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Take a normal deck of cards, 52 cards in total, and shuffle it. Now look through the order of the cards (e.g. King of spades, 2 of diamonds, 6 of clubs and so on...).
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This order of cards has never, ever been seen before. It has never existed before. You are almost certainly the first human being to have ever held a deck of cards in this order. All the casinos, all the home poker games, all the magician tricks, every place where a deck has been shuffled in all of human history has never resulted in this order of a deck of cards.
+ Show Spoiler +From reddit, "There are 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 in a deck of cards." You do the math of possible shuffles made so far in human history and you'll see it's almost certain that any shuffle you make will result in a completely new, never-before-seen order of cards. http://www.reddit.com/r/AskReddit/comments/jmz7n/what_is_your_favourite_holy_shit_fact_ill_go_first/c2dfxu8edit: If we assume that there have been 1000 shuffles every second for the past thousand years, and that every one of those shuffles has been unique (most generous scenario), then there have been 3.1556926 × 10^13 distinct deck orders created so far. From the reddit source, there are about 8.1x10^67 possible deck orders.
That means there are about 0.25x10^55 as many "never before seen" deck orders as there are already seen deck orders. So you are 0.25x10^55:1 to actually shuffle a deck the same way as someone else has before, or some machine has before.
That's probably about the same odds as winning a one-in-one-billion lottery about 5-6 times in a row.
For those interested in more mind-blowers, see http://www.reddit.com/r/AskReddit/comments/jmz7n/what_is_your_favourite_holy_shit_fact_ill_go_first/
Bonus:
+ Show Spoiler +The Amazon river is approximately 7000 km long. The number of bridges spanning it: zero." (again from reddit)
edit: Apparently a bridge crossing the Amazon was finished last year. So now it's one bridge. (http://www.guardian.co.uk/environment/2010/jul/29/manaus-bridge-amazon-rainforest)
 
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While definitely interesting, it is a bit flawed. That many possibilities does not directly equate to "no one has ever seen this order of cards before".
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You know, the most amazing thing happened to me tonight. I was coming here, on the way to the lecture, and I came in through the parking lot. And you won't believe what happened. I saw a car with the license plate ARW 357. Can you imagine? Of all the millions of license plates in the state, what was the chance that I would see that particular one tonight? Amazing!
- Richard Feynman
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On August 19 2011 13:39 RANDOMCL wrote:
While definitely interesting, it is a bit flawed. That many possibilities does not directly equate to "no one has ever seen this order of cards before".
Only 99.9999999999999999999999% chance or so.
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Actually, a more interesting question is how many cards you have to look through before you are 99% certain that this order has never occurred before. I'd guess it's within the first 5-10 cards.
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On August 19 2011 13:39 RANDOMCL wrote:
While definitely interesting, it is a bit flawed. That many possibilities does not directly equate to "no one has ever seen this order of cards before".
It effectively does, though. Say people have seen 10^15 different orders, which seems like a huge overestimate. Your order has never been seen with probability (# of total orders - 10^15)/# of total orders, which is sooooooooooo close to 1. It starts with more than 50 9's! That's so many 9's!
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That is neat it is amazing what you can do with numbers. Cards are probably the best items to use a counting system on.
+ Show Spoiler [Astounding but not as good as OP's] +Here is another astounding thing I have found out recently. I cannot unsee it now. Here is the portion of the Fedex logo you never really see but subconsciously you see. I might have just been really slow. ![[image loading]](http://i.imgur.com/oo1nH.gif) ![[image loading]](http://i.imgur.com/ZYEwp.gif)
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pretty interesting. never thought about it before but now I know!
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If we assume that there have been 1000 shuffles every second for the past thousand years, and that every one of those shuffles has been unique (most generous scenario), then there have been 3.1556926 × 10^13 distinct deck orders created so far. From the reddit source, there are about 8.1x10^67 possible deck orders.
That means there are about 0.25x10^55 as many "never before seen" deck orders as there are already seen deck orders. So you are 0.25x10^55:1 to actually shuffle a deck the same way as someone else has before, or some machine has before.
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On August 19 2011 13:41 Ryalnos wrote:
You know, the most amazing thing happened to me tonight. I was coming here, on the way to the lecture, and I came in through the parking lot. And you won't believe what happened. I saw a car with the license plate ARW 357. Can you imagine? Of all the millions of license plates in the state, what was the chance that I would see that particular one tonight? Amazing!
- Richard Feynman
How I feel about birthdays/anniversaries:
When some significant event happened, the Earth is in roughly the same position in its orbit around the Sun as it is today. Let's celebrate!
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On August 19 2011 13:47 Kralic wrote:That is neat it is amazing what you can do with numbers. Cards are probably the best items to use a counting system on. + Show Spoiler +Here is another astounding thing I have found out recently. I cannot unsee it now. Here is the portion of the Fedex logo you never really see but subconsciously you see. I might have just been really slow.
I remember the first time I saw this, it blew my mind. And it cannot be unseen.
