The probability of Batman finding that he survives after the first coinflip is not 50% or 100% in either interpretation. It’s more like one in several trillion. If you add “Given that you’re batman, and just did the experiment”, it’s clearly 100% in any interpretation.
There’s another, bigger problem. Compare quantum immortality to if he had actual immortality, and just never died. You make it sound like the probabilities will come out the same. They will not. The probability of being batman after flipping the coin is lower in the many worlds version is lower, since the probability amplitude is lower. For example, if he lived 20 years before the coin flip, and, if he survives, 20 years after, in the many worlds interpretation, he’d be twice as likely to be in the “before” section, whereas if it’s just guaranteed not to kill him, they’d be equal.
In addition, if you add a huge number of bystanders, one is less likely to be batman in the many worlds version, so it works out that one is about as likely to be batman before in either version, but more likely to be him after in the actual immortality version.
The probability of Batman finding that he survives after the first coinflip is not 50% or 100% in either interpretation. It’s more like one in several trillion. If you add “Given that you’re batman, and just did the experiment”, it’s clearly 100% in any interpretation.
There’s another, bigger problem. Compare quantum immortality to if he had actual immortality, and just never died. You make it sound like the probabilities will come out the same. They will not. The probability of being batman after flipping the coin is lower in the many worlds version is lower, since the probability amplitude is lower. For example, if he lived 20 years before the coin flip, and, if he survives, 20 years after, in the many worlds interpretation, he’d be twice as likely to be in the “before” section, whereas if it’s just guaranteed not to kill him, they’d be equal.
In addition, if you add a huge number of bystanders, one is less likely to be batman in the many worlds version, so it works out that one is about as likely to be batman before in either version, but more likely to be him after in the actual immortality version.