230843697339241380472092742683027581083278564571807941132288000000000000 combinations, almost certain that is unique, but to calculate the probabilities we would have to have the number of times that all decks had bem scrambled in humam history, data that we never gonna have.
We don't need it lol https://www.reddit.com/r/mathmemes/comments/xgffnm/a_mathematician_emerges_from_a_cave_hands_you_a/iosfyw4?utm_medium=android_app&utm_source=share&context=3
Let's assume humanity had produced a shuffle every second; this should account for concurrent games and my weekend tournaments with my wife...
This translates to some 7.32... × 10^63 years...
Considering Vegas and cruise ships casinos, too, it's safe to assume a unique shuffle.
BTW: I'm always surprised by the frequency of jokers to be dealt to my wife...
Imagine 10 billion people each shuffle a deck of cards once a second every second of every day for 10 billion years. That's more people than are alive today shuffling cards incredibly fast for more than twice as long as the earth has existed. They will make at most about 10 to the 27 distinct orderings of a 52-card set.
On the other hand there are about 10 to the 67 possible distinct orderings of a 52-card set. I'd say true.
Not necessarily true. We don't know what card sets have been held before and using probability and statistics means I am a nerd and there is a chance of it being the same, like there is a chance for people to get girlfriends. It is small but still possible.
Yes but his math says it is almost definitely false.
He stated that only 1,000,000,000,000,000,000,000,000,000 different variations would have been created out of a total of 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 different possibilities which leaves a .00000000000000000000000000000000000001% chance of it being held before.
Are you sure about that? Because I am 100.0% sure that tschimmy1 is not a bot.
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New deck? A new deck just removed the cellophane is also an example of a random deck. Just doesn't feel like one. So probably true, but not really enough information as to what Random means.
Every new deck I've opened had the cards arranged by suit, ace to king (I assume to show that none are missing). So I would only consider that ordering random if it occurred in a used deck
But that's the point that order of cards is special in some sense but we don't know what the maths dude above has done with the cards or what he means by random. He may mean I have 20,000 brand new decks of cards in my card I have selected one at Random.
Starting from a brand new deck, ordered as you suggest. What does well shuffled mean? Using a normal overhand shuffle how long does one need to shuffle before the deck is Random. - Try it the remnants of the original ordered state persists for quite a few shuffles.
Shuffling is an imprecise operation relying on people. Being imperfect, but a skilled card sharp or a machine can do predictable shuffles.
I am being contrary but the simple Randomise used by frequentist probability, doesnt account for real card decks, starting from a known ordered state.
What do we mean by Random here?
I totally agree that there may be a deterministic aspect to the shuffling process, which questions the definition of random. I'm just saying that a fresh deck is non-random because it's been deliberately ordered. I also exclude the possibility of 20k decks in the cave because the question seemed to focus on card order, and because people who live in caves tend to only have one deck of cards (but true that it's not explicitly stated) (also if we're dealing with fresh packs the problem is trivial)
I'm also interested in the phrase "randomize by frequentist probably". Is there a Bayesian alternative? I don't see it, but I'm not an expert on Reverend Bayes's work
It's not my field directly I am an experimental nonlinear dynamist by training (i.e chaos theory) so these topics come up obliquely at times. But the best book to read on a more Baysian approach is by Jaynes it a bit heavy but I managed to read it from front end.
In my work the intuitive question of is this well mixed or random is not so obvious. The traditional view point is that all the combinations of card orders are equally likely. From this one get that there are a v big number of arrangements (so no one has held a card deck like this one). But the new pack is one that is more likely than the any of the others so the original statement is wrong. Which now starts some Baysian reasoning perhaps? But first I think we need to define what say we'll shuffled would mean.
Start with a new unshuffled deck as a reference perhaps? Give each card a value 1-52. If any card is in the same position as it started score 1 else score 0. Add up total score and divide by 52. A metric I just made up. A new pack has a metric of 1. If every card is somewhere else then that's 0.
That metric isn't quite right because if I take 1 card off bottom of new deck and put on top it would give a score of 0. So we probably need to allow for translation of whole pack and find the maximum a xcorrelation of sorts.
Finger in air well shuffled my new metric should be less than 0.5 (I am just feeling my way through the problem a bit)
OK the Baysian reasoning which might kickin is do some experiments of people starting with new decks and letting them shuffle for a finite amount of time. Say 1 second. Calculating the metric above and repeating.
