4 Comments to “Testing the “Duplicated Shuffle” Odds in SQL Server”

  1. Jim Nelson

    Jan 6th, 2014

    I did not see a reference to where the number 3×10^14 game from. That is an unspeakably large number itself, and I don’t believe it.

    If there have been a billion people in the history of the world ever to shuffle a deck of cards (I doubt it), that would be 300,000 shuffles each. I have not done my part!

    That being said, I could be convinced.

  2. Eric

    Jan 6th, 2014

    Hi Jim, thanks for commenting. Check out that first link (http://math.stackexchange.com/questions/671/when-you-randomly-shuffle-a-deck-of-cards-what-is-the-probability-that-it-is-a). They’re even overinflating that number to make the odds as large as possible, and they’re still infinitely small. Here are their assumptions:

    * Playing cards in their current state have been around for approximately eight centuries
    * A deck of playing cards is shuffled to a random configuration one billion times per day
    * Every shuffle ever is completely (theoretically) random and unaffected by biases caused by human shuffling and the games the cards are used for

  3. Jim Nelson

    Jan 6th, 2014

    OK, that makes a lot more sense. Surely back in the 14th century there were a billion shiffles a day.

    I certainly understand the concept of overinflating the number of possible historical shuffles to demonstrate that even so the odds are still infinitesimally small. Nonetheless, I always like it when some huge number is pulled out of the air like that.

  4. Jim Nelson

    Jan 7th, 2014

    Any discussion of the number of unique hands that can be dealt (thinking of 4 hands of 13 cards each, such as when playing bridge)?

    Per wikipedia, the number of unique bridge deals is still 5.36 * 10 ^ 28 — still so large that the probability of a duplicate is essentially zero.


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