Fun Fact: Every Time You Shuffle A Deck Of Playing Cards, You've Produced A Sequence Of Cards That Has Never Existed Before.

[Skyshark]

This is a very oddly phrased question. I'm guaranteed to pull a sequence of cards from a deck. There's no uncertainty; I have a 100% chance of getting some arbitrary deal. However, if I were to try to name a sequence, and then pull that specific sequence, I would have a 1/52! chance of getting that particular sequence. Without any prior information, there's no meaningful probability to play with.



Yes, the odds of getting that same draw is the same as getting any other individual combination, but that's not what we're looking at. There is a singular success case, and there are (52! - 1) failure cases. It does not matter at all which of the failure cases you draw. Once you've defined a target, you either succeed or fail.

And it is absolutely impossible to do it again. It has never happened and will never happen in the span of human existence. 52! is that big.

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I'm simply saying the odds of pulling a any combination of cards is 1 in 52!, regardless of the previous draws. Each draw is it's own unique event and the odds don't get better or worse based on the previous draw. So I have just as likely a chance to pull the combination I just pulled as I do pulling any other combination, hence, making it by definition, not impossible.

 

[Feep]

For the 30th time. Im not disagreeing with the thread. Im disagreeing with the fact that someone was saying that this absolutely impossible because the odds are so small. That statement is ridiculous. Just because something has a tiny chance of happening doesnt mean it never will. Proof: Stuff with a smaller chance of happening has happened. Again: NOT DISAGREEING WITH THE PREMISE OF THE THREAD.

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You are almost certainly incorrect. I am quite confident in saying that absolutely nothing in the scope of humanity's purview has happened that is even close to as unlikely as this.

You saying things like "what are the odds that you were born?" suffers from the anthropic principal. The odds that some particular combination of alleles came from your parents is 100%. And any of one of those could say "wow, what are the odds that I was born?" because you *didn't specify in advance what you were looking for*. Because a whole butt-ton of versions of you would ask that same question, there is nothing particularly strange or unlikely about this.

As someone else noted, the sort of unlikelihood you're looking for would be if two humans from different parents coincidentally were given the exact same genetic code...and even that, I would wager, doesn't come close to the unlikelihood of a repeat of a true shuffle occurring.

tl;dr: if you don't specify in advance what combination you're looking for, there is nothing unlikely about it appearing. You were just looking for "a sequence", and you got one, ta da.

 

[Fugu]

Oh, I believe and understand the statement, my issue is purely semantic.


From the Oxford English Dictionary, the adjective "wet" is defined as consisting of moisture, liquid. By definition, water is wet.

Similarly, a probabilistic event is defined as "impossible" if it's probability is equal to 0. Hence, repeating a permutation of cards is possible. By definition.

In layman's terms, sure, it's impossible--I mean, those numbers are incomprehensible.
But if we're doing math, I insist upon being proper about it.

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We're not doing math. The math is done.

We're talking about whether you can say "this has never happened before" despite some very small degree of uncertainty married with the knowledge that it's technically possible. The answer to that has to be yes.

 

[THErest]

We're not doing math. The math is done.

We're talking about whether you can say "this has never happened before" despite some very small degree of uncertainty married with the knowledge that it's technically possible. The answer to that has to be yes.

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Agreed.

(I really don't get to go into math mode too often, it's a big step from grad school to teaching high school students, the ones that don't care for math).

 

[butzopower]

In layman's terms, sure, it's impossible--I mean, those numbers are incomprehensible.
But if we're doing math, I insist upon being proper about it.

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But we are talking about discrete sets of numbers here. The only way for the probability of collision to be mathematically impossible is to have an infinite (mathematically impossible) set of numbers. Insist as being proper as you want you are basically just arguing that the only proper discussion is to say 1 = 1.

 

[THErest]

But we are talking about discrete sets of numbers here. The only way for the probability of collision to be mathematically impossible is to have an infinite (mathematically impossible) set of numbers. Insist as being proper as you want you are basically just arguing that the only proper discussion is to say 1 = 1.

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Did you just say that it was mathematically impossible to have an infinite set of numbers?

