some other thoughts. the paradox exists because you cannot precommit yourself to taking the wager given you are in a green room as this commits you to taking the wager on 100% of coinflips which is terrible for you.
when you find yourself in a green room, the right play IS to take the wager. however, you can’t make the right play without committing yourself to making the wrong play in every universe where the coin comes up tails. you are basically screwing your parallel selves over because half of them exist in a ‘tails’ reality. it seems like factoring in your parallel expectation cancels out the ev shift of adjusting you prior (50%) probability to 90%.
and if you don’t care about your parallel selves, you can just think of them as the components that average to your true expectation in any given situation. if the overall effect across all possible universes was negative, it was a bad play even if it helped you in this universe. metaphysical hindsight.
some other thoughts. the paradox exists because you cannot precommit yourself to taking the wager given you are in a green room as this commits you to taking the wager on 100% of coinflips which is terrible for you.
when you find yourself in a green room, the right play IS to take the wager. however, you can’t make the right play without committing yourself to making the wrong play in every universe where the coin comes up tails. you are basically screwing your parallel selves over because half of them exist in a ‘tails’ reality. it seems like factoring in your parallel expectation cancels out the ev shift of adjusting you prior (50%) probability to 90%.
and if you don’t care about your parallel selves, you can just think of them as the components that average to your true expectation in any given situation. if the overall effect across all possible universes was negative, it was a bad play even if it helped you in this universe. metaphysical hindsight.