Of course you’re predicting something different. In all cases you’re making a conditional prediction of a state of the world given your epistemic state at the time. Your epistemic state on Wednesday is different from that on Monday or Tuesday. On Tuesday you have a 50% chance of not being asked anything at all due to being asleep, which breaks the symmetry between heads and tails.
By Wednesday the symmetry may have been restored due to the amnesia drug—you may not know whether the awakening you remember was Monday (which would imply heads) or Tuesday (which would imply tails). However, there may be other clues such as feeling extra hungry due to sleeping 30+ hours without eating.
you’re making a conditional prediction of a state of the world given your epistemic state at the time.
I think this is a crux. IMO, you can’t predict the state of the world, since you have no access to that except via your perceptions/experiences. You’re making a prediction of a future epistemic state (aka experience), given (of course) your current epistemic state, conditional on which prediction you make (what will happen if you guess either way, and if you’re right/wrong).
It’s perfectly reasonable to bet 1⁄3 if the reveal/payout is instantaneous and multiple, and to bet 1⁄2 if the reveal/payout is post-merge and singular. Each is correct, for predicting different future experiences.
Of course you’re predicting something different. In all cases you’re making a conditional prediction of a state of the world given your epistemic state at the time. Your epistemic state on Wednesday is different from that on Monday or Tuesday. On Tuesday you have a 50% chance of not being asked anything at all due to being asleep, which breaks the symmetry between heads and tails.
By Wednesday the symmetry may have been restored due to the amnesia drug—you may not know whether the awakening you remember was Monday (which would imply heads) or Tuesday (which would imply tails). However, there may be other clues such as feeling extra hungry due to sleeping 30+ hours without eating.
I think this is a crux. IMO, you can’t predict the state of the world, since you have no access to that except via your perceptions/experiences. You’re making a prediction of a future epistemic state (aka experience), given (of course) your current epistemic state, conditional on which prediction you make (what will happen if you guess either way, and if you’re right/wrong).
It’s perfectly reasonable to bet 1⁄3 if the reveal/payout is instantaneous and multiple, and to bet 1⁄2 if the reveal/payout is post-merge and singular. Each is correct, for predicting different future experiences.