I think the analysis in this post (and the others in the sequence) has all been spot on, but I don’t know that it is actually all that useful. I’ll try to explain why.
This is how I would steel man Sir Percy’s decision process (stipulating that Sir Percy himself might not agree):
Most bets are offered because the person offering expects to make a profit. And frequently, they are willing to exploit information that only they have, so they can offer bets that will seem reasonable to me but which are actually unfavorable.
When I am offered a bet where there is some important unknown factor (e.g. which way the coin is weighted, or which urn I am drawing from), I am highly suspicious that the person offering the bet knows something that I don’t, even if I don’t know where they got their information. Therefore, I will be very reluctant to take such bets
When faced with this kind of bet, a perfect bayesian would calculate p(bet is secretly unfair | ambiguous bet is offered) and use that as an input into their expected utility calculations. In almost every situation one might come across, that probability is going to be quite high. Therefore, the general intuition of “don’t mess with ambiguous bets—the other guy probably knows something you don’t” is a pretty good one.
Of course you can construct thought experiments where p(bet is secretly unfair) is actually 0 and the intuition breaks down. But those situations are very unlikely to come up in reality (unless there are actually a lot of bizarrely generous bookies out there, in which case I should stop typing this and go find them before they run out of money). So while it is technically true that a perfect Bayesian would actually calculate p(bet is secretly unfair | ambiguous bet was offered) in every situation with an ambiguous bet, it seems like a very reasonable shortcut to just assume that probability is high in every situation and save one’s cognitive resources for higher impact calculations.
Seconded. Or more generally, a framework for how to put together a good reading list, would be extremely helpful.