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cousin_it comments on Bayesian probability as an approximate theory of uncertainty? - Less Wrong Discussion
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It seems to me that if you have a coin, your probability distribution on envelopes should still depend on the strategy you adopt, not just on the coin. Are you sure you're not sneaking in "planning-optimality" somehow? Can you explain in more detail why the decision on each day is separately "action-optimal"?
I think I misunderstood what you meant by "impossible if you're making decisions using Bayesian probability." I wasn't trying to avoid being "planning-optimal". It is not as though the agent is thinking, "The PRNG just output 0.31. Therefore, this envelope is more likely to contain the money today.", which I guess is what "action-optimal" reasoning would look like in this case.
When I said that "you are making your decisions in accordance with Bayesian probability theory", I meant that your choice of plan is based on your beliefs about the distribution of outputs generated by the PRNG. These beliefs, in turn, could be the result of applying Bayesian epistemology to your prior empirical experience with PRNGs.
Yeah. It looks like there's a discontinuity between using a RNG and having perfect memory. Perfect memory lets us get away with "action-optimal" reasoning, but if it's even a little imperfect, we need to go "planning-optimal".