D&D General - Fantasy Heartbreaker: 2d6vs d20
The question of either d20 or 2d6 has mostly to do with the kind of genre you want to play.In D&D (as it is now) the goal seems to be that everyone can try to contribute to everything and have reasonable success. If you are trained, you fail less often.
Using DCs between 10 and 20 and modifiers between -1 and 11 for most characters with advantage here and there will work towards that goal. If you use some kind of auto success (take 10/passive checks or one of the DMG methods) you will get more reliability if you are trained.
Contrary in a 2d6 system. It works for games where you want to have dedicated specialists, where even a little bit of training will give you a big edge over someone untrained. If you even have just a +2 bonus, against DC 8 or 9, you will have an 11/36 =~ 30% better chance to succeed instead of just +10%. With slightly higher modifiers you soon reach the point where just it is just not worth using a skill at all.
A middle ground would be using a d12, where it is still linear but on a compressed scale. 3d6 is not better than 2d6, because of the shape of the distribution (most rolls are 9 to 12)
So it is a question of what you want. We tried 3d6 for a while, or 2d10 exactly for the reasons you stated. But we soon felt, that randomness helps keeping everyone relevant in many situation and difficult situations difficult for everyone.
In some regards I would have the system slightly modified, but using a different die would not be my choice.
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