You might want to look into the maths related to various paradoxes: unexpected hanging, Raven paradox, liar paradox, two envelopes problem, Zeno's paradox, Blue Eyes problem and game theory like the Prisoner's dilemma. Wikipedia, Math Stackexchange and Less Wrong have much discussion on these paradoxes.
If you want to improve your rationality, it's not enough to just know the solution. You have think very carefully about what reasoning made you believe the incorrect answer in the first place and how to adjust your intuitions so that they are correct.
I have started to put together a sort of curriculum for learning the subjects that lend themselves to rationality. It includes things like experimental methodology and cognitive psychology (obviously), along with "support disciplines" like computer science and economics. I think (though maybe I'm wrong) that mathematics is one of the most important things to understand.
Eliezer said in the simple math of everything:
I want to have access to outlook-changing insights. So, what math do I need to know? What are the generally applicable mathematical principles that are most worth learning? The above quote seems to indicate at least calculus, and everyone is a fan of Bayesian statistics (which I know little about).
Secondarily, what are some of the most important of that "drop-dead basic fundamental embarrassingly simple mathematics" from different fields? What fields are mathematically based, other than physics and evolutionary biology, and economics?
What is the most important math for an educated person to be familiar with?
As someone who took an honors calculus class in high school, liked it, and did alright in the class, but who has probably forgotten most of it by now and needs to relearn it, how should I go about learning that math?