Thanks for this, it really helped.

it doesn't guarantee that we have time, resources, or inclination to actually calculate it

Here's how I understand this point, that finally made things clearer:

Yes, there exists a more accurate answer, and we might even be able to discover it by investing some time. But until we do, the fact that such an answer exists is completely irrelevant. It is orthogonal to the problem.

In other words, doing the calculations would give us more information to base our prediction on, but knowing that we can do the calculation doesn't change it in the slightest.

Thus, we are justified to treat this as "don't know at all", even though it seems that we do know something.

Probability is in the mind

Great read, and I think things have finally fit into the right places in my head. Now I just need to learn to guesstimate what the maximum entropy distribution might look like for a given set of facts :)

Well, that and how to actually churn out confidence intervals and expected values for experiments like this one, so that I know how much to bet given a particular set of knowledge.