QI Card Shuffling - 52 Factorial
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- เผยแพร่เมื่อ 20 ต.ค. 2024
- The chances that anyone has ever shuffled a pack of cards in the same way twice in the history of the world are infinitesimally small, statistically speaking. The number of possible permutations of 52 cards is '52 factorial' otherwise known as 52! or 52 shriek. This is 52 times 51 times 50 . . . all the way down to one. Here's what that looks like:
80,658,175,170,943,878,571,660,636,856,403,766,
975,289,505,440,883,277,824,000,000,000,000.
To give you an idea of how many that is, here is how long it would take to go through every possible permutation of cards. If every star in our galaxy had a trillion planets, each with a trillion people living on them, and each of these people has a trillion packs of cards and somehow they manage to make unique shuffles 1,000 times per second, and they'd been doing that since the Big Bang, they'd only just now be starting to repeat shuffles.
So...you're saying there's a chance...
second Dumb and Dumber reference I've seen today! Woo!
three years later, and also the second dumb and dumber reference i've seen today.
lel
mathematically
Well, you know... He phrased it as: This pack of cards. It might as well have been a new pack of cards that had just been shuffled. He'd be technically telling the truth.
When Stephen started talking about the number and the stars and galaxies, all I could imagine was "Space is big. Really big. You just wouldn't believe how vastly, hugely, mind-bogglingly big it is."
I mean, you may think it's a long way down the road to the chemist's, but that's just peanuts to space.
Oh biggly big
@@gwh3013 It's so big that to attempt to quantify its bigness would be doing it a disservice!
Just... Reeeee....member that your standing on a planet that's evolving, and revolving at 900 miles an hour...
Yes, hitch hikers 😂
If it seems impossible ask yourself this question, how many times has anyone inadvertently shuffled the deck to the original order?
Never…. Its impossible
Well.... Not exactly impossible. It's no more impossable than any other order of cards that gets shuffled and they happen
@@John...44... I mean it's "impossible" to shuffle DNA into order by chance but atheists claim it time after time, and in only a few billion years rather than a few billion factorial years.
@@TimpBizkit is don't get your point?
With certain shuffling methods when you execute them perfectly they loop back to original order after couple of shuffles
Those final zeroes are suspicious!
But apparently very real. 52! indeed works out to 12 zeroes at the end....
I read two clever ways of putting it:
Take out a digital countdown timer and set it to at 52! seconds.
Scenario 1:
-stand on the equator and take a step *once every billion years*
-once you've circumnavigated the globe, take a drop of water from the Pacific
-when the ocean is entirely drained, refill it and place a piece of paper down. Repeat *until the pile reaches the Sun*
The first 3 digits haven't changed. You are 1/3000th done.
OR
Scenario 2:
-shuffle a pack of cards and deal yourself five cards, *once every billion years*
-when you get a Royal Flush, buy a lottery ticket
-when you win the lottery, put a grain of sand in the Grand Canyon
-when it is full, empty it out and take an ounce of rock off Mount Everest. Repeat *until the mountain is flat*
The first 2 digits have not changed. You are 1/256th done.
Ah! Czepiel's essay!
Despite the odds, you'll still get yelled at by the guy next to you at the blackjack table for "taking his card" when you deviate from basic strategy.
That's funny!!
That only happened to me one time. I didn't know it was a thing and the guy got mad at me. From then on when I sit down at a table I tell them I'm going to play the way I want to play, if they don't like it get up and go to another table.
imagine his face when he shuffles the exact same deck just a few hours later
He would probably take himself to a casino bc he must be the luckiest guy on the planet 😅
@@Diamondraw4Real luckiest living thing in the history of the universe that is
It's not impossible, just extremely improbable.
@@Mr-DNA_ basically impossible though. It's way way way more likely to win the lottery 10000 times in a lifetime without cheating.
It's that kind of unlikeliness you can just call impossibility
@@tacitozetticci9308 that is a VAST understatement compared to 52!. Compared to that you would be the unluckiest thing ever.
