I think some of those are a bit optimistic and some a bit pessimistic; perhaps the errors cancel out. My guess is that there are more ways for the chain to fail unexpectedly than to succeed unexpectedly, so most likely my estimate is too optimistic. Anyway, it ends up at 3/2048.

Here’s the thing: let’s say that there’re some “objective probabilities” out there, and that your estimate is indeed “most likely too optimistic” compared to those objective probabilities, but that there’s some significant (e.g., 10%) chance that it’s too pessimistic with compared to those same probabilities. If your estimate is “over optimistic”, its overoptimistic by at most 3/2048. If your estimate is “over pessimistic”, it could easily be over pessimistic by more than ten times that much (i.e., by more than 30/2048; Robin Hanson’s estimates the odds as “>5%”, i.e. more than 100/2048). And if you’re trying to do decision theory on whether or not to sign up for cryonics, you’re basically trying to take an average over the different values these “objective probabilities” could have, weighted by how likely they are to have those values -- which means that the scenarios in which your estimate is “too pessimistic” actually have a lot of impact, even if they’re only 10% likely.

Or in other words: one’s analysis has to be unusually careful if it is to justify a resulting probability as low as 3/2048. Absent a terribly careful analysis, if one is trying to estimate some quantity that kinda sounds plausible or about which experts disagree (e.g., not “chances we’ll have a major earthquake during such-and-such a particular milisecond), one should probably just remember the overconfidence results and be wary of assigning a probability that’s very near one or zero.