It seems to me that if you have a calculator, you should pay up exactly when you are in a counterfactual (i.e. you hypothetically observe Omega asserting an incorrect statement about the logical coin), but refuse to pay up if the alternative (Omega paying you) is counterfactual (in this case, you know that the event of being paid won’t be realized, assuming these are indeed the boundaries of the game). There doesn’t appear to be a downside to this strategy, if you do have a calculator and are capable of not exploding in the counterfactual that you know to be counterfactual (according to whatever dynamic is used to “predict” you in the counterfactual).
(Intuitively, a possible downside is that you might value situations that are contradictory, but I don’t see how this would not be a semantic confusion, seeing a situation itself as contradictory as opposed to merely its description being contradictory, a model that might have to go through all of the motions for the real thing, but eventually get refuted.)
It seems to me that if you have a calculator, you should pay up exactly when you are in a counterfactual (i.e. you hypothetically observe Omega asserting an incorrect statement about the logical coin), but refuse to pay up if the alternative (Omega paying you) is counterfactual (in this case, you know that the event of being paid won’t be realized, assuming these are indeed the boundaries of the game). There doesn’t appear to be a downside to this strategy, if you do have a calculator and are capable of not exploding in the counterfactual that you know to be counterfactual (according to whatever dynamic is used to “predict” you in the counterfactual).
(Intuitively, a possible downside is that you might value situations that are contradictory, but I don’t see how this would not be a semantic confusion, seeing a situation itself as contradictory as opposed to merely its description being contradictory, a model that might have to go through all of the motions for the real thing, but eventually get refuted.)