And, as has been mentioned, I was in a semantic argument.

 

[RaphaBE]

I'm a mathematician (sort of) and I think that some of you are being quite condescending. Sure, it's difficult for most people to grasp the scope of !52, but claiming that it's "impossible" is not helpful either. Where do you draw the line, exactly? Would it be impossible with a deck of 20 cards? 10 cards? Stick to actual numbers or to useful analogies - such as trillions of people shuffling millions of decks per second since the beginning of time - instead of assuming that people are stupid because they disagree it's impossible.

 

[HStallion]

it's next to impossible of course

 

[Lord Azrael]

whenever someone says "fun fact" it's never actually fun.

I suggest switching over to news flash! instead

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When people say fun fact what they really mean is unfun fact

 

[DealWithIt]

I'm a mathematician (sort of) and I think that some of you are being quite condescending. Sure, it's difficult for most people to grasp the scope of !52, but claiming that it's "impossible" is not helpful either. Where do you draw the line, exactly? Would it be impossible with a deck of 20 cards? 10 cards? Stick to actual numbers or to useful analogies - such as trillions of people shuffling millions of decks per second since the beginning of time - instead of assuming that people are stupid because they disagree it's impossible.

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Thank you.

That people refuse to accept the posters' *unstated* assumptions (fully random shuffles even though physical shuffles are not, a randomized starting deck setup) is a sign that the posters have failed to relay their assumptions in advance. To me, it's unproductive to complain about how the posters don't understand math. Simply refine your point.

Ironically, the folks saying it is *impossible* are functionally ignoring the incomprehensibility of infinity. As the number of cards in the deck approaches infinity, the actual probability of a repeat (with perfect randomization of shuffles) approaches zero. 52! is a very very very long way from infinity.

Thus, this *cosmically unlikely* event is *comparatively probable* at 52 cards. To make a repeat shuffle physically impossible you need an infinite deck.

Sure you can be *pretty goddamn certain* that a randomly ordered deck of 52 cards will occur in a configuration that has never happened before and will never happen again, but that is not the same thing as mathematical impossibility.

that same math breaks down if you physically riffle shuffle a new, ordered 52-card deck once. In that instance, chances are reasonable that you'll make a combo that's happened before.

Edit: this poster says it succinctly:

This would be true if we're using an unbiased algorithm (i.e. Fisher-Yates) for shuffling. However, the most common manual shuffling technique used (specifically, the one shown in the video) does ... not have a lot of entropy in it. I'd bet that if you gave 1000 people a brand-new deck of cards and asked each of them to do exactly one classic shuffle, you'd get more than a few duplicates.

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[A Strong Latte]

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This asshole definitely stacks his deck. The bottom half isn't moving at all!

 

[Deleted member 81119]

If a chessboard were to have wheat placed upon each square such that one grain were placed on the first square, two on the second, four on the third, and so on (doubling the number of grains on each subsequent square), how many grains of wheat would be on the chessboard at the finish?

Spoiler

18,446,744,073,709,551,615

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Some grains.

 

[divisionbyzorro]

Thank you.

That people refuse to accept the posters' *unstated* assumptions (fully random shuffles even though physical shuffles are not, a randomized starting deck setup) is a sign that the posters have failed to relay their assumptions in advance. To me, it's unproductive to complain about how the posters don't understand math. Simply refine your point.

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It's really, really important to consider both the theoretical statistics and the practicality of implementation to properly frame the issue. You need to both recognize that 52! is absurdly enormous and recognize that people can't shuffle perfectly. Anyone just looking at the numbers or just looking at shuffles is missing half the problem.

Why do I say this?

Ironically, the folks saying it is *impossible* are functionally ignoring the incomprehensibility of infinity. As the number of cards in the deck approaches infinity, the actual probability of a repeat (with perfect randomization of shuffles) approaches zero. 52! is a very very very long way from infinity.

Thus, this *cosmically unlikely* event is *comparatively probable* at 52 cards. To make a repeat shuffle physically impossible you need an infinite deck.

Sure you can be *pretty goddamn certain* that a randomly ordered deck of 52 cards will occur in a configuration that has never happened before and will never happen again, but that is not the same thing as mathematical impossibility.

