As an aside, I'll note that a lot of the solutions bandied around here to decision theory problems remind me of something from Magic: The Gathering which I took notice of back when I still followed it. When I watched my friends play, one would frequently respond to another's play with "Before you do that, I-" and use some card or ability to counter their opponent's move. The rules of MTG let you do that sort of thing, but I always thought it was pretty silly, because they did not, in fact, have any idea that it would make sense to make that play until after seeing their opponent's move. Once they see their opponent's play, they get to retroactively decide what to do "before" their opponent can do it. In real life, we don't have that sort of privilege. If you're in a Counterfactual Mugging scenario, for instance, you might be inclined to say "I ought to be the sort of person who would pay Omega, because if the coin had come up the other way, I would be making a lot of money now, so being that sort of person would have positive expected utility for this scenario." But this is "Before you do that-" type reasoning. You could just as easily have ended up in a situation where Omega comes and tells you "I decided that if you were the sort of person who would not pay up in a Counterfactual Mugging scenario, I would give you a million dollars, but I've predicted that you would, so you get nothing." When you come up with a solution to an Omega-type problem involving some type of precommitment, it's worth asking "would this precommitment have made sense when I was in a position of not knowing Omega existed, or having any idea what it would do even if it did exist?" In real life, we sometimes have to make decisions dealing with agents who have some degree of predictive power with respect to our thought processes, but their motivations are generally not as arbitrary as those attributed to Omega in most hypotheticals.