I think, but am not certain, that you’re missing the point, by examining Bob’s incredulity rather than the problem as stated. Let’s say your probability that the universe is being simulated is 2^x.
Alice flips a coin (x+1) times. You watch her flip the coins, and she carefully marks down the result of each flip.
No matter what sequence you watch, and she records—that sequence has less likelihood of having occurred naturally than that the universe is simulated, according to your priors. If it helps, imagine that a coin you know to be fair turns up Heads each time. (A sequence of all heads seems particularly unlikely—but every other sequence is equally unlikely.)
I agree that the probability of seeing that exact sequence is low. Not sure why that’s a problem, though. For any particular random-looking sequence, Bob’s prior P(see this sequence | universe is simulated) is pretty much equal to P(see this sequence | universe is not simulated), so it shouldn’t make Bob update.
I think, but am not certain, that you’re missing the point, by examining Bob’s incredulity rather than the problem as stated. Let’s say your probability that the universe is being simulated is 2^x.
Alice flips a coin (x+1) times. You watch her flip the coins, and she carefully marks down the result of each flip.
No matter what sequence you watch, and she records—that sequence has less likelihood of having occurred naturally than that the universe is simulated, according to your priors. If it helps, imagine that a coin you know to be fair turns up Heads each time. (A sequence of all heads seems particularly unlikely—but every other sequence is equally unlikely.)
I agree that the probability of seeing that exact sequence is low. Not sure why that’s a problem, though. For any particular random-looking sequence, Bob’s prior P(see this sequence | universe is simulated) is pretty much equal to P(see this sequence | universe is not simulated), so it shouldn’t make Bob update.