Nick: Sorry, I got it backwards. What you seem to be saying is that well-calibratedness means that relative entropy of your distribution relative to the "correct" one is equal to your entropy. This does hold for the uniform guess. But once again, considering a situation where your information tells you the coin will land "heads" with 99% probability, it would seem that the only well-calibrated guesses are 99%-1% and 50%-50%. I don't yet have an intuition for why both of these guesses are strictly "better" in any way than an 80%-20% guess, but I'll think about it. It definitely avoids the sensitivity that seemed to come out of the "rough" definition, where 50% is great but 49.9% is horrible.