Assumptions are that all dice are fair, and each is numbered 1 through X where X is the
number of die faces for all dice. The generating function used is based on Dr Math and also Wolfram

The program finds cumulative probabilities for a portion of a distribution which
is centered laterally on the mean. A cumulative p of 0.52 means that 52% of the time dice sums in the (red) range will occur. Individual outcome probabilities are displayed at the upper left. Due to the
perfect symmetry of all distributions, this probability also applies to its mirror image. For example,
the p of sum 16 is identical to the p of sum 12 for the default distribution.

Current settings are displayed in the form 'NDX'. The default is 4D6 (four six-sided dice).

Note that the mean is not a whole number when N is odd and X is even. For 5D6 the mean
is 17.5

Here are links to my other work recurse
and dicecomp