I’d summarize as “the probability of something that happened is 1”. There’s no variance in whether or not it will occur. If you like, you can add uncertainty about whether you know it happened, but a lot of things approach 1 pretty quickly.
The probability of future experiences will be 1 or 0 at some point, but for now, different agents assign likelihoods based on their priors. The probably that the next sequence of flips will be exactly this is, in the world, 0 or 1 - what will be will be. The probability that an agent can use to predict this experience is 1/2^n. That probability expectation changes as evidence is added, such as the evidence of seeing some or all of the flips.
alternate way of showing this: ask Bob to show his update after each of the N flips. The prior is indeed 1/2^n, but each observation makes it twice as likely.
2) Bob’s just wrong if his priors give a significantly higher chance to supernatural physics violations than to winning the lottery. This is probably some form of scope insensitivity. For both ghosts and lottery-winning, I do assign a much higher chance that I’m being tricked than that it actually happened, but if the question comes up, I can gather evidence to change those ratios.
two ways to approach this, depending on which direction Bob takes the argument.
1) Alice seems to be accepting Bob’s implication that probability exists in reality, rather than only in the minds and models we use to predict it
A fair bit of recent discussion can be found in this thread, and in the sequences in Probability is in the Mind.
I’d summarize as “the probability of something that happened is 1”. There’s no variance in whether or not it will occur. If you like, you can add uncertainty about whether you know it happened, but a lot of things approach 1 pretty quickly.
The probability of future experiences will be 1 or 0 at some point, but for now, different agents assign likelihoods based on their priors. The probably that the next sequence of flips will be exactly this is, in the world, 0 or 1 - what will be will be. The probability that an agent can use to predict this experience is 1/2^n. That probability expectation changes as evidence is added, such as the evidence of seeing some or all of the flips.
alternate way of showing this: ask Bob to show his update after each of the N flips. The prior is indeed 1/2^n, but each observation makes it twice as likely.
2) Bob’s just wrong if his priors give a significantly higher chance to supernatural physics violations than to winning the lottery. This is probably some form of scope insensitivity. For both ghosts and lottery-winning, I do assign a much higher chance that I’m being tricked than that it actually happened, but if the question comes up, I can gather evidence to change those ratios.