Players were given vague outlines of which each other player was about, but the contents of their powers were kept secret. As for rolling, I changed my preferred methods in later iterations (see the Blades in the Dark open strategy game):
If an action is unopposed or easy, it happens. If success is uncertain, the referee rolls 2d6. If likely, only one die needs to be 4 or higher. If unlikely, both need to be 4 or higher. Rolling doubles means something chaotic occurs.