# The Kelly Criterion

Yeah, I know.  The title of this article sounds like the title of a spy novel.  John Kelly was an interesting fellow, but as far as I know he was never an undercover agent.  John Kelly worked at AT&T’s Bell Labs in the fifties.  In 1956 he developed what has become known as the Kelly Criterion. His original formulas dealt with long-distance telephone transmission signal to noise ratios. Exciting stuff, right? But the gambling community quickly grasped that Kelly’s approach could be used to help calculate the optimal amount to bet on a horse race.

How does that work?  Essentially, the “Kelly”  is an “up as you win” wagering system designed to maximize the expected growth of the player’s bankroll. This is accomplished by adjusting the size of the bet to an optimum level based on the player’s advantage or positive expectation. It assumes that the player only places action when he has a positive expectation.

In horse racing, this is based on the player’s own handicapping of the race. Of course, the Kelly has also been adapted for other “bets,” including blackjack, sports betting, and playing the stock market. Does it have any application in casino craps? Well, the answer to that is – depends. It depends on your advantage – and how consistent it is.

Let’s walk through a simple example first, then I’ll show you how to determine just what fraction of your bankroll should be wagered based on the Kelly.

Let’s say you have \$100 bankroll and are skilled enough at tossing the dice to win on the ten fifty percent of the time. For the sake of this example we’ll bet \$20 – or 20% of your bankroll on the ten. Winning bets will be paid at 2-to-1. We’ll ignore the commission for now just to keep it simple. If you win this first \$20 bet, you win \$40, increasing your bankroll to \$140. How much is your next bet?