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You don't need an infinite deck to make a repeat sequence "physically" impossible. You only need an infinite deck to make the probability go to zero. In order to make a repeat sequence "physically" impossible as human beings with 52 card decks, you just need an infinitesimally small time window to run your test in. Given how large 52! is, the span of all human existence happens to be a plenty small enough window.

"But the probability is still not zero!"

But there are also a lot of other things that this 'mental experiment' assumes have a probability of zero that actually have a non-zero probability in the real world. For example: the probability that someone running the experiment makes a mistake, or the probability that they're lying, or the probability that the computer they're using for record keeping gets struck by a cosmic ray and modifies the history of shuffles you've been tracking...

...or most likely: the probability that you have calculated the probability of the event wrong because you left out some external factor.

When I say it's physically impossible, I mean that the probability of something interfering with the experiment dominates the probability of the event 'naturally' occurring.

This is where the importance of the errors inherent in physical shuffling come in. If you can prove with absolute certainty that nobody is lying, and can provide irrefutable evidence that two identical sequences actually happened, then the rest of us have to decide what physically happened: either you really got that cosmically lucky, or there is a flaw in your shuffling method. And 1/52! is so absurdly small that the probability of your shuffling method being flawed absolutely dominates it beyond a shadow of a doubt.

I posted the story about the perfect bridge deal earlier: a shuffle result that can never happen, but it did. But obviously it did because the probability of that event occurring from a freshly opened deck is significantly higher than the probability of that event occurring from an arbitrarily mixed deck. That's an example of what I'm getting at: if one of these 'cosmically unlikely' events happen, you can say with absolute certainty that something else is going on.

In closing - obviously this argument is semantic. If I put it into explicit terms, 'impossible' means 'if someone claims it happens, the rest of us should assume they're wrong.' And from the perspective of the human experience, that definition is functionally the same as 'the probability of that event occurring is zero,' even though 1/52! is obviously > 0.

 

[nihilence]

Is this similar to how GO has more moves than atoms in the universe? Boggling.

 

[Mona]

I'm simply saying the odds of pulling a any combination of cards is 1 in 52!

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dude its alright calm dwn

 

[RadzPrower]

As a thought experiment with pure mathematics, sure.

In the real world where starting decks are not fully randomized and cards are physically shuffled rather than theoretically shuffled in a truly random nature, the same deck has most certainly been shuffled before, especially in cases of a fresh deck of cards.

 

[butzopower]

So how many shuffles y'all shuffle in a shuffle?

 

[butzopower]

Thus, this *cosmically unlikely* event is *comparatively probable* at 52 cards. To make a repeat shuffle physically impossible you need an infinite deck.

Sure you can be *pretty goddamn certain* that a randomly ordered deck of 52 cards will occur in a configuration that has never happened before and will never happen again, but that is not the same thing as mathematical impossibility.

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While this is true in the purest sense of being a factual statement it reduces the conversation down to the utterly asinine place this thread has gone to where you are basically saying nothing of any significance.

You've sucked all the "fun" out of the "fun fact" and gone completely to a separate, utterly unfun fact that "nothing besides an unlimited choice is technically impossible".

 

[Shemhazai]

Okay sure, but that doesn't explain why I only ever draw 1 land or 6.

 

[butzopower]

Okay sure, but that doesn't explain why I only ever draw 1 land or 6.

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It's the Curse of Garfield. If you just played the game with like 1 of every card like Richard wanted you to, then you wouldn't have this problem.

 

[Wolf]

Factorially this is true but I would also not be surprised in the least if at some point there has been a duplicate. This claim takes in a bunch of assumptions.

 

[DealWithIt]

While this is true in the purest sense of being a factual statement it reduces the conversation down to the utterly asinine place this thread has gone to where you are basically saying nothing of any significance.

You've sucked all the "fun" out of the "fun fact" and gone completely to a separate, utterly unfun fact that "nothing besides an unlimited choice is technically impossible".

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This is the source of the conversation. To me, the "fun part" is considering the realities and assumptions behind the "fun fact."

