The Star Wars Roleplaying Game, released by West End Games in 1987, was one of the first RPGs to introduce a Dice Pool system - a ruleset where players resolve challenges by rolling handfuls of dice, rolling more dice the more skilled their characters are at a certain task. RPG systems like FATE or ' Powered By The Apocalypse,' where players roll and add a bonus to multiple dice, have more of a 'bell curve' of probabilities (as explained on the ' Game Master Dice' website) where average dice results are more likely than 'critical successes' or 'critical failures.'
The advantage and disadvantage of D20 systems like D&D is that every possible dice result has an equal (5%) chance of happening: this 'variance' makes it easy for Dungeon Masters to quantify the difficulty of a challenge on the fly, but also leads to scenarios where player characters unexpectedly succeed at challenges seemingly beyond them or fail miserably at the easiest of tasks. If the sum of the dice and bonus matches or exceeds a pre-determined difficulty number (10 often representing average difficulty) the player's characters succeeds at their challenge, and fails if they roll under. In many roleplaying system, players resolve skill checks, attacks, and the like by rolling a single dice - a twenty-sided die in Dungeons & Dragons games - then adding a flat numerical bonus such as +3 or +5.