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Probability for card shuffles

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  • 28 Jul 2022 9:04 AM
    Reply # 12864694 on 12863509

    I started trying to calculate this by working out the chance that each successive card does not match the previous, but ran out of patience. I think this should work. Anway, questions similar to this have caused some heated discussion it seems:  

    https://math.stackexchange.com/questions/2975602/in-a-shuffled-deck-are-the-probabilities-of-finding-one-pair-of-cards-and-a-sec


    Last modified: 28 Jul 2022 9:06 AM | Chris Lloyd
  • 27 Jul 2022 12:06 PM
    Message # 12863509

    Hi all!

    I'm working on a project where I'm wanting to find exact probabilities for events in regards to a shuffled deck of cards.  

    As the number of possible shuffles is so high, an analysis of a sample doesn't seem to be nearly accurate enough.  This seems like a simple task, but I just can't get my head around it!!

    So the question is this; if I were to shuffle a deck of cards properly, and then lay the cards out in the order in which they've been shuffled, what is the probability that two sequential cards would form a "pair"?  What are the chances of two "pairs" appearing anywhere in the shuffle?


    Thanks in advance!

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