Alice: "I just flipped a coin [large number] times. Here's the sequence I got:
(Alice presents her sequence.)
Bob: No, you didn't. The probability of having gotten that particular sequence is 1/2^[large number]. Which is basically impossible. I don't believe you.
Alice: But I had to get some sequence or other. You'd make the same claim regardless of what sequence I showed you.
Bob: True. But am I really supposed to believe you that a 1/2^[large number] event happened, just because you tell me it did, or because you showed me a video of it happening, or even if I watched it happen with my own eyes? My observations are always fallible, and if you make an event improbable enough, why shouldn't I be skeptical even if I think I observed it?
Alice: Someone usually wins the lottery. Should the person who finds out that their ticket had the winning numbers believe the opposite, because winning is so improbable?
Bob: What's the difference between finding out you've won the lottery and finding out that your neighbor is a 500 year old vampire, or that your house is haunted by real ghosts? All of these events are extremely improbable given what we know of the world.
Alice: There's improbable, and then there's impossible. 500 year old vampires and ghosts don't exist.
Bob: As far as you know. And I bet more people claim to have seen ghosts than have won more than 100 million dollars in the lottery.
Alice: I still think there's something wrong with your reasoning here.
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.