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ThrustVectoring comments on Probability and radical uncertainty - Less Wrong
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Meta-probability seems like something that is reducible to expected outcomes and regular probability. I mean, what kind of box the black box is, is nothing more than what you expect it to do conditional on what you might have seen it do. If it gives you three dollars the next three times you play it, you'd then expect the fourth time to also give you three dollars (4/5ths of the time, via Bayes' Theorem, via Laplace's Rule of Succession).
Meta-probability may be a nifty shortcut, but it's reducible to expected outcomes and conditional probability.
Laplace's Rule of Succession can only be used once you have identified a set of possible outcomes and made certain assumptions on the underlying probability distribution. That's not the case at hand.
Applying Bayesian reasoning to such cases requires an universal prior. It could be that humans do a form of approximate Bayesian reasoning with something like an universal prior when reasoning informally, but we know no satisfactory way of formalizing that reasoning in mathematical terms.