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Math Help - Dice game formula

  1. #1
    Newbie
    Joined
    Sep 2010
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    2

    Dice game formula

    There is a game in wich you roll a number of ten sided dice and look for matches, a match is when two or more dice turn up the same number, well I have this table:

    Dice pool
    Chance of getting one or more matches
    1
    0,00%
    2
    10,00%
    3
    28,00%
    4
    50,00%
    5
    70,00%
    6
    85,00%
    7
    93,00%
    8
    98,00%
    9
    99,60%
    10
    99'9%

    But I'm looking for the general formula that shows the chance of getting matches with n dice.
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  2. #2
    MHF Contributor
    Joined
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    P(some matches) = 1 - P(no matches)

    P(\text{no matches from n rolls}) = \frac{10!}{(10-n)!10^n}

    P(some matches) = 1 - \frac{10!}{(10-n)!10^n}

    with the understanding that the probability is 1 if n>10.


    The above formula seems to match your figures fairly closely (i checked 3 of them), hopefully differences are due to rounding and not a mistake
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