Homebrew 2d10 vs 1d20

Bell shaped curves (2d10, 3d6...) are good for non opposed rolls, where one side is variable (your skill/proficiency/ability to achieve the result) and the other (dificulty) is fixed. Since the variable side has a low variance/dispersion (when you're good at something that only depends on you, you're likely to succeed with regular frequency), the results are more predictable. Good for ability tests (non opposed rolls). The "take 10" rule goes in thia way, but it reduces the variance to 0, too drastic.
For tests where both sides are variable, like attacks or other opposed rolls, a linear result (1d20) is better since your skill is being tested against someone's else skill, so you want the results to be less predictable.
So if someone is open to abandon the d&d "1 roll to rule them all" rule from since 3e, I would recommend to use both rolls.
 

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Bell shaped curves (2d10, 3d6...) are good for non opposed rolls, where one side is variable (your skill/proficiency/ability to achieve the result) and the other (dificulty) is fixed. Since the variable side has a low variance/dispersion (when you're good at something that only depends on you, you're likely to succeed with regular frequency), the results are more predictable.
The results on the dice are more predictable. Whether the result of the skill check is more predictable depends entirely on the system built around the dice and the what the range of the variables is.

If the target is 8+ on 1d10 (fixed difficulty), basic proficiency provides +3, advanced proficiency gives +5 and expert gives +6, then advanced and expert characters succeed 80% and 90% of the time respectively. That's very predictable. Unskilled people fail 70% of the time, which is also quite predictable. You don't need a bell curve to have predictable outcomes.
 
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