This depends on how omega constructs his counterfactuals. Suppose the laws of physics make the coin land heads as part of a deterministic universe. The counterfactual where the coin lands tails must have some difference in starting conditions or physical laws, or non physical behavior. Lets suppose blatently nonphysical behavior like a load of extra angular momentum appearing out of nowhere. You are watching the coin closely. If you see the coin behave nonphysically, then you know that you are in a counterfactual. If you know that omegas counterfactuals are always so crudely constructed, then you would only pay in the counterfactual and get the full $10000.
If you can’t tell whether or not you are in the counterfactual, then pay.
This depends on how omega constructs his counterfactuals. Suppose the laws of physics make the coin land heads as part of a deterministic universe. The counterfactual where the coin lands tails must have some difference in starting conditions or physical laws, or non physical behavior. Lets suppose blatently nonphysical behavior like a load of extra angular momentum appearing out of nowhere. You are watching the coin closely. If you see the coin behave nonphysically, then you know that you are in a counterfactual. If you know that omegas counterfactuals are always so crudely constructed, then you would only pay in the counterfactual and get the full $10000.
If you can’t tell whether or not you are in the counterfactual, then pay.
We can assume that the coin is flipped out of your sight.