I threw together a Google Sheet which did the calculations for a given dice pool. For each round, I calculate the probability that you've hit zero, one, two, etc. dice on that round, based on the probabilities for the previous round. I ran it out to 100 rounds, which seemed good enough.Those match what I got for 6 and 10. What did you use to get them? (I'm going to feel silly if I did matrix stuff for nothing ).

The probability formula involved is ugly. Your code looks a whole lot cleaner -- I'm not a statistician, I just play one on the Internet.