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    Secret santa problem




    Hi everybody

    At my work we just started a secret santa game. We are 6 and we ended up getting an outsider to mix 6 pieces of paper, each with one name written on it, to hand them out to us, making sure nobody got their own name. Afterwards we started wondering, if we would've just each picked one piece of paper out of a hat - how likely would it be that someone would've picked the piece of paper with his own name written on it?

    At first I just thought that the likelihood of not picking your own name was 5/6 so it was (5/6)^6 but then I quickly realised I was wrong. I proceeded trying to work with Bayes theroem trying to adapt the problem to it but I couldn't work it out - not sure if I was even on the right path with choosing it to try out. Now this is just annoying me and I was wondering if anyone has the answer to the problem?

    Best regards,
    Haraldur Hugosson

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    Re: Secret santa problem

    This is a fairly well known problem but the name is eluding me at the moment. Your specific case works out to be a probability of 53/144 (about 36.8%) that nobody would pick their own name. It's also interesting that as you increase the number of people picking the probability of nobody getting their own name goes to \frac{1}{e} in the limit
    I don't have emotions and sometimes that makes me very sad.

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    Hugosson (11-28-2014)

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    Re: Secret santa problem


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    Hugosson (11-28-2014)

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    Re: Secret santa problem

    This is an example of the (popular) so-called "Matching Problem."

    See here as well: http://www.math.uah.edu/stat/urn/Matching.html

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    Hugosson (11-28-2014)

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    Re: Secret santa problem

    Thank you for your help

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    Re: Secret santa problem


    I really enjoyed this puzzle. I found the following expansion:
    http://probabilityandstats.wordpress...ching-problem/
    The author shows the development for exactly k matches, etc.

    Art

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