What is the Kelly Criterion?
Kelly’s Criterion is a mathematical formula that helps you decide what size your bets should be. The formula is often used in stock trading as well as when gambling at the Casino or on sports. There are many successful investors who use Kelly’s system for larger profits, including Warren Buffet.
Many believe that the Kelly Criterion is the most successful system that exists today in the betting market. But this often only applies in theory, there are circumstances when this theory is not as successful in reality.
The formula is only useful if you are sure that there is value in your investment or in your bet. If there is no value in a bet, then you should not use this formula. There are two important reasons for using this formula:
- Maximising your winnings depending on your advantage
- Reduce your chances of going bankrupt
How do you use Kelly’s Criterion?
The formula for Kelly’s Criterion is in principle very simple, it is about your bet being as large as the probability of a win minus the likelihood of a loss. This is to say, if you have a 55% chance of winning and a 45% chance of losing, you should bet 10% of your betting account (55-45+10). As mentioned earlier, the formula discourages you from betting on a game if the value of it is zero or minus. The system reduces the chances of becoming bankrupt because it assumes you always play a certain percentage of your bankroll.
The Kelly Criterion - Formula and example
(likelihood of a win x odds – 1) / (odds – 1) =Bet
You have thought about betting on Arsenal to win at home against Tottenham Hotspur. According to your evaluation, Arsenal has a 50% chance of winning. This also means that there is a 50% chance that the match will end in a draw or a Tottenham win, which would lead to a loss in total. The betting company offers odds of 2.10 on an Arsenal win. If we put all this in a formula, it looks like this:
(0.50 x 2.10 – 1) / (2.10 – 1) = 0.045
This means that according to Kelly’s Criterion, you should use 4.5% of your betting account on this match as this is the advantage you have against the betting company that is offering the odds.
Three disadvantages with the Kelly Criterion
- It requires that you can estimate a likelihood as an exact percentage.
- A problem occurs if you bet on multiple matches at the same time.
- May cause major losses.
1. Unfortunately, the system cannot help you find value in a bet. Finding value in the odds market is hard. It’s even harder to be able to judge the precise probability as a percentage for different outcomes in a match. To be able to judge if the outcome of a match has a 52% or a 54% likelihood you require a lot of knowledge, something that is a definite requirement when following Kelly's Criterion.
2. The other disadvantage with Kelly’s Criterion is the problem of betting on several matches at the same time. If you use the same betting account for all bets, you can end up betting huge sums. A clear example of this would be if you found four different matches that you bet on at the same time, and that was of value.
Match one has a value of 35% Match two has a value of 25% Match three has a value of 18% Match four has a value of 27%
Should you place bets on these four matches based on Kelly’s Criterion, it would mean you must bet 105% of your account. An impossibility.
3. Another problem with Kelly’s Criterion is that you can significantly alter the size of your betting account. Certainly, your account can grow rapidly, but at the same time, it can shrink just as fast. If you find a value of 50%, you will then invest 50% of your whole account. If you lost the bet, this would mean that your account would have halved with just one bet. Even if the bet has a mathematical grounding, there are few people who would be willing to bet half their account on one game.
The fractional Kelly method
Due to the disadvantages and risks associated with the system, many variants have been created. The most well-known variant is known as the fractional Kelly. This variant entails that you must reduce your bet at a certain percentage of the core system. It could be that you reduce the percentage by half or more, but the important thing is that the percentage decrease is constant and the same decrease should apply to all your bets. The Fractional Kelly Method is a significantly less risky method compared to the standard version.
An example of a fractional Kelly
You have found a value of 10% compared to the odds on a match. According to the Kelly Criterion, you should focus the 10% on your betting account. However, instead, you use the system for a ‘half Kelly’ which means that you half the bet as a percentage and bet 5% of you account instead.
This means that your winnings will be less but also that the risk of losing large sums of money on one bet will be reduced. The possibility of long-term profitability increases, even if it is unlikely to be fast. If you know that you have a long-term edge on the market, there is no point in striving for the quick and big wins. After all, betting is a marathon, not a sprint.