I keep thinking it's important that I write up a post explaining the multinomial distribution and how it's related to rolling dice since I've relied on it for several results now and rolling dice is the fundamental random process of D&D. I've sat down and tried to write it up three times now, and every time I do it, it ends up becomming a fairly involved project and I'm not sure I ended up clarifying anything. The first time I started, I ended up finding that I'd really just described the binomial distribution and hadn't illuminated the multinomial distribution at all. The second time I started to show how the multinomial distribution was a generalization of the binomial distribution and decided I wasn't clear enough. The third time I tried some combination of both approaches and just ended up being more long winded. The whole exercise has done nothing but reveal to me why there's so many lousy statistics books out there. It's actually pretty difficult to be clear. I also think the case of rolling dice is particularly difficult compared to say, coin flips.
None the less, I feel I have to tackle the problem if I'm going to keep explaining my thinking about tactics and decisions in D&D.