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The d20 is fickle. It has a very big swing that can mean, depending on the DC the DM has established, even highly capable characters fail. This is, in part, what makes Inspiration, guidance, and resources like the diviner's portent so valuable - you get to mitigate or in some cases eliminate the swing of the d20, to hopefully prevent it from killing you and everyone you've ever loved. Because it will, given half a chance.
In the context of the rules I paraphrased above and given the reality of the d20's swing, there's nothing in there that suggests to me that players should be asking to roll or declaring that they are rolling. .....
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I had a big discussion with one of my players who wanted to do 2d10 instead for more continuity.
But why do I want to roll a d20? Because I roll it on a skill I am good at! With a high bonus due to proficiency or attribute I got good chances to win the roll, as a rogue to be stealthy e.g.
If you use some rolling method to soften this up you make the rolls and skill building meaningless.
Especially 5e imho is totally NOT suitable for 2d10 or 3d6 instead of 1d20. You take all the fun out of the game.
Let it be fickle, even if you do autofail on a 1, then that's your bad day. I want the player who invested in a skill be rewarded for it not being mediochre.
In another game I where I play in I hate do do some checks:
e.g. climb a long rope ladder like it should be: DM make an acrobatics check Dex or Str DC 5-10 and lets see if you handle the task. Roll additionally a Con check DC10 if you are exhausted.
My DM: roll a dex check for the first 50ft roll another and another and a Con check each 100 ft and another. So your chances despite being a dex monkey with 14 con to master the rope ladder are really slim.
But still I want the game to be swingy that's part of the fun. Ain't no fun if something spectacular only happens every 100ths die roll