I guess this is the point where humans and theoretical rational agents diverge. Rational agents don't learn rationality - it's just assumed that they come pre-wired with all the correct mathematics and philosophy required to make optimal choices for all possible games.

But on the human side, I still don't think that's really a valid comparison. Being able to use Bayes' rule improves rationality in the general case. It falls under the heading of "philosophy, epistemology, mathematics".

Chess just gives you knowledge about a specific system. It falls under the heading of "science, inference, evidence".

There's a qualitative difference between the realm of philosophy and mathematics and the realm of reality and observation.