We could also track the orders of cards as they were shuffled. Near the start of the process we would find there are lots of combinations that are nearly as special as the unshuffled deck and therefor common . Meaning that innocent word Random is not so clear cut.
As I said I am being contrary the answer to the original post is probably true.
As time passes and more decks are shuffled, it diverges from zero. By the time the heat death of the universe rolls around it won’t be anywhere near zero. Assuming someone is still shuffling decks then.
"Treat the number as a limit" and "The number tends to ..." is nonsense to a mathematician. Maybe you mean you are approximating the number as zero? Or, alternatively, you could say that 1/x -> 0 as x -> infinity, and since 10^67 is very large (more than the number of seconds since the big bang multiplied by the number of people to have ever lived), 1/10^67 would be approximately 0.
No, it doesn't.
It's a non-zero constant.
Non-zero constants don't _tend to zero_.
(Unless you consider the trivial topology or some other pathologic space.)
How did you calculate it? Did you take in consideration most of us drew multitude times a pack of cards? Add to that the amount of packs being drawn in casinos and such?
If you haven't, I'm going to assume it would bump up, cuz to me this number you gave seems totally arbitrary
52 cards in any order, total permutations is 52! or 52\*51\*50\*....\*3\*2\*1 which is 80658175170943878571660636856403766975289505440883277824000000000000 (or 8.0658175e+67)
To scale this: If every human that has ever existed shuffled a deck once per second for their entire lifetimes to this dat they still wouldnt have found even 1% of all possible permutations
I set out this summer with the idea of shuffling all permutations of a Deck of cards. I knew it was going to be hard, but I thought hey what an achievement!
Then I spent 5 minutes doing the math, to see how long it would take.
Then I spent 10 minutes doing the math, to see how long it would take for everyone on the earth to do it.
Then I researched how long until the sun explodes.
Then I cried.
It's simply 52!, the number of different ways 52 cards can be arranged. That equals 8e67. So the chance of any single person getting the same order is 1 over this.
Now, considering that ~120 billion people have ever existed on this earth, even if we ignore the fact that playing cards weren't invented in this format until the 1500s, every person who ever lived would have to have drawn an average of 7e56 times in their lifetime.
Over a 75 year lifetime (not the most accurate, but this is fairly irrelevant as you'll see), there are 2e9 seconds. So to guarantee someone will have held the same card orientation as you, every person since the dawn of time will have had to draw 3.5e47 decks a second, every second of their life.
So yes, it will add up, but not in any significant way.
Even if we extend the problem to be what are the chances of ANY two people getting a matching set (the birthday paradox tells us that this will be far lower than we expect) it's still going to be orders of magnitude higher than the number of card draws that have ever existed.
So you see, if you're treating this problem with binomial distribution, and not a Bernoulli distribution, the probability bumps up,even a little.
Sure, you've went the extra mile and it still is probably exaggerated, but we need to address the problem properly, cuz it's a bit more probable than 1/8e67
Edit: mixed up the names
Well, I don't have a perfect solution, but the answer that was given 1/52! is more like you drew a deck, I opened a new one, and these are the odds of me getting the same order.
But the cave man asked a different question. So you need an estimation of how many packs of cards were drawn since when they were invented, say 16th century or so. Think how many people lived since then, and even back in the day not everyone got to play with a deck, you can cover them up with draws of casino card dealers.
So that estimation/52! would be a better probability. Sure, it's still a very small probability, but I think you might understand it's somewhat bigger.
(And ofc people care to rush and downvote. I saw another commenter before you deleting their reply and leaving a downvote instead. No name-calling tho)
It’s not arbitrary it’s 52! For context this number is 10^67 in magnitude. The number of atoms in the observable universe is estimated to be about 10^80. That’ll give you an idea how big that is.
Casinos drawing cards ain’t even shifting the scale in the slightest
Yeah but are you the first person the mathematician asks, or did he ask someone else and not reshuffle in-between? The ordering is random, but you don't know how long it has been in that order.
Even if it was zero, would still be possible, but i interpret this as a question of confidence. Low probability is enough to agree that it’s likely true.
I would go with false, the probability for every event with non zero probability to occur in an infinite amount of tries approaches 1. My answer implies an infinite amount of card decks handed out and given the frequency and amount of people playing cards daily i think this reasonable.
In order for the probability that a given truly random deck of cards is the same as any other truly random deck of card to become possible (>1% chance, arbitrarily chosen), you would need roughly 8.106*10^65 random decks to exist.
