I'm trying to figure out a good closed form solution for a problem which I have already simulated and have a rough answer to. The problem is basically rolling 9 dice- each of different face numbers- and seeing the odds of >= a certain sum. This specific example has 55, 28, and 14 sided dice, 3 each. So I roll
3 dice with 55 sides 3 dice with 28 sides 3 dice with 14 sides
and I want to know the odds that the sum is >180
I'm seeing some results for how to calculate the odds of a specific sum online. I'm also seeing the odds of a bracket of options cenetered around the mean, but I don't want a bracket centered around the mean. I want the entire right section of the bell curve.