Kelly Criterion: How to Maximize Your Gains & Minimize Your Losses

If you knew you would win 100% of your bets, you would be a fool not to bet your entire bankroll on each bet. This would maximize your return and, because you knew 100% of your bets would win, you would have 0% risk of going bust.

If you knew you had 0% chance of winning your bets, you would be a fool to bet – ever.

Luckily, we all have more than a 0% chance to win, but sadly, we also all have less than a 100% chance to win. Therefore, we must decide how much to wager each time based on some method. A method which seeks to maximize your bankroll, while minimizing the chances it goes to $0 is the Kelly Criterion method. This method, developed by John L. Kelly of Bell Labs in the 1950s, was developed to maximize return while minimizing chance of going broke. An interesting side note is Kelly died of a stroke on a Manhattan sidewalk at 41, and it is believed he never placed a bet. The Kelly formula is well documented, and a quick Google search will yield countless articles and Kelly calculators for you to peruse.

By employing the Kelly Criterion Method, one can calculate the maximum amount to wager, which will result in maximum growth in bankroll and minimum risk of going broke. Note the words “minimum risk,” as this does not equate to “zero risk of going broke.” Using Kelly still offers the opportunity for going broke. It just balances maximum growth in bankroll with risk of losing it.

The key variable in Kelly is the expected win rate. Most of us overestimate our chances of winning each bet. If you overestimate your chance of winning, no magical formula will save your bankroll. The other key variable in the Kelly method is the odds you are able to secure on the bet.

Here’s an example. If – given your history and future projections – you expect to win 55% of your bets and you get odds of 2.0 (+100 in US Odds), then Kelly says you should bet 10% of your bankroll each time to grow your bankroll as quickly as possible while minimizing the chances you go broke.

However, if your 55% win rate is really only 49% – then you WILL go broke. OR, if your 55% win rate is good, but you only get 1.5 odds – you WILL go broke. The odds you get are easy to figure out. Which is why many people who go broke using Kelly do so because they overestimate their chances to win. Don’t be deluded into thinking because you’ve employed some fancy empirical formula to figure out how much to bet that the most important part of that formula is still likely to fail you. Knowing your expected win rate is key.

Even those who have a statistically valid estimate of their win rate and employ Kelly still use an alternative version of Kelly which results in much less chance of going broke. Versions such as 1/2 Kelly and 1/3rd Kelly are common and, as the names imply, result in the bettor betting one-half or one-third of what the Kelly formula tells them to – thereby reducing the impact to their bankroll of any variance from expected winning percentage.

If you’re just throwing a little bit of extra cash in an account to play around and have some fun each season, then you don’t need to sweat this. But if you’re trying to figure out how to make some long-term money doing this, use Mr. Kelly’s cool formula to help you keep it between the ditches (and also potentially make a ton of money).