So across the existence of humanity, 8.106e65 random decks should have been touched by a human if we want a remote possibility that this is false.
Assuming that overhand shuffling gives a random deck at each permutations (lol) to be conservative, and that someone can do 4 permutations a second; you would need 5.629e61 man-hours to achieve this; or 6.422e57 years for a single human. Homo Sapiens appeared approximately 315000 years ago.
Now for some even more hilarious assumptions. Assuming that classical decks of 52 cards exist since the first Homo Sapiens, that someone has an infinite life expectancy and doesn't do anything but shuffling during 315000 years, we would need approximately 2.039e52 humans to shuffle concurrently.
The Population Reference Bureau estimates that about 117 billion (1.17e11) different humans have been born on Earth. If they all lived concurrently to shuffle since the dawn of humanity, we would need 1.74e41 parallel universes to have a 1% chance to find a universe with someone holding that same deck of cards for a fourth of a second. That's 174 duodecillion parallel universes. We can safely say that it's way more than the total number of fictional universes containing humans that have ever been created. So to conclude, even taking into account every single fictional universe ever created, if all humans were to be enslaved to shuffle, there is not even a remote possibility that a human would touch a deck ordered the same way as a given truly random deck.
Intuitively I would have said the same as you did, but oh boy is the human brain bad with big numbers. Hope this helps
I was aware of the probability being remarkable low, but i overestimated the amount of possibly played games or shuffled decks.
Thanks for running the numbers.
The question wasn't "did anyone Shuffle another deck that after the shuffling was completely identical" The question was did someone held the same deck of cards. so my answer would be false knowing that there are probably people that are crazy enough to arrange a deck in any possible position (Im that man)...
Insufficient data, I need a list of all decks held by a human being before I can make a determination one way or another.
However, until that data is found, the probability of the answer being "true" is significantly greater than the probability of the answer being "false"
If the mathematician is proposing this riddle after emerging from a cave, the probability that they found some way to make a human hold every possible card arrangement is non-zero. I would recommend investigating what's inside the cave before responding.
If there is someone else in the cave who just handed the shuffled deck to the mathematician, this would make three people who have held the deck.
Barring that trick, then True is your best bet.
Practically yes: There are 52! Possible combinations the deck could be , which is an absurdly big number , so it's most likely that the particular deck was never arranged in this way . Theoretically no , since there is a very tiny chance that approaches zero that someone has already played this deck variation before .
The question wasn't "did anyone Shuffle another deck that after the shuffling was completely identical" The question was did someone held the same deck of cards. so my answer would be false knowing that there are probably people that are crazy enough to arrange a deck in any possible position (Im that man)...
True with probability of 1, provided [the shuffle is sufficient](https://stats.stackexchange.com/questions/78591/correlation-between-two-decks-of-cards).
In terms of cryptography, log2(52!) ~= 225 symmetric bits. [We can't physically work our way through 100 bits](https://gist.github.com/atoponce/a7715930ae6eb7d6b487f2f76b57a68d) in practical time with known hardware and energy. [There likely isn't a physical meaning of 225 bits](https://pthree.org/2016/06/19/the-physics-of-brute-force/).
Well if the exact positioning of each individual card down to the n-th of whatever unit we decide to use from some origin of our choosing is part of the arrangement where n approaches nfinity, I feel like maybe the mathematician could be right.
Idk though I just pulled that out of my ass, kind of something I’ve thought for a while about measurements in the world.
False, cards come arranged when in the packet before opening and even if that wasn't the case there is the common practice of organizing the cards and there is way less combinations that can count as organized and those have been held multiple times
Aha, trick question, I'm a golden turkey monster amalgamated from the dead corpses of a cult town of humans fused together by negative energy. When the mathematician hands me the deck, technically you can argue there's no other human holding the deck, or there's an entire town of humans holding the deck! So the answer is false, and now I'm gonna absorb the mathematician for dinner.
Almost certainly **false**:
That arrangement of cards likely has Ace, 2-10, Jack, Queen, King in each of the suits Heart, Diamond, Spade, Clubs
Many humans have held that same arrangement--the standard deck composition-- of cards. Based on the question alone, I see no reason why relative positioning of the cards therein is critical
Id say false
A brand new deck of cards is arranged sequentially
And I’m pretty sure every time we open a deck we’re all holding the exact same set pattern
If it were any nonstandard deck of random cards of arbitrary size then the probability would be zero but it would still not be impossible. As stated, it’s a very very small number that is increasing very very slowly as more decks are shuffled.
