Here's some more info theory: the long-term payoff of a horse-race betting strategy is expressed by the "doubling rate" of your "portfolio," in which each set of bets is treated like an investment. If X is the outcome of the race, and you receive some side-information Y (for example, that Secretariat has been replaced by a horse which was stolen from the dog-food factory), then the doubling rate changes by an amount equal to I(X;Y), the mutual information between X and Y, which can in principle be computed.

In the stock market, side information changes your doubling rate by an amount less than or equal to I(X;Y). Perhaps, in some cases, omniscience won't help you.