What is the probability of getting 800+ with 10, 100 sided dice?
Pdq is right, it’s not so simple. This is a multinomial distribution (the more general form of the more commonly seen binomial distribution). However, I’m not going to solve it using the multinomial PGF. I think this can be solved using compositions. We’ll add the number of 9-compositions and 10-compositions of every number from 800 to 1000, with 100 being the maximum summand. Then we’ll add 1 (rolling 8 100’s). Then we’ll divide that by 100^10. Unfortunately, I don’t know how to calculate k-compositions when there is a maximum summand. There is an online composition calculator that can do it, but I’d rather not use that calculator the required 400 times. Looking at the source code of that page, there doesn’t seem to be a closed-form solution, the algorithm is recursive. So what I’ll do use the code to compile my own composition calculator, so that I can then tell it to compute all 400 values in one go. Then I’ll come back and give the exact answer. As for an approximate answer, I made
