Comment by AnotherGoodName

I back of the enveloped it wrong is what :(.

It's -log2(0.75) for getting a 75% chance right and -log2(0.25) for getting it wrong. I should have stated .4 bits and 2bits respectively not 0.5 and 2.4. Sorry! Good catch.

It's 3.2 vs 4bits. Now that may not seem huge but the probabilities tend to be at the more extreme ends if the predictor is any good. Once you start going towards the 99% range you get extreme efficiency.