For example, if you say, "The rational belief is X, but the true belief is Y" then you are probably using the word "rational" in a way that means something other than what most of us have in mind
This was copied from here.
Surely it is obvious that there are lots of examples when one might say this. Consider this:
Rob looks in the newspaper to check the football scores. The newspaper says that United won 3-2, but it is a misprint because City actually won 3-2. In this case, the rational belief is that United won, but the true belief is that City won.
Am I missing something?
So I can use "unjustifiable" methods to get even closer to the truth? Screw "rationality", then!
Yes, you can. But with a lower probability. At the limiting case you can add or subtract an epsilon from the 'rational' probability assignment and you will be closer to the truth (0.5 - _different_epsilon_) of the time.
This applies to instrumental rationality too. A lucky guess will win you the lottery. An expected utility calculation will not (except when extremely desperate and similarly lucky).