The probabilities are based on Omega’s state of knowledge. The original problem assumes that Omega is near-omniscient, so that he is extremely likely to make a correct prediction. If you assume that it’s possible at all to make a random choice then you must have some “hidden” source of information that Omega can’t see. Otherwise the strategy in the original post wouldn’t even work, Omega would know how your “random” choice was going to come out so every time you two boxed you would find the box empty and vice-versa.
So when I said “probability” I meant the probability as judged by Omega based on his near total knowledge of your brain and your environment, but with no knowledge of some source of randomness that you can use to generate decisions.
Many Worlds is deterministic. What relevant information is hidden? Omega can predict with certainty that both outcomes happen in the event of a quantum coin flip, in different Everett branches. This is only “random” from a subjective point of view, after the split. Yet given the rules of The Deal, Omega can only fill the box, or not, in advance of the split.
The probabilities are based on Omega’s state of knowledge. The original problem assumes that Omega is near-omniscient, so that he is extremely likely to make a correct prediction. If you assume that it’s possible at all to make a random choice then you must have some “hidden” source of information that Omega can’t see. Otherwise the strategy in the original post wouldn’t even work, Omega would know how your “random” choice was going to come out so every time you two boxed you would find the box empty and vice-versa.
So when I said “probability” I meant the probability as judged by Omega based on his near total knowledge of your brain and your environment, but with no knowledge of some source of randomness that you can use to generate decisions.
Many Worlds is deterministic. What relevant information is hidden? Omega can predict with certainty that both outcomes happen in the event of a quantum coin flip, in different Everett branches. This is only “random” from a subjective point of view, after the split. Yet given the rules of The Deal, Omega can only fill the box, or not, in advance of the split.