Nice video. With all the certainty we can realistically have, his statement is correct (that it's the first time that order has appeared). And yet the amazing thing is that this proves that even though things may be statistically improbable, they are actually possible.
Whatever the order of cards was that resulted from his shuffle, the odds of that order appearing were 1 in 80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000. And yet ... it happened.
love that way of interpreting it
That is a great point, yet it remains true that the deck has never before beein in that order.
I just watched the Vsauce video which had this and they used 2 analogies one was imagine you had a timer with 52! seconds counting down and you are standing on the equator every 1,000,000,000 years take a step when you go around the world take a drop of water from the pacific ocean when you empty the ocean put a piece of paper on the ground and do this every time you empty the ocean until the pile of paper reaches the sun if you do this 1000 times you will be 1/3 of the way done or every 1,000,000,000 years deal yourself 5 cards every time you deal a royal flush buy a lottery ticket if the ticket wins the lottery throw a grain of sand into the grand canyon and do this every time you win the lottery once the ground canyon is full remove 1oz of rock from mount everest and do this every time the grand canyon is full and until mount everest is level once you've done that 256 times then the timer will hit 0
I came from there too!
Me tooooo
+HexQuest you were almost right. after you do the walking, ocean, paper thing 1000 times and THEN do the cards, lottery, grand canyon, mount everest thing 256 times THEN your clock would hit 0.
***** nope. multiply 52x51x50x49x48 and so on until you reach x1 and then see what you get. you would get that number on the screen. that is how many times a deck of cards can be arranged in. that is so long, that by the time 52 factorial years passed, the universe would be completely dark and empty due to every start being dead. there would just be a few black holes here and there left in the universe.
its so big, that if you were to set a timer for 52! years and fly in an airplane across the universe, you could fly to the edge of the universe and back to earth hundreds of millions of times.....in a regular sized commercial airplane.
***** yep. there are known numbers that completely dwarf it though. numbers like a googolplex are so large that there isnt even room in the observable universe to write those numbers down. a piece of paper with a googolplex written on it couldnt even be crumpled into a ball small enough to fit into the observable universe. and there are numbers that completely dwarf that as well.
So proud that something so simple can be so unique.... amazing if u ask me
The way he described this seemed almost unbelievable to me, so I figured it out, and assuming 400 billion stars in the Milky Way (on the upper end of the average of current estimates), given the frequency of shuffles on all the decks on all the planets in the scenario described, it would take over 8.5 X 10^ 24 years (over 632 Brillion (corrected) times the age of the universe), to cycle through all possible permutations, unless there's an error in my figuring.
I think there's an error in Your maths. Using the lower estimate I came out with 4.3 x 10^64...which isn't far off. My maths: 100B x 1T x 1T x 1T x 1k x 60 x 60 x 24 x 365 x 13.7B. (stars x planets x people x decks x shuffles/second x minute x hour x day x year x age of universe)
@@John...44... You're right, my calculations only accounted for 1 shuffle per second, sorry.
@@John...44... you should have got 4.3x10^67. So if you say 2000 times per second instead you are basically bang on 52! (8.0658175e+67)
I took probability in College and I'm pretty sure I can't even grasp this in the nominal sense.
Its still wrong to assume 100% certainty even with outstanding odds on your side
*****
No, no no.
This is a common error made by people who don't understand how probability and statistics works. Any two shuffles of a deck of cards are very, very, very, very, very, very, very, very, very, VERY unlikely to be the same. But that is most emphatically NOT "mathematically provable they won't be the same."
And all the guys on all the stars shuffling, there's nothing at all preventing them from seeing repeat orders. It's just very....etc unlikely.
What they REALLY mean to say here is that you are not mathematically GUARANTEED to see a repeat until you have done 52! + 1 shuffles. OTOH, the closer you get to that figure, the more likely you are to see repeats. Indeed, the more shuffles you do, the more likely it becomes that you will see repeats...as long as you grasp that by "the more shuffles you do," we're talking significant fractions of 52!, a staggeringly large number.