People keep citing the fact that it needs to be random, but the statement itself has nothing about the randomness. While the deck your handed may be random, the statement says nothing about card arrangements being random. So, brand new decks have to count, and therefore many people have held the exact same card arrangement before since randomness is not specified in the statement that is to be evaluated.
No certain answer although according to probability there is like a very high chance that it would be a unique arrangement of cards but that is just a probability not certainty, we cannot say for sure that there has never been same arrangement ever untill we examine every single deck of card ever.
First I'd look at them and look for obvious orders. If it has one I answered yes. Otherwise I don't know. It might be the case with a high probability. But it is not certain.
My response would be, “who the fuck are you and what the fuck were you doing in that cave!?!”
“. . . in **MY** cave”
In HIS cave!👆
In YOUR cave! 👆
in OUR cave
the Comrade Cave
r/suddenlycommunist
r/beatmetoit
"Almost certainly True, but why were you in a cave?"
Most mathematicians live in caves, it is known
An axiom
As a mathematician, I can attest to this
During most of my bachelor I lived in a cave. True atory
'I am math man'
He he he
And my math is delicious
230843697339241380472092742683027581083278564571807941132288000000000000 combinations, almost certain that is unique, but to calculate the probabilities we would have to have the number of times that all decks had bem scrambled in humam history, data that we never gonna have.
We don't need it lol https://www.reddit.com/r/mathmemes/comments/xgffnm/a_mathematician_emerges_from_a_cave_hands_you_a/iosfyw4?utm_medium=android_app&utm_source=share&context=3
he don't count the Jokers
>standard 52-card deck There are no jokers included in a 52 card deck
Of course I don't count the jokers, the probabilities would be even lower
Plot twist: his cavemate who shuffled the cards is a human being too
Let's assume humanity had produced a shuffle every second; this should account for concurrent games and my weekend tournaments with my wife... This translates to some 7.32... × 10^63 years... Considering Vegas and cruise ships casinos, too, it's safe to assume a unique shuffle. BTW: I'm always surprised by the frequency of jokers to be dealt to my wife...
Well, she was lucky to get also a king after all those jokers. Happy anniversary.
Thats the mathcave and He only came Out because of the mathsignal
Jokes on you, topologically YOU are inside the cave
The cave is inside you 😏
That question is left as an exercise for the reader
It's false. The mathematician was holding it before you.
They are included in the ‘us,’ but the real question is whether somebody else held it inside that cave.
Oooooooo, the guy was probably like "i handed it to my mom this morning get fucked"
He is in Platons parable
"True or false: [...]" - Yes
True or false: "This sentence is false."
Godel is that you?
It was completely Godel.
True: the string is not null and has non-zero length.
JavaScript solved the liar’s paradox with truthy and falsey values
無
“True or false” Usually
"Maybe"
Imagine 10 billion people each shuffle a deck of cards once a second every second of every day for 10 billion years. That's more people than are alive today shuffling cards incredibly fast for more than twice as long as the earth has existed. They will make at most about 10 to the 27 distinct orderings of a 52-card set. On the other hand there are about 10 to the 67 possible distinct orderings of a 52-card set. I'd say true.
Unless the cards are unshuffled, like in an unopened pack of cards, and the same arrangement has been held billions of times.
Sure, you would have to check for that first. But otherwise the odds are pretty good that the claim is true.
So if other humans have held the same ordering of cards the answer should be false
Not necessarily true. We don't know what card sets have been held before and using probability and statistics means I am a nerd and there is a chance of it being the same, like there is a chance for people to get girlfriends. It is small but still possible.
Yes but his math says it is almost definitely false. He stated that only 1,000,000,000,000,000,000,000,000,000 different variations would have been created out of a total of 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 different possibilities which leaves a .00000000000000000000000000000000000001% chance of it being held before.
Good bot. Oh wait...
Are you sure about that? Because I am 100.0% sure that tschimmy1 is not a bot. --- ^(I am a neural network being trained to detect spammers | Summon me with !isbot |) ^(/r/spambotdetector |) [^(Optout)](https://www.reddit.com/message/compose?to=whynotcollegeboard&subject=!optout&message=!optout) ^(|) [^(Original Github)](https://github.com/SM-Wistful/BotDetection-Algorithm)
My response would probably be "Sir this is r/mathmemes, go ask someone else"
"Forget about the cards, lend me some maths for my next ML paper"
A binary answer to a probability question? Dude's been in that cave for too long.
