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AlexMennen comments on An Intuitive Explanation of Solomonoff Induction - Less Wrong
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If you update by a ratio s/p for one hit on the helmet, you should update by s^2/p^2 for two hits, which looks just like updating by s/p twice, since updating is just like multiplying by the Bayes factor.
Hmm. I'll have to learn a bit more about the actual theory and math behind Bayes' theorem before I can really go deeper than this in my analysis without spouting out stuff that I don't even know if it's true. My intuitive understanding is that there's a mathematical process that would perfectly explain the discrepancy with minimal unnecessary assumptions, but that's just intuition.
For now, I'll simply update my beliefs according to the evidence you're giving me / confidence that you're right vs confidence (or lack thereof) in my own understanding of the situation.