Came across this concept while preparing for my exams and found it very interesting. This is basically a rule which helps us decide how much of our wealth we ought to bet in a situation, in which we have a percentage advantage.
Simply put this formula says that the optimum fraction for the bet is "Edge over odds". That is bet a fraction your bankrole (wealth) equal to the advantage you have when compared to a fairgame. If you have a 52% chance of winning a fairgame, your edge is 2% (52%-50%) and your odds is 52%. Hence the optimal fraction that maximises the expected growth of the intial wealth is 2%/52% or 3.85%
Whats more intersting is that the way this formula was developed. This was originally developed by John Kelly (AT & T Labs) based on the work of his colleague (Claude Shannon) who had originally developed an application for dealing with noise issues arising over long distance telephone lines. Kelly then showed how Shannon's "information theory" could be applied to the problem of a gambler who has inside information about a horse race, trying to determine the optimum bet size. The gambler's inside information need not be perfect (noise-free) in order for him to exploit his edge.
This application now finds wide application in gambling, statistical logic, blackjack and in stock markets.