This fallacy is essentially the same reason people believe there are "hot lottery numbers" or that if a roulette wheel is red five times in a row, it's "overdue" to be black. There is no odds god that oversees this sort of thing.
goodkatYes, very unlikely to the point that it is more certainly false than many other things.
The gambler's fallacy is not relevant here, since were not trying to say that a previous arrangement is any less (or more) likely. It's just that 52! is so big that even the chance of any two identical real fully randomized shuffles having ever occurred is extremely unlikely.
Yes, it is rather more likely than 1:52!, but it's still extremely low. It doesn't get really small, like the Birthday paradox does.
ZipplyZane im not arguing agaisnt outstanding odds, my original point still stands that you cannot by definition assume 100% certainty
+goodkat By that definition you can't be 100% certain about damn near anything. That's fine and all but you really start to split hairs when you still insist that what Fry is saying isn't true. Yea, you're technically right, but you're right by such a small, insignificant, damn near meaningless margin that, honestly, who gives a shit?
+winowmak3r the problem is that he's talking about mathematical certainty vs. practical certainty. Those are different. As soon as he says "mathematically" certainty, he is wrong. He is factually wrong, because I can mathematically prove that it could possibly be in the same order, because it could, mathematically. Math provides the only certainties. It is based on unchangeable concepts. It was built that way. 2+2 will always be four. Always. If you come up with a different answer, it's because your concept of 2 has varied from the standard on which the equation is based. It is not mathematically certain to be different. It is mathematically CERTAIN that it COULD be the same. He couldn't be more wrong.
Practically certain, yes. More certain than any other assumption you've ever made in your entire life? yes. Still an assumption. Very good data to make a guess with. I would bet on it being different every single time. Not certain. Here's a good way to check to see if you have a bias:
You can take a bet. Someone shuffles the cards. Both you and the person offering have the ability to know if a deck has never been in that order before in the history of the universe. The other person shuffles. If you take the bet, and the cards have never been in that position before, you get a million dollars. If the cards have, by some coincidence, been in that order before, you and everyone you care about will be slowly tortured to death.
If it was mathematically certain, you could take that bet every day forever. You'd say yes in a heartbeat. It could never be wrong. So... he used the wrong language. His point is valid, but the language he used weakens his point. Theatrics are great, but miscommunications suck. He miscommunicated.
It's not fact it's just probabilities. You don't exhaust every possibility before you repeat stuff. All the stuff about "they would only now be done" would be assuming "every next shuffle will be a new order of cards until all possible orders have been exhausted."
It's not an "absolute fact" it's just very very high probabilities.
Yes, it's like the birthday problem. You don't need 365 people in a room for it to be statistically likely that 2 people share a birthday. But when you're dealing not with 2 people, but with a 52 card set, and not with 365 days but with 80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000 possible arrangements.
Except that its not. Aside from the fact that despite being such a high number, its not infinite, so you can't say its never happened, there's another reason. All decks start off in the same order, so that already stacks the odds of a repeat. Furthermore, people shuffle rather consistantly. People are likely to split the deck in half (rather than, say, fifteenths) and put the top half in their dominant hand before shuffling. People are likely to riffle shuffle, rather than putting each individual card down and picking them up in a random order. These small patterns and others we do mean that even though we shuffle, it's never a truly random arrangement of cards, and a repeat is more likely than true mathematical randomness.
***** That's taking it too far. There are factual statements in math that are inherently correct.
mchandler2112 The statement, when made properly, assumes a properly random shuffle. (For rifle shuffles, this takes seven times.)
+Jan Jappie Ukelele In mathematics, 2 + 2 = 4 is a fact. Based on our definitions of these numbers and the "+"-operator, this is a fact. In all likeliness this shuffle was unique, but there is not mathematics to guarantee it. Mathematically, this shuffle being unique is not a fact.
"Number of possibilities" "chances of a collision happening"
That's true. You're referring to the so called "Birthday paradox". Even though there are 365 days in a year, it only takes a random group of about 23 people for it to be more likely than not that there are multiple people in the group with the same birthday.
