which is probably the problem of the normal overhand shuffle. But I haven't tested this mathematically.
This video made me wanna try different kind of card tricks and shuffles with the deck.
I've seen a spring with the bicycles! Great!
Could one say that Mash shuffling produces the same results as Riffle?
Tempest and a Computer yes. The idea is that every card is below an average of one card from the other half before being below another one from the same half. It's identical in terms of math between the 2 so it's the same. I prefer mass shuffling
I thought dude was wearing a powdered wig there in the thumbnail
If I'm bored or having a conversation and we're not looking to go again quickly I'll typically start making piles, grabbing cards from the top of the deck and decide "randomly" if I want to put them in an existing pile (at "random") or if I want to make a new pile. Typically by the end I have anywhere from 5-10 piles of cards with varying numbers of cards. I then "randomly" decide what order to grab the stacks in, after which I might do a few clump shuffles, and then repeat the first step.
Great argument for plastic cards over paper ones!
Riffle shuffle is not enough for some game types. If you know that ace of hearts that was in previous play is very likely to be at the top half of the cards, you can count on the fact that one player is most likely having that particular card. When the game requires more than 50% of the deck to be used and enough cards are revealed, you can make money of from it. I did..
For those game types you have to split the deck between riffle shuffles a few times or you deliberately let one side of the "riffle" to get ahead of the other before they are joined (you let a block of cards to be at the bottom before the rest are shuffled) That takes about 10 shuffles in total ( 7 riffles + 3 other ) It is the blocks you have get rid of and those happen a LOT.. In 7 cards stud, you get 3 of a kinds a lot, when the cards are collected from the table, they are within the vicinity of each other and that can totally kill the randomness. Ans since 7 card stud often uses most of the cards on deck.. well, you can guess that i kept my eyes on the deck when it was collected from the table and shuffled.. ;) If you know that the last ace is at the bottom of the deck...
It was these blocks that gave me edge when there was a lazy shuffler but when i shuffled, i always used two types: blocks and riffles... If you mush them before riffle, that is one effective way too, players can "force" a mush by just putting the cards after the game in a wide pile that the dealer is forced to gather, it mixes those "blocks" pretty well too.
I've always taken a clump from the top and pushed it (as in forced, not opening a hole) into the middle of the deck. Would that be better or worse than overhand?
I don't know but it sure seems like a great way to ruin a deck of cards.
At least if you don't naturally let the cards riffle into each other (like a "perfect faro shuffle") and just force them together.
CrappyQualityWarfare You need to replace decks fairly regularly anyways as finger marks distinguish the cards after a few games, so it doesn't make much difference. Unless your using CTGs of course, 'cos then you should be using covers anyways which keep it protected and make it easier to slide them in.
SheezyBites Yes, I have still not found any deck of cards of any quality where the cards does not distinguish themselves after a few weeks of everyday use. But I mostly use my cards for playing around with while sitting at the computer or practicing some shuffles or tricks, the best way is really just to save a few decks for those occasions where you need a good quality/looking deck.
SheezyBites Logic follows that it would be better than overhand as there would be less clumps, but I'm too lazy to do any math to back that up.
SheezyBites i shuffle like that too! never met anyone else who did it like that :)
I like doing a mix between the overhand and riffle shuffle. So I rearrange the general clumps and then riffle shuffle them. And then alternate between them until I've done maybe 3-4 of each. Someone who wants can make sure that the bottom card always remains in place, by releasing that side first every time with riffle shuffles.
Cool, video. Thanks for making it. I found it very enjoyable
Time to change my shuffle.
what is the best way to shuffle 60 cards, with sleeves (so you don't want to smoosh (all cards on table making circular random movements) or bending the card, (poker 2 equal stacks, bending it and then one after one to one new stack))??
+Serieus Frank also not sideway shuffling
+Serieus Frank : Are you an MtG player, by any chance?
