GAMBLER'$ HANDBOOK

For example, we have a horse race where the bookies are offering 2-to-1 but on some inside information we judge the true odds to be around 3-to-1. Also, our current bankroll is $10,000. So according to the Kelly Criterion:-

b = 2-to-1 = 2
p = 3-to-2 = 40% = 0.4
q = (1-p) = 0.6

f* = ( (2 * 0.4) – 0.6 ) / 2
= 0.2 / 2
= 0.1 or 10%

So we should put 10% of our bankroll on the horse or $1000 of our $10,000 bankroll.

The Kelly Criterion is used by horse and sports gamblers but also by fund managers for stocks and other financial investments. You could even apply it to poker, where often the odds are as if all players have equal chance of winning but the probabilities of each player winning are not equal.

The Kelly Criterion is a much more sophisticated approach to bankroll management beyond the ad hoc rules of thumb. Yet, in chasing the fastest long run bankroll growth the Kelly Criterion is quite aggressive. In application there is a real risk in making a mistake in assessing the true odds. To reduce this risk and the inherent volatility of betting so much your bankroll, it is common to bet half of what the Kelly Criterion suggests. This approach sets the Kelly Criterion more as a maximum cap on the betting amount. This makes sense because betting anything over what the Kelly Criterion suggests is counter-productive and will only reduce long run bankroll growth. Never-the-less, if you want to go for maximum bankroll growth, the Kelly Criterion will tell you how much to bet in order to achieve the highest level of long run bankroll growth.

Good Luck

Notes