The thing that distinguishes the coin case from the wind case is how hard it is to gather additional information, not how much more information could be gathered in principle. In theory you could run all sorts of simulations that would give you informative data about an individual flip of the coin, it’s just that it would be really hard to do so/very few people are able to do so. I don’t think the entropy of the posterior captures this dynamic.
The thing that distinguishes the coin case from the wind case is how hard it is to gather additional information, not how much more information could be gathered in principle. In theory you could run all sorts of simulations that would give you informative data about an individual flip of the coin, it’s just that it would be really hard to do so/very few people are able to do so. I don’t think the entropy of the posterior captures this dynamic.