“How about “Omega knows whether you would pay in the counterfactual mugging setup if told that you had lost and will reward you for paying if you lose, but you don’t know that you would get rewarded once you pay up”. Is there anything I have missed?”—you aren’t told that you “lost” as there is no losing coin flip in this scenario since it is symmetric. You are told which way the coin came up. Anyway, I updated the post to clarify this
“How about “Omega knows whether you would pay in the counterfactual mugging setup if told that you had lost and will reward you for paying if you lose, but you don’t know that you would get rewarded once you pay up”. Is there anything I have missed?”—you aren’t told that you “lost” as there is no losing coin flip in this scenario since it is symmetric. You are told which way the coin came up. Anyway, I updated the post to clarify this