I see two answers on this board for the "Emphasis roll" mechanic and neither of them match how the Emphasis rolls work.
The idea behind the Emphasis roll is that you roll 2 d20's and take the result that is furthest from 10.
However, the probabilities should be arranged against a target number. For example, let's say you were trying to hit a AC 1. You roll 2 d20's and no matter what the rolls and the distance from 10, you should have a 100% chance of hitting a AC 1; none of the solutions posted here represent this fact.
What I'm looking for is a graph that should show what the probabilities are TO HIT an AC of 1, of 2, of 3, of 4 and up using the Emphasis roll mechanic.
The same could be applied for Saving Throws and DC's in D&D for Emphasis rolls.