If you're interested in this, check out Cover's Information Theory textbook — the rabbit hole goes much deeper. One of the most interesting examples, is that when you're betting on a random event, Shannon entropy tells you how much to bet & how quickly you can compound your wealth. Cover covers (heh) this, and the original paper is Kelly: http://www.herrold.com/brokerage/kelly.pdf
Kelly's paper (based on this paper by Shannon), is responsible for fundamentally reshaping equity, commodity and even sports betting markets.
I highly recommend William Poundstone's book, "Fortune's Formula" as a biography of those ideas - it's almost as good as any Michael Lewis book on the subject would be.