The other responder has framed the discussion around detectability, but that's not what the discussion is about. Sure, human error and other factors make it unlikely that we can accurately, certainly, detect a double, but that's not the frame we were presented. The title says: "

Fun Fact: Every Time You Shuffle A Deck Of Playing Cards, You've Produced A Sequence Of Cards That Has Never Existed Before.

and a lot of posters have pointed out that that framing is suspect at best. Unless you state multiple underlying assumptions it's not likely to be true.

 

[butzopower]

If you watch the video in OP the dude states "a properly shuffled deck" sure that's open to interpretation and it probably could have fit in OPs title but it's like completely pedantic, if we need to default on any assumption of what "properly" means here let's then lean more on the formal definition (cuz y'all wanna be pedantic) of shuffle which is randomized. Wikipedia to the rescue https://en.m.wikipedia.org/wiki/Shuffle_(disambiguation)

I think the problem is most people are just replying to the title and haven't watched any of the video or probably even read the OP but that's just ResetERA for ya.

 

[gozu]

i'm baffled by the amount of push back this got in the thread

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I guess a lot of people don't understand that their intuition can lead them very, very, very astray. I'm this particular case, they didn't reAlize we have so many zeros in our margin of error that you can throw half of them away and still have enough to blow our feeble little human mind.

Mad respect for my stochastics teacher for crushing everybody's intuition all semester long with interesting examples. I will never trust my intuition again.

 

[Burbank]

Not if you're bad at shuffling.

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Or really, really good 😉

 

[iapetus]

You are almost certainly incorrect. I am quite confident in saying that absolutely nothing in the scope of humanity's purview has happened that is even close to as unlikely as this.

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You're wrong.

I shuffle a deck of cards (well). I note down the order of the cards.

I shuffle it a second time (well). What is the probability of it being in exactly the same order as the previous deal?

Well, that's obvious. It's 1/52!.

So I compare it to the previous order. And unsurprisingly, it isn't in the same order. I mean, it's fairly unlikely that even the first card is the same.

You might think this proves your point, but in fact it crushes it. Because although it isn't the same order (there was only a 1/52! chance of that, after all), the probability of me dealing *this* specific order after the previous one was (drumroll) 1/52! - exactly the same probability.

Just because matching the order perfectly is more interesting to our dumb pattern-matching brains doesn't mean the specific order I got was any more likely.

 

[Nax]

Cool video, thanks for sharing!

Brings me back to my days in Astronomy class. Where numbers are all huge.

 

[ty_hot]

I like that this thread basically became a discussion of how close to zero a number has to be to be considered zero. Or how big it has to be to be considered infinite.

I just know that in real life decks come out of the factory in the same order and that people not only don't know how to shuffle properly, but they do it similarly, so yeah I am 100% confident that the same deck order was shuffled not once but quite a few times because of these real life aspects.

 

[Ororo]

In other words there's nothing special about having a unique sequence of cards, if you had one that has already been done then only then would it be special.

 

[divisionbyzorro]

You're wrong.

I shuffle a deck of cards (well). I note down the order of the cards.

I shuffle it a second time (well). What is the probability of it being in exactly the same order as the previous deal?

Well, that's obvious. It's 1/52!.

So I compare it to the previous order. And unsurprisingly, it isn't in the same order. I mean, it's fairly unlikely that even the first card is the same.

You might think this proves your point, but in fact it crushes it. Because although it isn't the same order (there was only a 1/52! chance of that, after all), the probability of me dealing *this* specific order after the previous one was (drumroll) 1/52! - exactly the same probability.

Just because matching the order perfectly is more interesting to our dumb pattern-matching brains doesn't mean the specific order I got was any more likely.

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I promised myself that I wouldn't engage in this thread anymore, but this is such a common misunderstanding of probability that I have to come back and correct it.

You're claiming that the probability of a match is the same as the probability of pulling any arbitrary sequence. And since you're capable of dealing out any arbitrary sequence you want, obviously this supposedly unlikely event has occurred, so people saying this can never happen must be wrong.

