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JGWeissman comments on Frequentist Magic vs. Bayesian Magic - Less Wrong
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Thank you for introducing me to the "universal prior".
The model I'd have used in explaining a sequence of such coin flips would indeed assume that the machine generates each coin independently as heads-biased with fixed probability H. But rather than fixing H=1/2, I'd have a prior distribution for H (probably uniform).
How superior would the universal prior be to this? I confess I can't do the math.
One way that the universal prior is superior to the one you propose is that it can notice that the machine alternates between producing heads-biased and tails-biased coins.
In this comment, I described another prior (still much easier to use that the universal prior) that could detect this pattern, and also noted another behavior the machine can have that my prior can't notice.
The advantage of the universal prior is that it assigns non-zero probability to all computable behaviors the machine might have, so that it can concentrate probability into that behavior if the machine exhibits it.