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Math Help - Probability of roll X or greater on Y Dice.

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    Probability of roll X or greater on Y Dice.

    I want to make sure my analysis of the problem thus far is correct. I'm just learning about integer partitions so I am not sure exactly how to calculate the function I define as G(x).

    Assume that  P(x,y) is the probality of rolling exactly X on Y Dice.
    This should be:
    P(x,y)=\frac{\binom{x-1}{y}-G(x)}{6^Y}
    where:
    G(x) is the number of partitions of X that include Y members and at least 1 member over 6.

    The probability of rolling X or greater on Y dice is then:
    \sum_{i=x}^{6^y} P(x,y).

    Calculating G(x):
    Define part(n,k) to be the number of partitions of n each of whose member is \geq k. This is equivalent to the partitions of n which have at least k members.

    part(n,k) = 0\ for\ k>n
    part(n,k) = 1\ for\ k=n
    part(n,k) = part(n,k+1)+part(n-k,k)
    part(n,1) = all the possible partitions of n

    So
    part(x,y) -part(x,y-1) should be the all the ways I can partition X into exactly Y parts. However this could include members whose vlaue > 6.
    (Also is the above just equal to \binom{x-1}{Y}
    Or does the above imply that every member is also at least Y? (which is not at all what i want.)

    I'm not sure at this point how to weed out the partitions that include invalid dice rolls?
    Last edited by takatok; November 14th 2011 at 05:36 PM.
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