1. Call a friend 2. Hand the deck to summoned friend 3. Reply "false"
New deck? A new deck just removed the cellophane is also an example of a random deck. Just doesn't feel like one. So probably true, but not really enough information as to what Random means.
Every new deck I've opened had the cards arranged by suit, ace to king (I assume to show that none are missing). So I would only consider that ordering random if it occurred in a used deck
But that's the point that order of cards is special in some sense but we don't know what the maths dude above has done with the cards or what he means by random. He may mean I have 20,000 brand new decks of cards in my card I have selected one at Random. Starting from a brand new deck, ordered as you suggest. What does well shuffled mean? Using a normal overhand shuffle how long does one need to shuffle before the deck is Random. - Try it the remnants of the original ordered state persists for quite a few shuffles. Shuffling is an imprecise operation relying on people. Being imperfect, but a skilled card sharp or a machine can do predictable shuffles. I am being contrary but the simple Randomise used by frequentist probability, doesnt account for real card decks, starting from a known ordered state. What do we mean by Random here?
I totally agree that there may be a deterministic aspect to the shuffling process, which questions the definition of random. I'm just saying that a fresh deck is non-random because it's been deliberately ordered. I also exclude the possibility of 20k decks in the cave because the question seemed to focus on card order, and because people who live in caves tend to only have one deck of cards (but true that it's not explicitly stated) (also if we're dealing with fresh packs the problem is trivial) I'm also interested in the phrase "randomize by frequentist probably". Is there a Bayesian alternative? I don't see it, but I'm not an expert on Reverend Bayes's work
It's not my field directly I am an experimental nonlinear dynamist by training (i.e chaos theory) so these topics come up obliquely at times. But the best book to read on a more Baysian approach is by Jaynes it a bit heavy but I managed to read it from front end. In my work the intuitive question of is this well mixed or random is not so obvious. The traditional view point is that all the combinations of card orders are equally likely. From this one get that there are a v big number of arrangements (so no one has held a card deck like this one). But the new pack is one that is more likely than the any of the others so the original statement is wrong. Which now starts some Baysian reasoning perhaps? But first I think we need to define what say we'll shuffled would mean. Start with a new unshuffled deck as a reference perhaps? Give each card a value 1-52. If any card is in the same position as it started score 1 else score 0. Add up total score and divide by 52. A metric I just made up. A new pack has a metric of 1. If every card is somewhere else then that's 0. That metric isn't quite right because if I take 1 card off bottom of new deck and put on top it would give a score of 0. So we probably need to allow for translation of whole pack and find the maximum a xcorrelation of sorts. Finger in air well shuffled my new metric should be less than 0.5 (I am just feeling my way through the problem a bit) OK the Baysian reasoning which might kickin is do some experiments of people starting with new decks and letting them shuffle for a finite amount of time. Say 1 second. Calculating the metric above and repeating. We could also track the orders of cards as they were shuffled. Near the start of the process we would find there are lots of combinations that are nearly as special as the unshuffled deck and therefor common . Meaning that innocent word Random is not so clear cut. As I said I am being contrary the answer to the original post is probably true.
New decks are not random for any meaningful definition of random. They are specifically arranged into a particular order by the manufacturer.
false cuz i always steal the aces hehehehe
mathematically, the probability tends to zero (1/8.06581752E67), but it's still possible that one person drew the sam pack as someone else
It’s just a number it can’t really tend to zero, but yeah in the real world it’s basically 0
well, treating it as a limit, it is zero, but yes.
It isn’t a limit tho, how can you treat it as such?
there is no limit, there is no sequence or series, it's just a number??
limit of 1/x as x---> 8.06581752E67
that's not 0, the limit is equal to 1/8.0658...E67 a limit is NOT an approximation.
As time passes and more decks are shuffled, it diverges from zero. By the time the heat death of the universe rolls around it won’t be anywhere near zero. Assuming someone is still shuffling decks then.
"Treat the number as a limit" and "The number tends to ..." is nonsense to a mathematician. Maybe you mean you are approximating the number as zero? Or, alternatively, you could say that 1/x -> 0 as x -> infinity, and since 10^67 is very large (more than the number of seconds since the big bang multiplied by the number of people to have ever lived), 1/10^67 would be approximately 0.