But in the case of a deck of cards the reduced odds, those of any collision, makes no humanly-comprehensible dent in the enormity of the number.
I wouldn't call it certain, but highly probable.
So highly probable it blows my mind.
So what you're saying is there's a chance... :D
52! That's how big it is!
Sorry for being so rude, but if you're not certain that that pack of cards has never been done before in history, you're an idiot.
It's absolutely 100% certain
Stephen seems quite proud of himself.
Its amazing because the large number comes from a relatively small number 52.Part of the fascination of cards
Stephen awarded himself points but I take them away for calling them a pack of cards when any decent person knows it’s a deck of cards.
To put it in perspective, there are about as many ways to arrange 52 cards as the number of grains of sand it would take to fill the whole Milky Way Galaxy
What
I read a thing where it talked about 52! and how long that amount of Seconds would be. He described it like this: deal five cards (randomly), and wait for a billion years. Then, deal another five cards. When you get a royal flush, buy a lottery ticket. Keep doing the dealing and waiting thing untill you win the lottery. When you do, put a grain of sand in the Grand canyon. Keep doing this, untill you fill the entire Grand canyon with sand. When this is done, take one oz (ca 28 grams) of rock out of mount Everest. When it is level, all the time hasnt passed, you have to do this whole thing 256 times.
The_Sad_Wallet that sounds like a vsauce thing. Was it Vsauce? That sounds familiar anyway.
Or a 10^50 light years long line of different ordered decks!
While what he says about 52! being a gigantic number and how long it would take for repeats and all that is technically true, it is only true if you are granting that every shuffle is, in fact different. The thing about random chance is that the probability of a repeat is never at 0% and it grows faster than the number of instances themselves (exponentially). For example when looking at birthdays there is a 50% chance that 2 people in any given group of 23 people share a birthday. When you have 70 people the probability is 99.9%. That is a crazy fact considering that there are 365 (70 days of the year is only 19% of the year) options and I'd imagine that a similar curve would be applied to card shuffling. Now while it is still a huge amount of time if the curve is anywhere near similar then we'd expect to see repeats about a fifth of the way through the time he said. That being said it's still highly unlikely that throughout human history we've reached anything near a fifth of all potential shuffles so he's more than likely still correct.
Anyway forgive my nerdy nitpicking ramble, it is always cool to see 52! being explained.
LoneW0lf11 You went off on a bit of a tangent there. However your possible error was in the first few lines. You said that if we're "granting" that each shuffle is different when the mathematical geniuses are saying it's a fact that each is 100% different. I'm not saying they're correct, but your argument against was built on the one simple point that if we grant that each will be different when that isn't what the geniuses were saying. They weren't saying "just take my word for it".
Near a 5th?? Do you have any idea what you're talking about? Do you actually study Probability and Statistics or are you just being a bellend? I'm fairly certain it's the latter.
A 1/5th? Haha. No. 52! is huge. Far beyond any idea you have about "chances of winning the lottery" or other 'unlikely events' - that, yes, are unlikely but do happen. Mostly because we have millions of people doing the lottery or billions of people on the planet, so a few get hit by lightning or whatever. A billion people all shuffling cards since the dawn of time wouldn't have made a dent in 52! let alone reached 1/5th.
Surely though as the cards are always in the same order when new out of the box, the probability getting all the cards in the same order after the initial shuffle (depending on how well the deck is shuffled) will be lower than if the cards were completely random before shuffling? Therefore, certain combinations of cards must be more common than others. Or am I just delusional?
You are 100% correct. What you said is exactly the mitigating factor. Additionally, Fry's comment on it taking a long time before repeating implies that all combinations must first be exhausted before a repeat can happen, which of course, is not true.
@@trekkiejunk no, but when the number is so vast that throughout human history, we have yet to produce 0,00...01% of the possibilites, the chance of it being in an order already seen, are just so small, that it can be said with certainty.
It needs to be a proper shuffle, where you randomly select each card individually to create a new order
Mind. Blown....
For those new to QI, it's really not about maths at all. It's mostly just a fact show with lots of funny people. Highly recommended.
