There are loads of ways to tinker. If you want to run it for kids, use d6s and suddenly it feels like a light-hearted and easy game (significantly easier to get successes with smaller dice pools).

The math is hardly impossible, but at least for d10, someone else has done the math. https://www.darkshire.net/~jhkim/rpg/nemesis/probability.html

I used to have a better link where someone had a graph that gave a better sense of width likelihoods. Long story short, the curve is highly centered on twos and threes, and anything bigger is laughably unlikely unless you have special "master" dice.

EDIT: I FOUND IT!!!

https://asteroid.divnull.com/2008/01/chance-of-reign.html

Good grief. I made the system by instinct and the "poke it with a stick until it hollers" method. Maybe I shouldn't have admitted that. Ah well. I'ma hit "submit reply" anyway.

Greg Stolze, upon reading this analysis

That's a lot of non-trivial math. Do I understand it, I hear you ask? Nice weather we're having today...