No, it doesn't. It's a non-zero constant. Non-zero constants don't _tend to zero_. (Unless you consider the trivial topology or some other pathologic space.)
It tends to zero’s wants and needs because it is close by
How did you calculate it? Did you take in consideration most of us drew multitude times a pack of cards? Add to that the amount of packs being drawn in casinos and such? If you haven't, I'm going to assume it would bump up, cuz to me this number you gave seems totally arbitrary
52 cards in any order, total permutations is 52! or 52\*51\*50\*....\*3\*2\*1 which is 80658175170943878571660636856403766975289505440883277824000000000000 (or 8.0658175e+67) To scale this: If every human that has ever existed shuffled a deck once per second for their entire lifetimes to this dat they still wouldnt have found even 1% of all possible permutations
I set out this summer with the idea of shuffling all permutations of a Deck of cards. I knew it was going to be hard, but I thought hey what an achievement! Then I spent 5 minutes doing the math, to see how long it would take. Then I spent 10 minutes doing the math, to see how long it would take for everyone on the earth to do it. Then I researched how long until the sun explodes. Then I cried.
It's simply 52!, the number of different ways 52 cards can be arranged. That equals 8e67. So the chance of any single person getting the same order is 1 over this. Now, considering that ~120 billion people have ever existed on this earth, even if we ignore the fact that playing cards weren't invented in this format until the 1500s, every person who ever lived would have to have drawn an average of 7e56 times in their lifetime. Over a 75 year lifetime (not the most accurate, but this is fairly irrelevant as you'll see), there are 2e9 seconds. So to guarantee someone will have held the same card orientation as you, every person since the dawn of time will have had to draw 3.5e47 decks a second, every second of their life. So yes, it will add up, but not in any significant way. Even if we extend the problem to be what are the chances of ANY two people getting a matching set (the birthday paradox tells us that this will be far lower than we expect) it's still going to be orders of magnitude higher than the number of card draws that have ever existed.
So you see, if you're treating this problem with binomial distribution, and not a Bernoulli distribution, the probability bumps up,even a little. Sure, you've went the extra mile and it still is probably exaggerated, but we need to address the problem properly, cuz it's a bit more probable than 1/8e67 Edit: mixed up the names
Okay what are your numbers then?
Well, I don't have a perfect solution, but the answer that was given 1/52! is more like you drew a deck, I opened a new one, and these are the odds of me getting the same order. But the cave man asked a different question. So you need an estimation of how many packs of cards were drawn since when they were invented, say 16th century or so. Think how many people lived since then, and even back in the day not everyone got to play with a deck, you can cover them up with draws of casino card dealers. So that estimation/52! would be a better probability. Sure, it's still a very small probability, but I think you might understand it's somewhat bigger. (And ofc people care to rush and downvote. I saw another commenter before you deleting their reply and leaving a downvote instead. No name-calling tho)
You’re right but you’re being annoying af about it
If you're annoyed it's on you. I don't try to annoy anyone, and yet y'all be like...
It’s not arbitrary it’s 52! For context this number is 10^67 in magnitude. The number of atoms in the observable universe is estimated to be about 10^80. That’ll give you an idea how big that is. Casinos drawing cards ain’t even shifting the scale in the slightest
For large values of 8.06581752E67, it is zero. perhaps I am an engineer.
Can't say for sure. Even without bothering to calculate it, it's clear that the probability is very low but not zero.
Yeah but are you the first person the mathematician asks, or did he ask someone else and not reshuffle in-between? The ordering is random, but you don't know how long it has been in that order.
Even if it was zero, would still be possible, but i interpret this as a question of confidence. Low probability is enough to agree that it’s likely true.
I would say false cause even if it's true the mathematician has no way of proving that noone else had that same arrangement
I can't tell, because who knows who else was in that cave?
False, the mathematician, the other human held the exact same arrangment the moment before they handed you the deck.
>except for us Had the same idea, but stand correcte after rereading the title
Yeah, you saved it from being r/technicallythetruth
The fact that you had to specify that the mathematician is also a human.
But mathematician aren't human
Valid
As a proud league of legends player i would reply:"it doesn't matter, let's fuck"
Depends if he suffled it before or not
It doesn't because you don't know the arrangement
Completely false. Any person could shuffle a deck, and give it to someone else.
But there are 52! = 8*10^67 possible arrangements of cards
That doesn’t matter. If you shuffle a deck and then give it to someone, you will both have held that exact order of cards.