That's some rain man information right there!
On your part. Probability that someone already did same shuffle is so small that you can call it absolute certainty.
Just to be sure, I think we should add a 53rd card soon to decrease those odds even more ;)
You must mean increase the odds even more.
Casinos use pre-shuffled decks for baccarat. The casinos get them pre-shuffled from the manufacturer. In 2012, a baccarat table at the Golden Nugget casino in New Jersey had 2 consecutive decks that had been shuffled in exactly the same order.
It sure sounds like the shuffling algorithms mechanical randomness management function might not quite work as well as one might wish.
And just think of all the things like this, that surround us in our daily lives, that we just take for granted that are even more complex than that
It's been a very long time since I've done maths beyond counting change, but if I'm correct, the chance of a deck of cards repeating itself is 1/52! * 100% ≈ 1.24*10^-66% ≈ 0.00000000000000000000000000000000000000000000000000000000000000000124%
How many different ways can uno cards be arranged
I'm pretty sure the birthday paradox applies here and the numbers are reduced by HUGE quantities.
Beautiful.
Mind BLOWN!
'I can say with all the mathematical certainty that is possible...'
*Mathematicians all over the world cringing*
possible being the key word there
Yes, but what do you do about those land cards? Doesn't that reduce the x variable in x! ?
Rain Man has verified this fact.
I believe this statistic whole heartedly imagine shuffling a shuffled deck of cards back to its original out of the packet in order state you basically couldn't do it it
You could do it. But that wouldn’t be a ‘proper’ shuffle.
so first the sun isn't there, and now he wants a nobel prize for shuffling cards! phil jupitus must be going bananas
Not impossible, just very, very improbable. So, no, you can't know for sure.
Yes but at some point surely something so "very, very improbable" that can be easily mathematically proven becomes synonymous to impossible in real life terms.
@@Roger__Wilco Society is to blame 🙂
Please tell the couple that shuffle the cards 14 TIMES after every 2 minute game while I'm trying to play the piano 😢
I work in a casino and deal 150-200 hands of poker 5 days a week, so that's how many times I make history each day.
This is not entirely true: shuffling by hand will never been a true random shuffling
One way to help visualize this - imagine you place the cards in a specific order such as all aces together, all twos together, etc. and then imagine how many times you would have to shuffle the deck until they were in that exact same order again. It would absolutely never happen.
Thanks, Captain Obvious
@@GroundhogRoy wow, you’re really showing your super intelligence with that eloquent reply . Certainly not an anonymous keyboard warrior regurgitating a trite cliche to make himself feel important by putting someone else down. No, I’m pretty sure you’re a genius! Have a great day!
* Some dude spits facts about math*
People applaude.
My type of show.
What about organised shuffling?
This would be great patter for a card trick...
Yup, the number is larger than the amount of atoms in our galaxy!... Unreal!
About the same as the number of grains of sand it would take to fill the entire Milky Way Galaxy
If you organize the enough amount of decks of cards in all the possible different ways and place them side by side they would correspond to a length of around 8*10^50 light years.
Is that true?
Yes, see the calculation below. Everything is in approximate numbers, but since the numbers are so huge it has minimal significance in this context.
* Combinations (52!): 8x10 ^ 67
* One deck (width): 0.05 meters
* 1 light year: 9.5x10 ^ 15 meters
Length of 8x10 ^ 67 card decks in a row: (8x10 ^ 67 x 0.05) = 4x10 ^ 66 meters.
This corresponds to (4x10 ^ 66 / 9.5x10 ^ 15) light years, ie hardly (10 ^ 66/10 ^ 16) light years.
According to mathematical principles, division with exponential numbers is calculated as follows:
(10 ^ 66/10 ^ 16) light years = 10 ^ (66-16) light years = 10 ^ 50 light years.
The answer is thus a distance of about 10 ^ 50 light years.
@A Slice of Fruitcake: Spontaneously I would probably say that it is a bit narrow minded to focus on one little word instead of the nearly inconceivable fact that the number of different mixed decks in a row would correspond to a distance of 800,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 light years, but I guess we just have a different angle of approach in this case.
