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Thread: un-shuffling a deck of cardsall

  1. #1

    un-shuffling a deck of cardsall

    Lets say you buy a brand new deck of cards. all of the cards are in order when you buy them by suit. if you shuffle them 3 times using any shuffling method. do you think its ever possible to if you kept shuffling to get it back to its original state as it was when you first opened it?
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  3. #3
    entropy -- the tendency of a closed system to descend into chaos.

    the law of entropy -- (second law of thermodynamics) -- all closed systems will move from a state of relative 'order' to a state of relative 'disorder' over time. this is a one-way street.

    (It's. The. Law).

    so : it's HIGHLY unlikely , that the cards would ever find themselves back in their original configuration.

    theoretically possible? yes. statistically probable? No. not in a million years.

    Statistical mechanics demonstrates that entropy is governed by probability, thus allowing for a decrease in disorder even in an isolated system. Although this is possible, such an event has a small probability of occurring, making it unlikely
    https://en.wikipedia.org/wiki/Entropy

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    Last edited by Cobalt60; 11-19-2017 at 05:53 PM.
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  4. #4
    High Admiral Sizzzler's Avatar
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    I'm not sure what the shuffling them 3 times by any method is suggesting, but with 52 cards in a deck, isn't that 52! (factorial) for the number of combinations there can be? If you want to assume that once you reach a combination, it can't occur again, then it should take no more than 52! for each combo to occur. Thus if you start with one combo in mind (the first one) that's the most it should take to come up again.
    Of course, there isn't anything stopping duplicate combinations from occurring, so it could be much more than that.

    By the way, I saw this online when trying to find the number fully written out:
    So how many ways can you order all the 52 cards in a pack?

    The sum is 52x51x50x49x48....x4x3x2x1 and the answer is:
    80,658,175,170,943,878,571,660,636, 856,403,766,975,289,505,440, 883,277,824,000,000,000,000

    That's roughly the same as an 8 with 67 zeros after it.
    To put this in perspective, the dinosaurs died out 65,000,000 years ago, and the age of the earth is just 4,500,000,000 years. Now suppose everybody in the world was to arrange packs of cards at the rate of one per second, it would take 600,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000,000 years to get all the combinations! That's why you're VERY unlikely ever to shuffle a pack of cards the same way twice.

    http://www.murderousmaths.co.uk/cardperms.htm

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    Last edited by Sizzzler; 11-20-2017 at 12:27 AM.
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  5. #5
    Grand Moff Utinniii's Avatar
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    It might also depend if one shuffles them face up or not.

  6. #6
    Quote Originally Posted by lumat View Post
    Lets say you buy a brand new deck of cards. all of the cards are in order when you buy them by suit. if you shuffle them 3 times using any shuffling method. do you think its ever possible to if you kept shuffling to get it back to its original state as it was when you first opened it?
    To get back to its "original state," i.e. brand new? No. To get back to the original order? Yes, assuming that the entropy Cobalt sighted hasn't first caused the cards to disintegrate.
    Last edited by mousedroid; 11-21-2017 at 10:05 AM.
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  7. #7
    ^^ ..and that would happen. after 80X10*67 tries, the cards would be "dust". cheers.
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  8. #8
    You forgot to put supposedly died out and roughly 65,000,000 years ago.
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  9. #9
    High Admiral Sizzzler's Avatar
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    No, you forgot to read. As I wrote, I saw that online. If anyone forgot anything it was the one who wrote it out in the first place. I merely posted something I saw.
    Last edited by Sizzzler; 11-21-2017 at 08:03 PM.
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