I am wondering if the precise dmg from the arcane duelist works on each attack or just on the first.
What would lead you to believe it only work on the first attack?
It works on every attack, same as Sneak Attack. If you meet the conditions for it, it always works.
that was the opinion of my old DM. It could of been a house rule
i dont ask instead if answering to mock your question or anything, I was trying to coerce you into answering your own question. I find it good practice to hone one's deductive reasoning skills in a game like this.