And as you may have guessed: English is not my native language but Google translate is a good friend 😉.
@A Slice of Fruitcake: No
not strictly true. by sheer coincidence that particular combination could have been done already, though unlikely.
also, in reality shuffling does not perfectly randomize the cards and decks are always packaged in order. so the order after the first shuffle of a fresh deck would be far more likely to match the order of other first shuffles than 52! to 1.
I think he is right as he says " THIS pack of cards has never been in that order"
The comparison I heard was that there are more arrangements of 52 cards then atoms making up the earth. And the ratio between number of atoms of earth and arrangements of 52 cards is the same as $3.50 and the value of all money on earth.
Would this simple fact work for other packs of cards, like Magic: The Gathering or Sopio cards?
Likely so, or worse. The more unique cards in the deck, the faster it grows. Factorial goes up astonishingly fast.
scientifically speaking, we would assume he's correct because the chance of a repeat shuffle being 1.2e-66%
this is 50/50 chance to get it
A one in a million chance happens 9 times out of 10
In an infinite universe, this exact same shuffle has been repeated an infinite amount of times on an infinite number of airings of this particular episode of QI and so too has this edited comment.
The universe is clearly not infinite, nothing real is.
@@TransoceanicOutreach So you keep saying.
Strange, whenever I try to shuffle the cards the stay in new deck order. Bizarre...
It is not impossible for that order to have happened before, however it is extremely unlikely.
It's true, but I feel as if 'extremely unlikely' doesn't even begin to do it justice.
But neither does 'impossible'
The key is how many shuffles have already been completed if you include all planets throughout the history of the universe.
For example, four billion years ago, Martians in masses may have shuffled playing cards continuously.
It actually takes 7 riffle shuffles to fully randomize a deck of cards. If that was a new deck in order then the shuffles he did would not be sufficient to randomize them, although if they were randomized to start with then the order would indeed be unique
It's more like a 99.999% chance that it had not been shuffled before
Add a shit-ton more 9s and then yes
More like 99.9999999999999999999999999999999999999999999999999999999999999999999 percent
+LikerPenger but I can't fit millions of nines in just one reply
Damn I thought I had it perfect.
+LikerPenger oh well
If that was true, how is it possible for blackjack players to track the value of cards in a single deck game?
That's big, but not as big as 53!, or 54! come to think of it
You mean with the Jokers still in the deck, lol
In a related question, are some infinities bigger than other infinites?
does he mean the whole order he shuffled in, or the final order of the 52 cards?
What show is this?
So how did evolution create a simple protean that is more like a billion factoid?
52! is roughly 80 unvigintillion. Of course most people don't know how much a unvigintillion
Mind blowing stuff!
So, written out in non-numeric form, the order of a pack of 52 standard playing cards could be any one out of eighty unvigintillion, six hundred and fifty eight vigintillion, one hundred and seventy five novemdecillion, one hundred and seventy octodecillion, nine hundred and forty three septemdecillion, eight hundred and seventy eight sexdecillion, five hundred and seventy one quindecillion, six hundred and sixty quattuordecillion, six hundred and thirty six tredecillion, eight hundred and fifty six duodecillion, four hundred and three undecillion, seven hundred and sixty six decillion, nine hundred and seventy five nonillion, two hundred and eighty nine octillion, five hundred and five septillion, four hundred and forty sextillion, eight hundred and eighty three quintillion, two hundred and seventy seven quadrillion, eight hundred and twenty four trillion possible combinations.
And if you think that wall of text is big, just imagine the sheer enormity of ALL of those card order combinations if they were layed out next to each other. oO'
You're so right: laid out in a row the length would exceed 10 ^ 50 light years!
That’s Quite Interesting.
Best fact ever.
Well, fuck my old boots. You learn something new everyday.
likewise, I can say that at least 95% of playing cards in the world have been arranged in the proper sequence at least once ;D
It's not a mathematical certainty. Its a mathematical near certainty, because there is an infinitesimally small chance that it will have been in that order somewhere.
