In general, I agree that there's no paradox. But, what worries me is the last statement you're making there: there's never any question that there's a nonzero chance that everyone will escape alive: as I see it, at any given instant, there should be a 97.2% chance that everyone will escape alive, and that past experiments don't matter to the individual. The house always wins, though.

However, I'm still bothered by all that. To my thinking, infinite timeframes shouldn't matter from a calculational standpoint. Of course, I should probably sit down and think out if this is a converging series before I say that, but I have similar difficulties with questions like

Schrödinger's cat. For example, let's say it's a pair of fecund cats. As time progresses, the number of cats increases exponentially, but the chance that all the cats die is also increasing. It seems reasonable that the mean number of cat corpses in the box might be computable, if I'm following the experiment from beginning to end.

That said, if I'm randomly sampling a known experiment which I have no idea when it began, I can't make conclusions like John Leslie is making. It's the guessing, that I'm near the "end" or near the "beginning" that really bothers me.