In black flag nightless - expected value for town to win by random lynching is 50%
As I showed earlier today, it seems that for us - town only wins when they have Distorted.
In the White Flag setup - Towns EV by random lynching is 48%. But they only have 29%.
Long story short: don't let anyone fool you in believing that you are doing a educated lynch at D1. At D1 D2 lynch those who slow down the flow of information. Don't fool yourself. First lynches are more random than you are making yourself believe almost always.