I am an agnostic believer on this, I dont onow that the pack has never existed before but given the probabilities I think it so unlikely that i can say i do believe it has not.
surely there are other variables to this because people shuffle the same way especially if you are doing a weave shuffle
I don't think enough trillions fit into that number displayed there.
2:39 "I'm not impressed" face to cover up the fact she doesn't get it.
It's about the same odds as me winning the bloody lotto......and that's HIGH.
In that case it’s an extremly lousy lotto!
there is more chance of me shuffling a pack in exactly the same order as stephen than there is of Roma getting to the champions league final
My next question would be......... If you took all the card games in all the casinos from all over the world, found out how many times packs of cards were shuffled per day in total on average. How many days/years/centuries would it take at most to achieve all combinations?
Casinos change to new decks too often
@@richmoore3957 he said a trillion stars, with a trillion PLANETS. so 1 trillion times 1 trillion... and each of those trillion planets on 1 trillion stars, so 1 trillion trillions planets with 1 trillion people each. If they were shuffling for since the big bang non stop they would just now be getting done to getting all combos. This dude is asking about all casinos in the world lmao.
we talking about trillions trillion trillion trillion decks being shuffled for billions of years in the videos example. So to answer him, it would take until the death of every atom in the universe lmao
tl;dr Just nitpicking about probabilities. The number of attempts necessary to have a good chance of finding the same combination twice or more is way smaller than 52!.
Seems to me that there is a misunderstanding of the probability to draw the same combination cards 2+ times. First of all there is a non-zero probability to draw the same combination twice in a row. 52! is simply the upper limit after which you are bound to repeat combinations.
There is a well known problem that is similar to this: how many students do you need to have in a classroom for the odds of having 2+ students sharing the same birthday to be over 50%? Here the upper bound is 366, meaning that if a classroom has 366 students, 2 or more are bound to share the same birthday.
Well for the probably of a shared bday to be >50%, there only needs to be 23 students in the classroom, assuming that bdays are randomly distributed. That's an order of magnitude less than 366.
Going back to the pack of cards, it's basically the same problem with 52! days in the year and not 366. I tried to compute the 50% probability, but the numbers are still so big that I'm reaching the limits of software and hardware capabilities. I'm conjecturing that it's orders of magnitudes smaller than 52!, something like billions of times smaller. If anybody has a workaround (or a quantum computer) to calculate that I'd be very interested; there's gotta be a way.
Something else to consider is that Steven Fry seems to assume here that every shuffle ever performed perfectly randomized the deck of cards being shuffled. That's unlikely to say the least. It's very probable that some combinations showed up many many times already. Maybe following a power law distribution, not sure about that.
I'm not a mathematician, so if you see any flaw in my reasoning please let me know. Thanks for reading!
It seems quite extraordinary but for anyone trying to get their head around it just imagine it with a smaller number and scale it up. Lets say a deck has 2 cards. There are only 2 combinations (1,2 and 2,1) if it had 3 cards (3,2,1 3,1,2 2,1,3 2,3,1 1,2,3 1,3,2) it all scales up. A deck of cards with 2 cards has two possibilities (2! = 2x1) same with 3! (3x2x1 = 6) etc. it is amazing though that such a large number can come from just 52 cards
Not if you think about how much 10^52 is. The exponential effect is extremely big and gets bigger and bigger with factorial numbers.
Which episode is this from?
the latest one - ep 10 I think
Ah yeah, well, joke's on him. I've seen this one before
The number of possibilities is less than an infinity, that means the chance is bigger than zero. So there is a chance... BTW this isn't nothing exceptional just basic math.
"Isn't nothing"? slightly less than exceptional.
+Loaf of Bread Just because there are huge numbers involved here doesn't make the maths exceptional. Like Cedric said, this is basic math, taught in high school.
I wasn't aware of an expiration date on responding to youtube comments.
