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I have been able to successfully persuade multiple times with characters that have 0 points in persuasion and only 2-3 points stat difference. Maybe you just need at least as much persuasion as the other character or the difficulty of persuasion is not based on teir stats.
Looks like some of the persuasion choices are auto fail or auto succeed, and some are chance based on persuasion skill. Seems like a pretty poorly designed system as it currently stands
In the very first room I have stolen a book next to Magister Siwan. When she accused me of thievery, I vehemently denied that. Persuasion failed and a combat was initiated. Upon reload, I got a persuasion success. That means that persuasion is a chance check.
It would be very nice to have more testing. If you still have the save, could you reload it a few more times and see if it changes again?
I just whip out the D-Piece and I persuade 100% of the time.
Persuasion definitely is attribute based, In drift wood at 1 persuasion and 21 strength I consistently failed the persuasion check for the executioner but after eating a mushroom and a strength pot to get to 24 strength I passed the check. Similarly on the boat to fort joy I would consistently failed the speech check to convince the magisters hiding in the room up stairs to let me go, but after buffing my intelligence by 1 i succeeded.
It seems to me like Persuasion acts as a multiplier, perhaps x1.5 or x2 at 1 point. This would mean that it hugely influences Persuasion checks, but also that increasing your Strength by 3 points would add even more than that to the check.