vanhees71 said:
Of course you can use a Bayesian interpretation of probabilities to use probability theory as a way to make decisions, e.g., whether after some probability analysis you decide to gamble at the casino or not, but this has nothing to do with physics. In physics all you can decide is which observable(s) you want to observe and how to construct a measurement device to do so. Then you can model this setup within QT and test the probabilistic predictions against your experimental data on ensembles
If you're interested, and this doesn't really have much to do with QBism, this is handled in Bayesian theory by de Finetti's theorem, which replicates your intuition here. Basically if you have an ensemble with members labelled ##i = 1 \ldots n## each with a possible outcome for some observation ##x_i## and you assume members of the ensemble can be exchanged:
##P(x_{1}, \ldots x_{i}, \ldots, x_{j}, \ldots , x_{n}) = P(x_{1}, \ldots x_{j}, \ldots, x_{i}, \ldots , x_{n})##, i.e. it is not important that one member or another gave a particular outcome, then as ##n \rightarrow \infty## you have:
##P(x_{1}, \ldots , x_{n}) \approx \int{P(\rho(x))d\rho}##
where ##\rho(x)## is the probability distribution for the outcomes, i.e. a model, and ##P(\rho)## is the probability of that model being correct.
In plainer terms under the assumption that you are dealing with a large ensemble of identically prepared systems then beliefs/credences about the outcomes
are standard hypothesis testing where one is verifying models ##\rho(x)##.
So it's built into Bayesian theory that testing on large identical ensembles is testing scientific models, but it also allows you to do interesting things like capture errors when you have only medium sized ensembles, i.e. when you're "halfway" between pure "gambling" like in a casino or horse-racing for one shot events and the other extreme with scientific hypothesis testing on large ensembles. In this way your point about the difference between a casino and experimental ensemble is made rigorous as being two different limiting cases of the general theory of probability.