I'm trying to find a general method for working out the probability of a score from rolling several dice with varying sides.
For example, the probability of getting a result of 12 when rolling two six-sided dice and three 100-sided dice.
I'm a programmer looking to use this formula for a function, so please be gentle. Thanks!
On
Try to manipulate a generating function that represent the dice that you want following the example on this link.
For your example the generating function will be
$$f(x)=(x+x^2+\cdots+x^{D_\alpha})^{n_\alpha}\cdot(x+x^2+\cdots+x^{D_\beta})^{n_\beta}\cdots(x+x^2+\cdots+x^{D_\omega})^{n_\omega}$$
where $D_i$ is the number of sides of the dice and $n_i$ is the number of dice of each type rolled. This is for homogeneous and fair dice from 1 to D, for other type of dice you must change the function.
I found a solution to this specific problem by treating each dice roll as a one-dimensional array containing the probability distribution, and then convolving the arrays into a single distribution.
I've uploaded a demonstration here.