I want to point out that your internal logic is actually in conflict with itself. To calculate the probability of two events occurring, we multiply the probability of each individual event occurring together. So if the probability of Event A is P, then probability of that event occurring twice is P^2.

You've claimed in the second part of that the probability of pulling any arbitrary sequence is 1/52! So if you want to pull that sequence twice, the probability must be (1/52!)^2. But you're claiming that the probability of a match is only 1/52!; what gives?

Here's what you've done wrong. Your first set of calculations were correct. You (correctly) noted that the first sequence wasn't special, so you (correctly) assigned it a probability of 1 without even thinking, because 1 is the probability of pulling a random sequence of cards from a deck. Thus, the probability of getting a match = (Probability of getting any sequence) * (Probability of getting that one specific sequence again) = 1 * (1/52!) = 1/52!

However, you then went on to say that the odds of getting the second sequence were also 1/52!, but that's not internally consistent with the odds you assigned to getting the first sequence. If you state that the odds of getting Sequence 2 for the first time are 1/52!, then you must also state that the odds of getting Sequence 1 for the first time are also 1/52!

You want to throw out the 'dumb pattern matching brain' part of probability, but as it turns out, assigning meaning to patterns is extremely important when calculating probabilities. You can't look backward at an event and assign it a meaningful probability unless that event was known to be significant before it occurred.

 

[Nooblet]

ehh theres only 52 cards in a deck, so its 52 x 52 possible combinations plus or minus a few. not even close to one million etc

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It's 52! So 52*51*50...

 

[CarpeDeezNutz]

I like that this thread basically became a discussion of how close to zero a number has to be to be considered zero. Or how big it has to be to be considered infinite.

I just know that in real life decks come out of the factory in the same order and that people not only don't know how to shuffle properly, but they do it similarly, so yeah I am 100% confident that the same deck order was shuffled not once but quite a few times because of these real life aspects.

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I always that the whoa part about this was that you could shuffle a deck in a way no one has ever had in history.

 

[Feep]

You're wrong.

I shuffle a deck of cards (well). I note down the order of the cards.

I shuffle it a second time (well). What is the probability of it being in exactly the same order as the previous deal?

Well, that's obvious. It's 1/52!.

So I compare it to the previous order. And unsurprisingly, it isn't in the same order. I mean, it's fairly unlikely that even the first card is the same.

You might think this proves your point, but in fact it crushes it. Because although it isn't the same order (there was only a 1/52! chance of that, after all), the probability of me dealing *this* specific order after the previous one was (drumroll) 1/52! - exactly the same probability.

Just because matching the order perfectly is more interesting to our dumb pattern-matching brains doesn't mean the specific order I got was any more likely.

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A very good post was just written explaining why you are incorrect, and there's no need to dogpile. Please read that!

 

[Fugu]

You're wrong.

I shuffle a deck of cards (well). I note down the order of the cards.

I shuffle it a second time (well). What is the probability of it being in exactly the same order as the previous deal?

Well, that's obvious. It's 1/52!.

So I compare it to the previous order. And unsurprisingly, it isn't in the same order. I mean, it's fairly unlikely that even the first card is the same.

You might think this proves your point, but in fact it crushes it. Because although it isn't the same order (there was only a 1/52! chance of that, after all), the probability of me dealing *this* specific order after the previous one was (drumroll) 1/52! - exactly the same probability.

Just because matching the order perfectly is more interesting to our dumb pattern-matching brains doesn't mean the specific order I got was any more likely.

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How does this point keep getting made?

It's not about the specific order you got being more likely, it's about it being more likely that you got a unique deck from your good shuffle than a non-unique deck.

The first person who shuffled a deck of cards got a unique deck. On the second shuffle, the odds of getting a unique deck were (52! - 1)/52!. The odds of getting a unique shuffle at any point are (52! - n)/52!, where n is the number of unique shuffles produced up until this point in human history.

The entire object of this thread (and of this thought experiment) is that no amount of humanly-achievable shuffling will move the needle on the odds of a unique shuffle enough to make a non-unique shuffle a reasonable possibility. Indeed, even if the entire human race had dedicated itself to the task of shuffling cards it would take an absurdly long time to move the needle.

