Tim - In the example we have been discussing, no confirmation of the actual theory (the one I gave in approximate outline) happens. The actual theory makes probabilistic predictions about events (it also makes non-probabilistic predictions) and tells you how to bet. Getting 20 white beans doesn't make the actual theory any more probable - the probability was a prediction of the theory. Note also that a theory that you are being tricked might recommend that you choose the mixed bag when you get 20 white beans. Lots of theories are consistent with the evidence. What you need to look for is things to refute the possible theories. If you are concerned with confirmation, then the con man wins.

So I am not agreeing that induction and confirmation are fine any percentage of the time (how did you get that 90% figure?). When you consider the actual possible theories of the example, all that is happening is that you have explanatory theories that make predictions, some probabilistic, and that tell you how to bet. The theories are not being induced from evidence and no confirmation takes place.

You haven't explained how we assign objective probabilities to theories that are false in all worlds.