I can say with certainty that my dick won't be cut off in a car accident 10 minutes from now. Doesn't mean it isn't impossible
+Cedric Liemessing
Wrong. Again: Because very rarely do cards *actually get fully shuffled*. Want an example of it being a *100%* chance of getting the same result? I open a fresh deck of cards. I cut it by taking one card off the top and putting it on the bottom. Boom, shuffled. I then repeat this with a second deck of cards. Boom, shuffled. 100% of them being identically shuffled decks.
And yes, that is a shuffled deck. It doesn't matter if you "shuffle" one card, a single time, or a billion times, it's all still a shuffle. *And* since most people rarely do more than three or four shuffles with a new deck, the chances of getting a repeat are *waaaaaaaaaay* further away from 0% than the "perfect shuffle" of 1 in 52!.
What calculator did they use... jeez
What we're taught in medicine - never say never, and never say always. Of course there is a tiny chance that deck-order has existed before, a very tiny chance.
It doesn't even begin to make sense to conflate medical outcomes from proven treatments with the astronomical odds of a shuffled card deck ramdomly repeating.
There is always one.....
while this makes sense, there is no way of knowing that he didn't shuffle those cards the exact same way as someone else has..
52! extremely difficult to imagine how large that number is. Add a joker and multiply it by 53 omg! (that's not omg factorial)(but might as well be)
The number of perfectly randomising shuffles to get a deck the same as Stephen's is indeed on the order of 52!. Specifically after 52! shuffles the chance of a deck the same as Stephen's having happened is 1-exp(-1).
However the chance of any two decks being the same is far higher. To have a decent chance of any two decks matching you need on the order of the square root of 52! shuffles. 1.057x10^34 would give a roughly 50-50 chance. With trillions of people on trillions of planets doing 1000 shuffles a second you'd repeat a shuffle after about 4 months.
john smith How are you getting "on the order of the square root of 52! shuffles"? The original birthday problem has the halfway point between 23 and 24, while the square root of 365 is closer to 19.
I ask not because I think you're wrong, but just to educate myself. I couldn't find any formula that would generalize that well. Fermi calculations kept giving me 0 chance (since 52! - all the shuffles that could have happened is still 10^68, and 10^68/10^68 = 1).
+ZipplyZane -- to a mathematician, to the order of is entirely correct, an error of 4 out of 23 is not considered to wrong as the order of calculation is "more or less" then same thing compared to being say 10 times as large or small as the correct answer. A more accurate approximation is sqrt(2*m*ln(1-(1/p))) m is number of unique events and p is the chance of at least 1 duplicate (.5 for the birthday problem)
The whole setup/pretense is wrong. The same order could have happened multiple times. Probability does not mean it will or won't happen in a set amount of tries, mathematically probability requires infinite tries in order to be true.
Quick wolfram alpha calculation shows that the average number of shuffles you would need to go through every possibility is way larger - I got 1.2101169951...e67
If we're talking about statistics, then he should also have pointed out that a very small chance doesn't mean "never".
@IUPLOADALLSORTS:
I'm sorry, but bigybop is right. It's not a fact. It's incredibly unlikely, but there's no way to prove that any individual shuffle has never been done before. Not only that, but the more new combinations that have been tried ADDS to the probability of the next one being a repeat.
Is that Gordon Gordon Wyatt
There are problems with this, starting with his opening statement. It's impossible for anyone to say it's never been done since the beginning of time. (He later clears that up, saying that it is possible but mathematically unlikely.) A greater problem is with how he illustrates the unlikeliness of it. Try telling a friend what he said two days after watching this. ("Wait, was that shuffling a thousand times a second or a thousand times a minute?")
A description I've seen said that gives a better idea of the magnitude of the number of possible combinations was simply that the number is greater than the number of atoms making up Earth.
Oh get over it, killjoy
0:18 "crash a plane?" bit mean that
Can't prove it, still somebody could have put it in that exact order.
That chance is about 0.000000000000000000000000000000000000000000000000000000000000000000000000000001%
You can't really be certain the order fo a deck has never been in a certain order twice. You can only be certain that it would take a really long time to get all combinations.