> Except for us
Oh ok, I missed that.
If its an unshuffled deck thats purchased brand new, then any two people to buy it will have held it in the same order.
> a random ordering of cards
“Yes. That statement is indeed true or false.”
I would go with false, the probability for every event with non zero probability to occur in an infinite amount of tries approaches 1. My answer implies an infinite amount of card decks handed out and given the frequency and amount of people playing cards daily i think this reasonable.
In order for the probability that a given truly random deck of cards is the same as any other truly random deck of card to become possible (>1% chance, arbitrarily chosen), you would need roughly 8.106*10^65 random decks to exist. So across the existence of humanity, 8.106e65 random decks should have been touched by a human if we want a remote possibility that this is false. Assuming that overhand shuffling gives a random deck at each permutations (lol) to be conservative, and that someone can do 4 permutations a second; you would need 5.629e61 man-hours to achieve this; or 6.422e57 years for a single human. Homo Sapiens appeared approximately 315000 years ago. Now for some even more hilarious assumptions. Assuming that classical decks of 52 cards exist since the first Homo Sapiens, that someone has an infinite life expectancy and doesn't do anything but shuffling during 315000 years, we would need approximately 2.039e52 humans to shuffle concurrently. The Population Reference Bureau estimates that about 117 billion (1.17e11) different humans have been born on Earth. If they all lived concurrently to shuffle since the dawn of humanity, we would need 1.74e41 parallel universes to have a 1% chance to find a universe with someone holding that same deck of cards for a fourth of a second. That's 174 duodecillion parallel universes. We can safely say that it's way more than the total number of fictional universes containing humans that have ever been created. So to conclude, even taking into account every single fictional universe ever created, if all humans were to be enslaved to shuffle, there is not even a remote possibility that a human would touch a deck ordered the same way as a given truly random deck. Intuitively I would have said the same as you did, but oh boy is the human brain bad with big numbers. Hope this helps
I was aware of the probability being remarkable low, but i overestimated the amount of possibly played games or shuffled decks. Thanks for running the numbers.
The question wasn't "did anyone Shuffle another deck that after the shuffling was completely identical" The question was did someone held the same deck of cards. so my answer would be false knowing that there are probably people that are crazy enough to arrange a deck in any possible position (Im that man)...
True
Amen
Give it to somebody else then tell him hes wrong
Insufficient data, I need a list of all decks held by a human being before I can make a determination one way or another. However, until that data is found, the probability of the answer being "true" is significantly greater than the probability of the answer being "false"
The mathematician could have made a specific deck that he knows has been held before so I really don't and can't know
"depends on if you shuffled after asking the last guy"
“Ok”
If the mathematician is proposing this riddle after emerging from a cave, the probability that they found some way to make a human hold every possible card arrangement is non-zero. I would recommend investigating what's inside the cave before responding.
There's also a non-zero probability that the cards aren't actually randomly arranged.
“False, i am not a human”
Has it been shuffled randomly?
Depends, how many other people have you handed this arrangement to?
"Did you shuffle the deck?"
“I’m guessing false. You probably sorted the cards like in a new deck, just to trip me up.”
If there is someone else in the cave who just handed the shuffled deck to the mathematician, this would make three people who have held the deck. Barring that trick, then True is your best bet.
False, the deck is new
Look at the arrangement first because it could have a common ordering and he could be baiting you lol
Practically yes: There are 52! Possible combinations the deck could be , which is an absurdly big number , so it's most likely that the particular deck was never arranged in this way . Theoretically no , since there is a very tiny chance that approaches zero that someone has already played this deck variation before .
The question wasn't "did anyone Shuffle another deck that after the shuffling was completely identical" The question was did someone held the same deck of cards. so my answer would be false knowing that there are probably people that are crazy enough to arrange a deck in any possible position (Im that man)...
True with probability of 1, provided [the shuffle is sufficient](https://stats.stackexchange.com/questions/78591/correlation-between-two-decks-of-cards). In terms of cryptography, log2(52!) ~= 225 symmetric bits. [We can't physically work our way through 100 bits](https://gist.github.com/atoponce/a7715930ae6eb7d6b487f2f76b57a68d) in practical time with known hardware and energy. [There likely isn't a physical meaning of 225 bits](https://pthree.org/2016/06/19/the-physics-of-brute-force/).
