I asked a question about some dice probability a while back for a hobby of mine, and was greatly helped by an introduction to Binomial Distribution (https://math.stackexchange.com/a/2355623?noredirect=1). However, I'm hoping to change up my system a little bit.
So I'm trying to find the probability of getting Y successes using X dice, where the probablilty of a success is 1/3 (a 4 or a 5); I already have equations set up for this. What I'd also like to find out is how having a 6 be worth 2 successes would work out (along with 4 and 5 being worth 1 success). Ideally I'd like to know if there's any way to incorporate this into excel where the majority of my data is already.
To sum up: Proability of getting Y in X trials, with a 1/3 chance of getting 1 success, and a 1/6 chance of 2 successes.