This seems like a dead thread, but I'll chance it anyway.

Elizer, there's something off about your calculation of the expected score:

The expected score is something that should go up the more certain I am of something, right?

But in fact the expected score is highest when I'm most uncertain about something: If I believe with equal probability that snow might be white and non-white, the expected score is actually 0.5(-1) + 0.5(-1) = -1. This is the highest possible expected score.

In any other case, the expected score will be lower, as you calculate for the 70/30 case.

It seems like what you should be trying to do is minimize your expected score but maximize your actual score. That seems weird.

Looks like you've just got a sign error, anukool_j. -1 is the lowest possible
expected score. The expected score in the 70/30 case is -0.88.
Graph
[http://www.wolframalpha.com/input/?i=graph+x+*+%28log+base+2+of+x%29+%2B+%281+-+x%29+*+%28log+base+2+of+%281+-+x%29%29%2C+x+%3D+0+to+1]
.

This seems like a dead thread, but I'll chance it anyway.

Elizer, there's something off about your calculation of the expected score:

The expected score is something that should go up the more certain I am of something, right?

But in fact the expected score is highest when I'm most uncertain about something: If I believe with equal probability that snow might be white and non-white, the expected score is actually 0.5(-1) + 0.5(-1) = -1. This is the highest possible expected score.

In any other case, the expected score will be lower, as you calculate for the 70/30 case.

It seems like what you should be trying to do is minimize your expected score but maximize your actual score. That seems weird.