I listed one of the things that could be going on as one's distribution being skewed, which however standardly happens for a distribution of one's future probabilities as one veers away from .5, so I was confused and shouldn't have listed it as a thing going on. I ended up defining "chunks of equal size" in an unreasonable way by relating them to binomial with p=.5, though the math is correct given that unreasonable definition. My brain barfed on that; sorry for making you read this. The idea for the post came more from a utility estimate being a random walk if one learns about independent random components to it, and I'm now rewriting the post in a way that's correct.

(Whew, it took me a while to articulate the exact thing I did wrong.)