 

[Skyshark]

I promised myself that I wouldn't engage in this thread anymore, but this is such a common misunderstanding of probability that I have to come back and correct it.

You're claiming that the probability of a match is the same as the probability of pulling any arbitrary sequence. And since you're capable of dealing out any arbitrary sequence you want, obviously this supposedly unlikely event has occurred, so people saying this can never happen must be wrong.

I want to point out that your internal logic is actually in conflict with itself. To calculate the probability of two events occurring, we multiply the probability of each individual event occurring together. So if the probability of Event A is P, then probability of that event occurring twice is P^2.

You've claimed in the second part of that the probability of pulling any arbitrary sequence is 1/52! So if you want to pull that sequence twice, the probability must be (1/52!)^2. But you're claiming that the probability of a match is only 1/52!; what gives?

Here's what you've done wrong. Your first set of calculations were correct. You (correctly) noted that the first sequence wasn't special, so you (correctly) assigned it a probability of 1 without even thinking, because 1 is the probability of pulling a random sequence of cards from a deck. Thus, the probability of getting a match = (Probability of getting any sequence) * (Probability of getting that one specific sequence again) = 1 * (1/52!) = 1/52!

However, you then went on to say that the odds of getting the second sequence were also 1/52!, but that's not internally consistent with the odds you assigned to getting the first sequence. If you state that the odds of getting Sequence 2 for the first time are 1/52!, then you must also state that the odds of getting Sequence 1 for the first time are also 1/52!

You want to throw out the 'dumb pattern matching brain' part of probability, but as it turns out, assigning meaning to patterns is extremely important when calculating probabilities. You can't look backward at an event and assign it a meaningful probability unless that event was known to be significant before it occurred.

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I happen to agree with the poster you quoted. So can I ask you this? If I flip a coin what are the odds it's heads or tails? I think we both agree it's 50%. So say it's tails and I flip again. What are the odds now that it's heads or tails? It's still 50%, correct? The first flip has nothing to do with the second flip as they are each independent of one another. So on a much larger scale, how is a random draw any different? Each possible hand is it's own unique event and has nothing to do with the first hand. Each draw has a 1/52! chance of happening. Idk, maybe I'm missing something, but this seems pretty simple to me.

 

[Fugu]

I happen to agree with the poster you quoted. So can I ask you this? If I flip a coin what are the odds it's heads or tails? I think we both agree it's 50%. So say it's tails and I flip again. What are the odds now that it's heads or tails? It's still 50%, correct? The first flip has nothing to do with the second flip as they are each independent of one another. So on a much larger scale, how is a random draw any different? Each possible hand is it's own unique event and has nothing to do with the first hand. Each draw has a 1/52! chance of happening. Idk, maybe I'm missing something, but this seems pretty simple to me.

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What do you think this proves? I'm genuinely confused how stating this is an argument or a response to anything.

 

[subpar spatula]

A shitty shuffle is still a shuffle. That is like saying it isn't random just because only 2 things were swapped.

Anyway, you don't have to hit that number. It is possible the same combination has occured. The thing is there is no way to know.

 

[CasuallyDressed]

I'm out in the middle of nowhere, so no video for me, but I found this example to show how large the number is:

Say that there exists 10 Billion people on every planet, 1 Billion planets in every solar system, 200 Billion solar systems in every galaxy, and 500 Billion galaxies in the universe. If every single person on every planet has been shuffling decks of cards completely at random at 1 Million shuffles per second since the BEGINNING OF TIME, every possible deck combination would still yet to have been "shuffled".

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I watched the video and my brain still doesn't believe this. Absolutely mindboggling.

 

[loco]

Trust the math

 

[Rockodile]

oops! I forgot to take the Jokers out of the deck. How many combinations now?

 

[Guppeth]

oops! I forgot to take the Jokers out of the deck. How many combinations now?

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230,843,697,339,241,380,472,092,742,683,027,581,083,278,564,571,807,941,132,288,000,000,000,000

 

[Fugu]

230,843,697,339,241,380,472,092,742,683,027,581,083,278,564,571,807,941,132,288,000,000,000,000

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Don't forget the rules card!

