For the first point, you could use a random generator and make it pick from a Gaussian or Poisson or other probability distribution depending on the situation.

Many RPGs that aren't so closely related to DND use a dice pool. Instead of like 1d20, you might roll 3d6. Now you're more likely to get an average result. Only one way to roll 3, but a bunch of ways to roll 10.

The nWoD games you roll d10s and count how many come up 8,9, 10. Very fast, and once you're good at a task you know you'll generally succeed. It's more a question of how well you'll succeed and how strong the opposition is.

I'm not mathy enough to talk beyond that, but I find it much more satisfying.