Obviously most RPGs use some sort of randomizing technique to determine the outcomes of actions that could fail in some interesting way. Most systems leverage the randomizer to give advantage to skilled actions and disadvantage to unskilled ones: generate a random total, add your skill, compare the total to some target, maybe.

- FATE

You roll four Fate dice. Each one is a special d6 with 2 faces showing a plus (+), 2 faces showing a minus (-), and two blank faces. Pluses count as 1, minuses as -1, and blanks as 0. Total ranges from -4 to +4, with 0 being the most likely outcome. Adding this total to your skill gives you a minimum of Skill value -4, potentially a negative score. The possibility for a negative score is brutal. However, by rolling 4 dice you increase the likelihood of an average roll, meaning your most likely score will be close to your skill value. - D&D / Pathfinder / D20 systems

Here you roll just the one d20 and add your skill value. The minimum score is skill value + 1, and you are equally likely to get an average roll, a very high roll, or a very low one. This maximizes randomness, but we are all so accustomed to rolling d20s, that who would really notice? - Percentage systems

You roll d100 and try to roll UNDER the target. Still basically the same as d20, as far as I can tell. - Burning Wheel / Mouse Guard / Torchbearer

You roll a number of d6s equal to your skill value. Each d6 that shows a certain number or higher is a success; other dice are failures. Your score is the number of successes. Minimum score is 0; Most rolls will come out to roughly 1/2 the number of dice you roll. These systems rely on an objective sense of how a given task is to set a target number, and assert a certain level of mastery for each skill rank. If polished work is difficulty 3, then to reliably DO polished work you need to roll 6 or more dice. These systems allow you to use extra dice by spending points that you earn through roleplaying. This indirectly means roleplaying improves your chances of successful action. - Dice pool systems

Sometimes you just roll a number of dice and add up all the pips. Usually a higher skill value means you roll a higher number of dice. In this case, your minimum value would be equal to your skill number, and the results curve would be steeper the more dice you roll – the chance of getting your minimum on a single d6 is 1/6; the chance of getting your minimum on 2d6 is 1/36; on 3d6 it’s 1/216; the more dice you roll, the less likely you are to get an extreme roll. Of course, the size of your average roll also increases, so that’s nice, too. - There’s no reason you couldn’t design a system that always rolls 5d6 and adds the total to a skill value. this would be effectively equivalent to d20, but the distribution of scores would be more predictably average the more dice you roll. And the more dice you roll in such a hybrid system, the less impact your skill value would have.
- Savage Worlds

If you are good at a skill, you roll a bigger die; if you are bad, you roll a smaller one. Minimum score is 1, regardless; the reward of being skilled is in the higher maximum. If you roll your maximum on the die, you get to reroll and add the totals together, and you repeat this as long as you keep rolling the max on each die. PC/hero characters also roll a d6, so I guess the minimum is really 2. Notice that your chance of rolling the max value on a die decreases the bigger the die is. It’s ok, though. To get an 8 rolling a d8, you have a 1/8 chance. To get the same 8 on 2d4, you have a 1/16 chance. This system has a lot of volatility, maybe more than d20. Roleplaying can earn you bennies in this system, and these can be used to improve your action outcomes. - Cortex

Games using the Cortex system (Firefly RPG, for example, or Castlemourn) also reflect higher skill with a larger die, but you roll TWO varying dice rather than one varying die and d6 as in Savage Worlds. For example, to fight with a club, you would roll your Melee Combat die and your Strength die, so if you are weak (d4 strength) but highly trained with the club (d12 Melee/club) you roll a d4+d12. Depending on your intention you might roll a different attribute; for example, if you were trying to use your club with FINESSE, instead of your strength die, maybe you roll your agility die and your melee/club die. If you are less clumsy than weak, this could improve your outcome substantially. This flexibility of choice emphasizes player choice and role playing in a way that interests me. Drama points also available to improve outcomes here. Not sure how they are earned. - Clockwork: Dominion

This system also asks you to choose a skill and an attribute, but instead of dice rolling, you add the two scores together and draw a card that could be any number from -5 to +5. I’m not sure the distribution of the cards, so I don’t have anything useful to say about the results curve, but I like systems that allow the player to choose HOW to execute the action by specifying which combination of skill and attribute to use. - Torg: Eternity

You roll a d20, reroll 10s and 20s and add them to the total. Compare the total against a table to determine the relevant bonus, and add that bonus to your skill value. This is unnecessarily complicated. It’s designed to create a LOT of volatility in the outcomes. Minimum outcome is still your skill plus 1, though, and you can spend possibility points to increase your total. I feel like possibilities accrue automatically, though, without regard for roleplaying. This system is a refreshment of the 90s Torg. I wonder if Luke Crane saw possibilities in Torg and said “I can do more with those! and then wrote Burning Wheel. I should look up the relative publication dates.