"if you had told me the relevant facts up front, I would've made the right decision"

This is a statement about my global strategy, the strategy I consider winning. In this strategy, I one-box in the states of knowledge where I don't know about the monster, and two-box where I know. If Omega told me about the monster, I'd transition to a state of knowledge where I know about it, and, according to the fixed strategy above, I two-box.

In counterfactual mugging, for each instance of mugging, I give away $100 on the mugging side, and receive $10000 on the reward side. This is also a fixed global strategy that gives the actions depending on agent's state of knowledge.