While the Oracle’s prediction only applies to the world it was delivered in, you don’t know which of the as-yet hypothetical worlds that will be. Whatever your decision ends up being, the Oracle’s prediction will be correct for that decision.
If you hear that you will win, you bet on the Red Sox and lose, then your decision process was still correct but your knowledge about the world was incorrect. You believed that what you heard came from an Oracle, but it didn’t.
This also applies to Newcombe’s problem: if at any point you reason about taking one box and there’s nothing in it, or about taking two boxes and there’s a million in one, then you are implicitly exploring the possibility that Omega is not a perfect predictor. That is, that the problem description is incorrect.
While the Oracle’s prediction only applies to the world it was delivered in, you don’t know which of the as-yet hypothetical worlds that will be. Whatever your decision ends up being, the Oracle’s prediction will be correct for that decision.
If you hear that you will win, you bet on the Red Sox and lose, then your decision process was still correct but your knowledge about the world was incorrect. You believed that what you heard came from an Oracle, but it didn’t.
This also applies to Newcombe’s problem: if at any point you reason about taking one box and there’s nothing in it, or about taking two boxes and there’s a million in one, then you are implicitly exploring the possibility that Omega is not a perfect predictor. That is, that the problem description is incorrect.