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On August 19 2011 13:47 Kralic wrote:That is neat it is amazing what you can do with numbers. Cards are probably the best items to use a counting system on. + Show Spoiler [Astounding but not as good as OP's] +Here is another astounding thing I have found out recently. I cannot unsee it now. Here is the portion of the Fedex logo you never really see but subconsciously you see. I might have just been really slow.
I literally just screamed out loud.
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Here's a different look at it:
Take that same pack of cards and completely reshuffle them.
The likelihood that they are in the same sequence is exactly the same as the likelihood they are in any other specific sequence.
Or in other words, you are no more likely to get a specific different sequence of cards than you are to get the same.
Weird, but oddly logical 
See "Rosancrantz and Guildenstern are Dead" for a very nice example of this.
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United States24483 Posts
This isn't surprising to me, although another aspect of this to consider is that decks are often re-organized... so the first shuffle or two after that is much more likely to be similar to another shuffle. If you shuffled a deck of cards rather randomly for four hours then sure... you aren't getting another shuffle like that in the foreseeable future.
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On August 19 2011 14:10 micronesia wrote:
This isn't surprising to me, although another aspect of this to consider is that decks are often re-organized... so the first shuffle or two after that is much more likely to be similar to another shuffle. If you shuffled a deck of cards rather randomly for four hours then sure... you aren't getting another shuffle like that in the foreseeable future.
True. Someone on reddit said it was calculated that it took 9 or so shuffles to be pretty much certain that a brand new deck was random/never before seen. I don't know how he defined "shuffle" or "pretty much certain" though.
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On August 19 2011 13:55 GreEny K wrote:Show nested quote +On August 19 2011 13:47 Kralic wrote:That is neat it is amazing what you can do with numbers. Cards are probably the best items to use a counting system on. + Show Spoiler +Here is another astounding thing I have found out recently. I cannot unsee it now. Here is the portion of the Fedex logo you never really see but subconsciously you see. I might have just been really slow. I remember the first time I saw this, it blew my mind. And it cannot be unseen.
What am I supposed to be seeing? I don't notice anything weird, and the text inside the spoiler confuses me.
OT: That's pretty cool, OP! :p
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United States24483 Posts
On August 19 2011 14:16 cz wrote:Show nested quote +On August 19 2011 14:10 micronesia wrote:
This isn't surprising to me, although another aspect of this to consider is that decks are often re-organized... so the first shuffle or two after that is much more likely to be similar to another shuffle. If you shuffled a deck of cards rather randomly for four hours then sure... you aren't getting another shuffle like that in the foreseeable future. True. Someone on reddit said it was calculated that it took 9 or so shuffles to be pretty much certain that a brand new deck was random/never before seen. I don't know how he defined "shuffle" or "pretty much certain" though.
Depending on how you shuffle the deck you might not be randomizing it much at all. If you just weave the two decks together one card at a time then you get a fully predictable pattern :p
BTW the number of shuffle to create a random situation is pretty much arbitrary just like saying the number of times you need to flip a coin to be pretty much sure that you'll see tails at least once.
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On August 19 2011 14:20 micronesia wrote:Show nested quote +On August 19 2011 14:16 cz wrote:On August 19 2011 14:10 micronesia wrote:
This isn't surprising to me, although another aspect of this to consider is that decks are often re-organized... so the first shuffle or two after that is much more likely to be similar to another shuffle. If you shuffled a deck of cards rather randomly for four hours then sure... you aren't getting another shuffle like that in the foreseeable future. True. Someone on reddit said it was calculated that it took 9 or so shuffles to be pretty much certain that a brand new deck was random/never before seen. I don't know how he defined "shuffle" or "pretty much certain" though. Depending on how you shuffle the deck you might not be randomizing it much at all. If you just weave the two decks together one card at a time then you get a fully predictable pattern :p BTW the number of shuffle to create a random situation is pretty much arbitrary just like saying the number of times you need to flip a coin to be pretty much sure that you'll see tails at least once.
Right, but if you define "shuffle" and the number of shuffles you can have a confidence interval for how likely this is to be a unique deck order. Same thing with the coinflip: you create a confidence interval which is mathematically correct given the premises (50/50 chance of head or tails). That doesn't tell you how it will end, but give a big enough sample and it is true. For a deck of cards though, even a crappy shuffle is going to rapidly reach a 99.9999999999999% confidence interval for a new order, just because you have 52 cards instead of a 50/50 coinflip.
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On August 19 2011 14:18 Mr. Wiggles wrote:Show nested quote +On August 19 2011 13:55 GreEny K wrote:On August 19 2011 13:47 Kralic wrote:That is neat it is amazing what you can do with numbers. Cards are probably the best items to use a counting system on. + Show Spoiler +Here is another astounding thing I have found out recently. I cannot unsee it now. Here is the portion of the Fedex logo you never really see but subconsciously you see. I might have just been really slow. I remember the first time I saw this, it blew my mind. And it cannot be unseen. What am I supposed to be seeing? I don't notice anything weird, and the text inside the spoiler confuses me. OT: That's pretty cool, OP! :p
It's an outlined arrow, dude!!! MIND BLOWN :O
Also, that's an interesting point...I think new decks are almost always arranged in the same order, so we may in fact see versions that have been seen before unless we shuffle a substantial number of times.
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EPT