+Lee Fisher yes
+Serieus Frank : Best shuffle method is... MTGO :)
A question I have always had. Thank you.
I numbered a regular deck of cards 1-52 and found the r-value of the sequencing after each of several riffle shuffles. The r-value leveled off at .05 after 7 shuffles. I'm happy with saying shuffle 8 times without feeling the need to take this to the 8th decimal.
I can't shuffle cards. I'm such a failure.
yo check out reddit.com/r/cardistry and maybe you'll get it from the tutorials!
+cookieaddictionsOh come on. Even a toddler could do the wash/ corgi/ chimmey/ smoosh method.
***** yeah. Since posting that comment, I have also since realized that this method takes up the most time and space on the table. but the way I see it, ranking the three methods presented here goes as follows:
Cutting the deck takes thousands of tries to shuffle the deck even decently, so it's right out.
riffling the deck takes a mere seven tries, and takes up very little space, but the ordinary method of riffling takes a lot of practice, and I speak fro mexperience when I say that trying to squeeze the two deck halves together can seriously damage the cards if you aren't careful.
corgi takes up a lot of space on the table and also takes much longer compared to the other methods, but if you have enough space and a mere minutes worth of patience, you can produce a deck that is *mathematically proven* to be *perfectly* random.
First off, I would love to point out that at no point did anyone bring up squishing decks together, especially with regard to riffling. That's a very bad idea that immediately damages the cards.
@OP
The shuffle is all about letting it do it itself, and you just set it up. The riffle is the easiest part; cut your deck, fold them together like playing a controlled version of 52 card pickup. For the bridge, you have to hold the far edges together firmly (the bases of the 'bridge') with your fingers and another finger or two higher up can help stabilize the very bottom cards. Then you try and let it all go by removing any 'stabilizing' fingers and letting the base go, while still firmly keeping your hands in the arch position so the cards don't go flying.
Do smooching! It's easy and apparently effective.
I shuffle by dealing out into 8 piles (non equal, of course), and then riffle shuffling them into each other. I think that should be random enough (it's how I shuffle my MTG decks ;))
+Jordan Gilbert I guess that depends on the order in which you put the piles back together ;)
+mushkamusic Usually if I split it into piles (call them A-H) I mix AE, BF, CG, DH. then I mix AECG, BFDH and then all together.
+Jordan Gilbert Well that certainly sounds reasonable to me, mind you, I'm neither a mathematician nor a card player :D
+Jordan Gilbert So, assuming you pile shuffle from the top of the deck, we know that the top card (let's say it's a Storm Crow) is at the bottom of pile A. We riffle shuffle pile A and D together, and now we aren't sure if Storm Crow is on the bottom or not, but we do know he's not at the top. So then we mix AE and CG together, and he's still not at the top, but he's still towards the bottom. Finally you mix AECG and BFDH together, and again you don't know where he is exactly, but you know he's not on the top.
Doing it just once, as you can see, isn't truly random, because while we don't know the exact positions of the cards, we can assume that the cards at the bottom of the piles (or the cards at the top of the deck when you shuffled) are never going to be on the top. We can reasonably assume that one of the last 8 cards in the old order is on top, as they were on the tops of the piles.
We can do it a second time, and now we're still not sure exactly where Storm Crow is, since we was near the bottom of the deck after the first shuffle, we can now assume he's near the top. Probably not at the top of the deck, but near it. Maybe between around the 10-15th card. Do it again and now he's probably about the 20th card from the bottom, and so on.
So, essentially, each time we do that process we're only switching the tops and bottom of the deck, and leaving the card in the middle in the middle. Now cards do slowly shift up and down and will make their way to the middle and push those cards up and down. You'd probably have to do this around 7 times like with a riffle shuffle to ensure you had no idea where Storm Crow was in the deck.
I'd wager that that method (which is the predominant shuffling method among Magic players) is roughly the same as just riffle shuffling the deck several times. I am unfortunately not that advanced with probabilities, so I can't do the math to verify that, but I would guess it's close to the same, maybe slightly more random.
