As a gamer, I sure do love my polyhedral dice. On the other hand, a lot of modern games aim to streamline dice usage to simplify conflict / skill resolution to a couple of little rolls.
Numenera, for example, pretty much just uses the d20 for things. Occasionally you need a d100 to see if your widget broke when you turned it on, but it's really just a d20.
The way skill resolution works is, the GM figures out what the difficulty of the task is, on a scale of 1-10. The PC figures out if they have assets (tools), skills (duh), and effort (spending dice pool points that take a while to refresh) that will reduce the difficulty of that skill, by one level per thing. Then you multiply the difficulty by 3 and try to roll that number or higher on a d20. So, unmodified task difficulty 7 or higher things are not achievable.
The problem is, based on about eighteen months of running this game, this is still a really hard thing to figure out. My players get tripped up on the whole "modify challenge level down by your skill / effort, multiply by three" part. I get stuff like this:
GM: The ravage bear takes a vicious swipe at your face. Defend yourself!
PC: (rolls a d20)... I get a four.
GM: Did you roll a four, or did you succeed at a skill level four challenge by rolling a 12, or did you apply some effort to that roll beforehand and actually roll a 9?
They answer differently each time, by the way. Sometimes they'll just roll and forget to account for effort ahead of time, or they'll get it right all the way through. It's not hard, it's just kind of complicated.
Instead of rolling a d20, roll a d6. That's the challenge level you succeeded at. If you roll a 6, roll again. If you're in combat, that second roll is the bonus damage you do with your hit, and in any case, if you roll a 5+ on the second roll, you've critically succeeded (whatever that means).
Players declare their bonuses ahead of time (skills, effort1, assets).
That's it. There's no multiplying by three. Note that in the base game, it is vanishingly rare to get a +1 or +2 on some d20 roll - PCs get assets and training for the full difficulty level change.
The point of declaring bonuses instead of using effort / training / assets to reduce difficulty is a subtle but important one. Even though these processes are isomorphic, there's a big difference mentally between me saying, "this foe defends at difficulty 5, add your bonuses", and "for you, since you are specialized in speed attacks, and have a light weapon, hitting this monster is difficulty 2". Those are effectively the same thing, but the former is just simpler - think of it as the difference between positive and negative AC in transition from 2e to 3e D&D.
This system makes it impossible to outright fail a difficulty 1 task. That's something I can live with, especially since such a failure is relatively rare anyway, and I can always stick failures in with GM Intrusions anyway (I love the GM intrusion mechanic). It also isn't quite the same rate of critical success (1 in 18 rather than 1 in 20), but hey crits can still be intruded too, so if you get someone with hot dice they'll love when you hand them an XP.
This also removes the critical failure / free intrusion on a roll of 1, which you could re-introduce with a similar mechanic (on a roll of 1, a second roll of 3+ is fine, a roll of 2 is a regular failure, and a roll of 1 is a critical failure), but I don't actually like critical failure systems anyway - they tend to penalize characters that have a lot of actions2 (and while the action economy is annoying in all games, this is not, IMO, the way to solve it).
Anyway. At the end of the day, this rule simplifies the math translating between roll and success, and changes the player calculation from subtractive to additive.
This is a bigger issue in systems like 3.5ed D&D, where you've got dual-wielders and monks making a lot of small attacks, subject to weird house rules about weapon drops and breakages on a nat 1 that are waaay more likely to happen than to the big brute of a barbarian with a 2H weapon that hits like a truck. ↩