For example, if I watched my friend survive 100 rounds of solo Russian Roulette, then Baye's theorem would lead me to believe that there was a high probability that the gun was empty or only had 1 bullet. However, if I myself survived 100 rounds, I couldn't afterward conclude a low probability, because there would be no conceivable way for me to observe anything but 10 wins. I can't observe anything if I'm dead.

Obviously you can't observe anything if you are dead, but that isn't interesting. What matter is comparing the various hypothesis that could explain the events.

The case where you yourself survive 100 rounds is somewhat special only in that you presumably remember whether you put bullets in or not and thus already know the answer.

Pretend, however that you suddenly wake up with total amensia. There is a gun next to you and a TV then shows a video of you playing 100 rounds of roulette and surviving - but doesn't show anything before that (where the gun was either loaded or not).

What is the most likely explanation? 1. the gun was empty in the beginning 2. the gun had 1 bullet in the beginning

With high odds, option 1 is more likely. This survorship bias/observation selection effect issue you keep bringing up is completely irrelevant when comparing two rival hypothesis that both explain the data!

Here is another, cleaner and simpler example:

Omega rolls a fair die which has N sides. Omega informs you the roll comes up as a '2'. Assume Omega is honest. Assume that dice can be either 10 sided or 100 sided, in about the same ratio.

What is the more likely value of N?

1. 100

2. 10

Here is my solution:

priors: P(N=100) = 1, P(N=10) = 1

P(N=100 | roll(N) = 2) = P(roll(N)=2 | N=100) P(N=100) = 0.01

P(N=10 | roll(N) = 2) = P(roll(N)=2 | N = 10) P(N=10) = 0.1

So N=10 is 10 times more likely than N= 100.