I guess the stupid question is does it follow from Bayes that if you keep measuring the same probability over and over that you will converge on the 'actual' probability.
That's more like the Bernstein-von Mises theorem, I think. But that only applies if what you're doing is actually Bayesian updating, and it's not obvious to me that that's necessarily happening in the system you describe. (The actors might happen to be doing that, but you haven't said anything about how they make their decisions. Or there might be some more "automatic" bit of the system that's equivalent to Bayesian updating -- e.g., maybe some of the money flows might adjust themselves in ways that correspond to Bayesian updating -- but I don't see any reason to expect that from what you've said.)
This thread is for asking any questions that might seem obvious, tangential, silly or what-have-you. Don't be shy, everyone has holes in their knowledge, though the fewer and the smaller we can make them, the better.
Please be respectful of other people's admitting ignorance and don't mock them for it, as they're doing a noble thing.
To any future monthly posters of SQ threads, please remember to add the "stupid_questions" tag.