The source of the apparent paradox here is that the perceived absurdity of ‘getting lucky N times in a row’ doesn’t scale linearly with N, which makes it unintuitive that an aggregation of ordinary evidence can justify an extraordinary belief.
You can get the same problem with less anthropic confusion by using coin-flip predictions instead of Russian Roulette. It seems weird that predicting enough flips successfully would force you to conclude that you can psychically predict flips, but that’s just a real and correct implication of having on nonzero prior on psychic abilities in the first place.
Shorter statement of my answer:
The source of the apparent paradox here is that the perceived absurdity of ‘getting lucky N times in a row’ doesn’t scale linearly with N, which makes it unintuitive that an aggregation of ordinary evidence can justify an extraordinary belief.
You can get the same problem with less anthropic confusion by using coin-flip predictions instead of Russian Roulette. It seems weird that predicting enough flips successfully would force you to conclude that you can psychically predict flips, but that’s just a real and correct implication of having on nonzero prior on psychic abilities in the first place.