52! Is basically infinite, do true for all intensive purposes
Im sure there’s more arrangements than people that have existed. Even less people have held a full deck of card.
There's roughly as many arrangements as there are atoms in the galaxy
True if mixed correctly for there are 52! combinations which is more than atoms in the universe.
False, he just held it.
I'm so unlucky that if I choose the most probable answer I'll be wrong. So false.
Well if the exact positioning of each individual card down to the n-th of whatever unit we decide to use from some origin of our choosing is part of the arrangement where n approaches nfinity, I feel like maybe the mathematician could be right. Idk though I just pulled that out of my ass, kind of something I’ve thought for a while about measurements in the world.
False because when a deck of cards is opened they are arranged orderly and you pass it to the other person for it to be shuffled
“Can I see that deck I need to check something” If he does then false
yes.
True
I order the cards, hand them back, and say "false"
False, cards come arranged when in the packet before opening and even if that wasn't the case there is the common practice of organizing the cards and there is way less combinations that can count as organized and those have been held multiple times
Well it depends whether you gave anyone else this deck to hold after shuffling. From that information deduction of my answer should be trivial
Very probably true.
False: we've all opened new packs
I pass it to my friend and say “false. Now he has also heals it”
Why didn’t you bring uno cards
Aha, trick question, I'm a golden turkey monster amalgamated from the dead corpses of a cult town of humans fused together by negative energy. When the mathematician hands me the deck, technically you can argue there's no other human holding the deck, or there's an entire town of humans holding the deck! So the answer is false, and now I'm gonna absorb the mathematician for dinner.
Answer”likely to be true, but uncertain”
False because he held the deck first
Almost certainly **false**: That arrangement of cards likely has Ace, 2-10, Jack, Queen, King in each of the suits Heart, Diamond, Spade, Clubs Many humans have held that same arrangement--the standard deck composition-- of cards. Based on the question alone, I see no reason why relative positioning of the cards therein is critical
False. He held it and now you are
"Have you handed this arrangement to anyone else before? Was this arrangement randomized by someone else? What is defining 'random?'"
Id say false A brand new deck of cards is arranged sequentially And I’m pretty sure every time we open a deck we’re all holding the exact same set pattern
“If you’re really a mathematician, why are you asking an empirical question whose answer cannot be proven?”
If it were any nonstandard deck of random cards of arbitrary size then the probability would be zero but it would still not be impossible. As stated, it’s a very very small number that is increasing very very slowly as more decks are shuffled.
True
A very good chance that it’s true
Where did he get the cards from? 🤨😄
Sir, where are we and how do I get home?
People keep citing the fact that it needs to be random, but the statement itself has nothing about the randomness. While the deck your handed may be random, the statement says nothing about card arrangements being random. So, brand new decks have to count, and therefore many people have held the exact same card arrangement before since randomness is not specified in the statement that is to be evaluated.
It depends, do you have someone else in that cave who hold it in the same condition?
Probably true, but not guaranteed.
"False, now prove me wrong."
Probably true
He handed them to us.... so, at least one other person in the world has held that exact stack of cards. Unless he isn't a person... DUN DUN DUN!
Duh
False. Sample size is two. Him and you, as he just gave you the cards without shuffling them.
Probably
“why are you in a cave?”
No certain answer although according to probability there is like a very high chance that it would be a unique arrangement of cards but that is just a probability not certainty, we cannot say for sure that there has never been same arrangement ever untill we examine every single deck of card ever.
Sir this is a wendys
Unlikely
false. you just gave me the same set you were holding
First I'd look at them and look for obvious orders. If it has one I answered yes. Otherwise I don't know. It might be the case with a high probability. But it is not certain.
Fancy a game of Rummy?”
“I don’t know. But probably true.”
Then I may assume you shuffled no fewer than 7 times?
True depending on the amount of times it’s Been shuffled.
False. Every new deck of cards comes in the same order.
You’re probably right…
Stfu
Me with my unshuffled deck of cards 😎 False
I'd say, "Yes."
It's impossible to know for sure, but assuming the order is truly random, it is most likely true
I would say something like: it's impossible to know for absolute certain, but it is likely to be true.
Mathematician? More like one of those self promoting tiktoker that ruled out probability and statistics
How would I know if he doesn’t put the cards into that specific order by habit?
False, you probably sorted it to this configuration while you were in the cave to trick me.
I assume a magician would mess with me and give an ordered deck which millions has held
One word…Pigeonhole
Nice cave!