The fundamental rule of Dungeons and Dragons is how you resolve actions: roll a 20-sided die, add or subtract modifiers based on your attributes or skills, and compare the result to a Target Number given by your Dungeon Master. This is not, however, the only way D&D has done this in the past, nor is it the only way other tabletop role-playing games do it.
When you roll a d20 each number, from 1 to 20, has an equal chance of coming up. On a 3d6 throw the middle numbers between 3 and 18 are far more likely to appear than the extremes. While this makes extreme success less likely, it also makes extreme failure far less likely.
Historically, third edition D&D had a 3d6 alternate rule in Unearthed Arcana, which let you to convert your campaign from a d20 system to a 3d6 system.
That was not the only time D&D used a 3d6 roll as its basic mechanic. In the little known introductory adventure The Crypt of the Smoke Dragon, published between second and third edition, an action’s success is determined by rolling under a number on a pre-created character’s sheet. Further back, in 1992’s single volume Rules Cyclopedia for Basic-line D&D, and optional rule introduced skill checks by allowing you to roll 1d20 under your ability score, itself determined by a 3d6 throw.
Other games, most famously including GURPS, resolve all actions by using 3d6 under the relevant skill – and GURPS has a lot of relevant skills.
If you were hack 5e D&D and replace the d20 throw with 3d6, there would be significant downstream consequences. In all modern versions of D&D, including 5e, bonuses play an important roll in shifting the distribution of result distributions. These become much narrower when you’re talking about a bell curve instead of a flat line. More importantly, it would necessitate rethinking the out of the book Target Number/Difficulty Class chart to reflect the different probabilities of certain outcomes.
5e’s extremely popular advantage/disadvantage system would also need to be rethought. On a 3d6 throw would this mean you’d roll the set of dice twice? Roll 6 dice and pick the best 3? Roll 4 dice and drop the lowest 1, like 5e’s character creation rules tell you to do? Each of these approaches would distribute results very differently, and whether you’re hacking 5e or making your own system this is worth bearing in mind.
Most importantly, the probability of success on a single die throw is second only to how frequently you roll dice in establishing the feel of your game. How often should characters succeed when the undertake an action – and should player’s fear and dread rolling a die, or look forward to it? When they do roll should they have some confidence of success or should they know where that single number lands is where it lands – and feel the exhilaration of a natural 20 or a natural 1?
The answers to those questions are going to be different for every game, and cannot be made for you. What feeling do you want to create?
