If you believe that you'll win a lottery, and you win, it doesn't make your belief correct. Correctness comes from lawful reasoning, not isolated events of conclusions coinciding with reality. A correct belief is one that the heuristics of truth-seeking should assign.
It's semantics, but in common usage the "correct belief to have given evidence X" is different than the belief "turning out to be correct", and I think its important to have a good word for the latter.
Either way, I said "accurate" and was referring to it matching the territory, not to how it was generated.
First, there is a decision to assign a belief (that money will be in the box) for reasons other than it being true, which is contrary to heuristics of correctness. Second, with that decision in place, there are now reasons to believe that money will be in the box, so the heuristic of correctness can back the belief-assignment, but would have no effect on the fact it's based upon.
That's one way to do it, in which case it is pretty similar to forging beliefs that don't end up matching the territory. The only difference is that you're 'coincidentally' right.
It's also possible to use your normal heuristics to determine what would happen conditional on holding different beliefs (which you have not yet formed). After finding the set of beliefs that are 'correct', choose the most favorable correct belief. This way there is never any step where you choose something that is predictably incorrect. And you don't have to be ready to deal with polluted belief networks.
Am I missing something?
Omega appears to you in a puff of logic, and presents you with a closed box. "If you open this box you will find either nothing or a million dollars," Omega tells you, "and the contents will be yours to keep." "Great," you say, taking the box, "sounds like I can't lose!" "Not so fast," says Omega, "to get that possible million dollars you have to be in the right frame of mind. If you are at least 99% confident that there's a million dollars in the box, there will be. If you're less confident than that, it will be empty. I'm not predicting the state of your mind in advance this time, I'm reading it directly and teleporting the money in only if you have enough faith that it will be there. Take as long as you like."
Assume you believe Omega. Can you believe the million dollars will be there, strongly enough that it will be?