I'm actually not quite satisfied with it. Probability is in the mind, which makes it difficult to know what I mean by "perfect knowledge". Perfect knowledge would mean I also knew in advance that the coin would come up tails.

I know giving up the $100 is right, I'm just having a hard time figuring out what worlds the agent is summing over, and by what rules.

ETA: I think "if there was a true fact which my past self could have learned, which would have caused him to precommit etc." should do the trick. Gonna have to sleep on that.

ETA2: "What would you do in situation X?" and "What would you like to pre-commit to doing, should you ever encounter situation X?" should, to a rational agent, be one and the same question.