EDIT: After some thinking, I realized that Storm Crow will be in the bottom 8 positions after the first shuffle, the top 16 after the second shuffle, bottom 24 after the third shuffle, and so on. So you would need to shuffle a deck using that method about 8 times to ensure that Storm Crow has at least a 1/60 chance of being in any position in the deck, unless my logic and math are off.
+Evelyn Finegan Note that he's not pile shuffling, just breaking the deck into piles of roughly similar size.
And for your example, all you really have to do to completely lose a card is to perform a cut on each riffle-shuffled pile to completely lose cards even if you know their position when shuffling started.
always wanted to see Persi Diaconis
smooshing is similar to the ribbon shuffle where your spread. I noticed overhand didn't randomize, didn't know 10000 times it takes, glad I got rid of doing that solely.
Fischer, can you see this?
Now I'm wondering if the "reverse riffle shuffle" used by over-protective card-game-collectors everywhere is just as mathematically rigorous as this one.
For the uninitiated, one takes a deck of cards, and card by card, semi-randomly distributes it onto a few smaller piles (usually 3-6). Once the deck is exhausted, the piles are stacked on top of each other, and the process is repeated, at least once or twice more (although rarely to the full seven or eight it probably needs). Plenty of examples in the first five minutes of any MTG or Yu-Gi-Oh tournament video.
+GelidGanef
Table-shuffling (The term I use for the shuffling you have described there) is often not random, as many players will not put the cards in random piles (if there are 3 piles, they will put a card on pile A, then one on pile B, then one on pile C, then repeat). If the placement of the cards into the piles is not random, players can easily manipulate the deck for their desired outcome.
That being said, I remember being told that the optimum number of piles for a table shuffle that is being performed with random pile distribution is 7, although there was no mention on how many times this needed to be performed.
Pile shuffle doesn't really help the randomness. It only makes it easier to distribute different card types across the deck. Usually you riffle shuffle between pile shuffling to really randomize it. It's a grey area shotcut for people that riffle shuffle well (or don't want to, like you said: card collectors).
But the pile method makes it so cards that were used in comboes (ie, right next to each other in order) are almost guaranteed to be farther apart. The problem with riffle and overhand shuffling is that often times comboed cards (cards played consecutively) may remain next to each other.
I'm loving the slow mo stuff in some of the latest NP videos.
(Yes NP...)
This was fascinating. As someone who enjoys playing M:tG I’ll be shuffling the middle way from now on...
Don't rifle shuffle mtg cards, sleeve them and mash shuffle
6:07 and keep going like an idiot
Lol
I prefer to use a combination of riffle and overhand. In my experience if you just riffle, the bottom few cards never move up the deck. Similar to the king of hearts in his poke example. My preferred method is riffle + overhand alternating 5 times.
What I do is four riffles, then cut the deck myself about 25% of the way down, then four more riffles before I offer it to an opponent to cut. That 25% cut takes the cards that were at the top and bottom of the deck and puts them smack dab in the middle of the next riffle.
Coolest Numberphile video ever! I love cards.
I've always done the overhand shuffle. I might learn the riffle shuffle.
8:23 did he mean natural log?
Yup
When real mathematicians say "log", they're referring to the natural log, because it's so much more useful than the common log.
Log without a base bro just a natural log as in what the log is in a natural state untouched
2:09 The commonly accepted answer for the number of particles in the observable universe is 10^80 which is > 10^68 :-P
+DJGerritProductions Thats the theorised amount for the number of atoms. Adding the number of sub atomic particles would be way bigger.
dangriff12 k. that would still be bigger than 10^68 :-P
10^68 is more like the number of particles in our universe
ViperDaniel What are atoms made of? Elemental particles... it would be way more
I love this guys voice
The explanation of when the deck is fully random was really awesome. Never thought of it like that before.