Your Favorite Resolution Systems

[Telok]

Paranoia's d20 blackjack system: you have a "thing", like melee combat, nuclear engineering, boot licking, or ink squirting, with a 1-20 number. Roll that number or under, 1s are success with a drawback, the number exactly is success with a boost, 20s are comedic utter failure (because its Paranoia and possibly lethal because you have clones you need to use up). No math at the base rolls, opposed checks are dirt simple 'who rolled higher yet still under their number, you can do margins of success easily, modding the game tone or content is super easy. Bonus; its really fast, super newbie friendly, and you only need one die.

Also really fond of 3d6 vs 11 or less. All character stuff is a number (default 11) you need to roll under. Or you can flip it to emulate 3d6 + bonus vs 11+ if you have to, then all the character numbers are just low bonuses. Again, simple, flexible, easily moddable (you can go 4d6 drop lowest/highest if you don't want numerical modifiers), and its a normal probability distribution so you can't "roll too much" and bust the gameplay without also having to screw up somethings else like stacking penalties all over the place. Bonus; slots into AD&D really super well and makes the difference between say, strength 10 & 17 matter more than 1/6 times.

Generally I like 1-3 die fast & easy (theoretically the wotc d20 stuff should be but the exception stuff and constsntly changing numbers don't), or some sort of well mathed bell curve with 10 or less dice that doesn't break at the extremes of character math or too many/few rolls.