Huh, I must have "remembered" that term into the post. What I mean is more succinctly put in this comment.

Can we apply that to decisions about very-long-term-but-not-infinitely-long times and very-small-but-not-infinitely-small risks?

Hmm... it appears not. So I don't think that helps us.

This question still confuses me, though; if it's a reasonable strategy to stop at N in the infinite case, but not a reasonable strategy to stop at N if there are only N^^^N iterations... something about it disturbs me, and I'm not sure that Eliezer's answer is actually a good patch for the St. Petersburg Paradox.