12 696 403 353 658 275 925 965 100 847 566 516 959 580 321 051 449 436 762 275 840 000 000 000 000

 

[ty_hot]

I promised myself that I wouldn't engage in this thread anymore, but this is such a common misunderstanding of probability that I have to come back and correct it.

You're claiming that the probability of a match is the same as the probability of pulling any arbitrary sequence. And since you're capable of dealing out any arbitrary sequence you want, obviously this supposedly unlikely event has occurred, so people saying this can never happen must be wrong.

I want to point out that your internal logic is actually in conflict with itself. To calculate the probability of two events occurring, we multiply the probability of each individual event occurring together. So if the probability of Event A is P, then probability of that event occurring twice is P^2.

You've claimed in the second part of that the probability of pulling any arbitrary sequence is 1/52! So if you want to pull that sequence twice, the probability must be (1/52!)^2. But you're claiming that the probability of a match is only 1/52!; what gives?

Here's what you've done wrong. Your first set of calculations were correct. You (correctly) noted that the first sequence wasn't special, so you (correctly) assigned it a probability of 1 without even thinking, because 1 is the probability of pulling a random sequence of cards from a deck. Thus, the probability of getting a match = (Probability of getting any sequence) * (Probability of getting that one specific sequence again) = 1 * (1/52!) = 1/52!

However, you then went on to say that the odds of getting the second sequence were also 1/52!, but that's not internally consistent with the odds you assigned to getting the first sequence. If you state that the odds of getting Sequence 2 for the first time are 1/52!, then you must also state that the odds of getting Sequence 1 for the first time are also 1/52!

You want to throw out the 'dumb pattern matching brain' part of probability, but as it turns out, assigning meaning to patterns is extremely important when calculating probabilities. You can't look backward at an event and assign it a meaningful probability unless that event was known to be significant before it occurred.

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It seems to me that you both are saying the same thing but not communicating it well with each other. They said that the 1/52! is the odds of shuffling the cards and getting the same sequence again. Which basically means what are the odds of shuffling and getting this one pre determined sequence. They worded it in a confusing way and you understood that they meant shuffling twice and getting the same sequence twice.

 

[Skyshark]

What do you think this proves? I'm genuinely confused how stating this is an argument or a response to anything.

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And I'm genuinely confused as to how people don't understand. Again, unless I'm missing something, which nobody seems able to explain, then the chance of drawing an collection of cards is exactly the same, irregardless of the previous draw. You can't just say the probability of it happening twice is impossible because there's 52! possible combinations when each draw is it's own experience and whatever happened before or whatever happens after has no affect. It's like people assume that it can't happen again just because the numbers are so large, which is why I give the coin flip example. It's such a smaller scale and easier to understand. If you understand that every coin flip has 50/50 odds, then you should understand that every card draw has 1 in 52! odds, basically rendering whatever occurred beforehand useless information. Unless you can explain it instead of simply dismissing it by questioning how it makes any sense, then I'll assume you have no idea what you're talking about.

 

[Guppeth]

And I'm genuinely confused as to how people don't understand. Again, unless I'm missing something, which nobody seems able to explain, then the chance of drawing an collection of cards is exactly the same, irregardless of the previous draw. You can't just say the probability of it happening twice is impossible because there's 52! possible combinations when each draw is it's own experience and whatever happened before or whatever happens after has no affect. It's like people assume that it can't happen again just because the numbers are so large, which is why I give the coin flip example. It's such a smaller scale and easier to understand. If you understand that every coin flip has 50/50 odds, then you should understand that every card draw has 1 in 52! odds, basically rendering whatever occurred beforehand useless information. Unless you can explain it instead of simply dismissing it by questioning how it makes any sense, then I'll assume you have no idea what you're talking about.

Click to shrink...

Toss a trillion, trillion coins, one after the other, and write down the sequence. Whatever it is, it's not particularly remarkable.
Now repeat the process and get the same result. Suddenly, you have a miracle on your hands.

