But what is your watching friend supposed to think? Though his predicament is perfectly predictable to you - that is, you expected before starting the experiment to see his confusion - from his perspective it is just a pure 100% unexplained miracle.

OK, I don't get this at all, but I totally understand the lottery example. I think Tyrrell McAllister raised this question, but only his other question was ever addressed. Are the two cases really the same? If so, how?

It's true that, as the person next to the gun, you should expect to live with the same probability you give to the truth of the QTI. And that your friend should expect you to live with probability 2^(-n), where n is the number of coinflips. But for each branch where you live, both you and your friend are getting evidence for the truth of QTI. The only difference is that if you die from your POV, that pretty much disproves QTI, but if you die from your friend's point of view, he only gets n bits of information (number of coinflips before you die). So after a million - 1 flips, both you and your friend are virtually certain of QTI. But if, on the millionth flip, you die, it's disproved from your perspective, but virtually unchanged from your friend's.

It's true that only a small fraction of branches will contain a friend (or a public, for that matter) that becomes convinced of QTI, and that even if QTI isn't true, and even if MWI isn't true, that there would still be a very small chance that you would live (and thus be falsely convinced of the truth of QTI--poor you!). But the special distinction in the holodeck case is that winning the lottery personally would be more likely to happen in a sim, whereas someone else winning it would not. In the QTI case, there isn't any alternate theory that becomes more or less likely just because you're the one behind the gun.