Related to: Extreme Rationality: It's Not That Great

A while back, I said provocatively that the rarefied sorts of rationality we study at Less Wrong hadn't helped me in my everyday life and probably hadn't helped you either. I got a lot of controversy but not a whole lot of good clear examples of getting some use out of rationality.

Today I can share one such example.

Consider a set of final examinations based around tests with the following characteristics:

* Each test has one hundred fifty true-or-false questions.
* The test is taken on a scan-tron which allows answers of "true", "false", and "don't know".
* Students get one point for each correct answer, zero points for each "don't know", and minus one half point for each incorrect answer.
* A score of >50% is "pass", >60% is "honors", >70% is "high honors".
* The questions are correspondingly difficult, so that even a very intelligent student is not expected to get much above 70. All students are expected to encounter at least a few dozen questions which they can answer only with very low confidence, or which they can't answer at all.

At what confidence level do you guess? At what confidence level do you answer "don't know"?