Every time you shuffle a deck, there's a ~100% chance you will create a sequence that has never been seen before.
And there's a ~0% chance you will create a sequence that has been seen before.
That's why the previous sequences matter to the observer. Because they are the "impossible outcomes". They will never happen again.

 

[Fugu]

And I'm genuinely confused as to how people don't understand. Again, unless I'm missing something, which nobody seems able to explain, then the chance of drawing an collection of cards is exactly the same, irregardless of the previous draw. You can't just say the probability of it happening twice is impossible because there's 52! possible combinations when each draw is it's own experience and whatever happened before or whatever happens after has no affect. It's like people assume that it can't happen again just because the numbers are so large, which is why I give the coin flip example. It's such a smaller scale and easier to understand. If you understand that every coin flip has 50/50 odds, then you should understand that every card draw has 1 in 52! odds, basically rendering whatever occurred beforehand useless information. Unless you can explain it instead of simply dismissing it by questioning how it makes any sense, then I'll assume you have no idea what you're talking about.

Click to shrink...

I really wish you would've answered my question, because I am genuinely struggling to figure out how this is relevant.

Yes, the draws do not affect each other. So what? How is this relevant to the expression that "every time a deck has been properly shuffled, a unique shuffle has been formed"? This statement is not based on the belief that dealing one set of cards somehow makes dealing that same set again impossible, it's based on the fact that 52! is such a gargantuan number that even if humanity dedicated itself solely to the task of shuffling cards for the rest of time we'd make no appreciable progress on the odds.

I think what you are saying is that the odds are not literally zero because generating one set of cards doesn't actually prevent you from generating that set again, but the point of this whole exercise is that it doesn't matter because the odds are so profoundly unlikely that it happening even once would be an event so unlikely that it's seemingly without precedent.

 

[Spinluck]

If you're good at math go fuck yourself

 

[Skyshark]

I really wish you would've answered my question, because I am genuinely struggling to figure out how this is relevant.

Yes, the draws do not affect each other. So what? How is this relevant to the expression that "every time a deck has been properly shuffled, a unique shuffle has been formed"? This statement is not based on the belief that dealing one set of cards somehow makes dealing that same set again impossible, it's based on the fact that 52! is such a gargantuan number that even if humanity dedicated itself solely to the task of shuffling cards for the rest of time we'd make no appreciable progress on the odds.

I think what you are saying is that the odds are not literally zero because generating one set of cards doesn't actually prevent you from generating that set again, but the point of this whole exercise is that it doesn't matter because the odds are so profoundly unlikely that it happening even once would be an event so unlikely that it's seemingly without precedent.

Click to shrink...

That is exactly what I'm saying any have been saying for the last two days. The post you originally quoted today was not my first of the thread. I thought I made it clear earlier in the thread that the odds are extremely unlikely but still possible, even if that possibility is 1 out of 52!. So I apologize if I wasn't clear, but yes, my issue is that it's literally, mathematically, not impossible, even if the chances, as you correctly pointed out, are so profoundly unlikely. Maybe it's just me making a mountain out of a molehill, but I just don't like the phrasing of it's impossible when it's not, regardless of how extremely rare the odds may be.

 

[Fugu]

That is exactly what I'm saying any have been saying for the last two days. The post you originally quoted today was not my first of the thread. I thought I made it clear earlier in the thread that the odds are extremely unlikely but still possible, even if that possibility is 1 out of 52!. So I apologize if I wasn't clear, but yes, my issue is that it's literally, mathematically, not impossible, even if the chances, as you correctly pointed out, are so profoundly unlikely. Maybe it's just me making a mountain out of a molehill, but I just don't like the phrasing of it's impossible when it's not, regardless of how extremely rare the odds may be.

Click to shrink...

It is impossible. It's not impossible in the sense that mathematically 1/52! > 0, but it's impossible that in any remotely human time scale two deck of cards will be (properly) shuffled into the same order.

If someone asked you whether it was possible for a block of ice to spontaneously sublimate, you'd probably say no even the answer is actually yes, it's just incredibly, ridiculously unlikely. This is the same sort of situation.

 

[siteseer]

time it takes a quantum computer to shuffle a duplicate deck: 42 seconds.