The Kelly Criterion

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The Kelly Criterion was developed by scientific researcher J.L. Kelly in 1956, and has become one of the world’s most well-known betting strategies. It is a method used to maximise the potential return of any particular bet or investment, and can be applied to any form of sports betting. It has also been widely used in financial markets. While there is a level of complexity involved in its use, as well as a degree of risk, it has become popular amongst bettors.

What is the Kelly Criterion?

The Kelly Criterion is a relatively simple mathematical formula that can be used to work out the ideal level of stake to be used for any particular bet by working out the expected level of return from the bet, and applying this to the bettor’s betting bank.

Although this sounds straightforward, there is an element of complication. One effect of the Kelly Criterion is that the greater the expected probability of the win, the higher the level of the stake, thus maximising the return. So to be able to use the formula in the most efficient way, you need to be able to calculate the chances of any particular bet being successful.

john larry kelly

How does it work?

For the sake of demonstrating how the Kelly Criterion works, we can assume that you are able to assess the probability of a particular bet being successful with a reasonable degree of accuracy. With this information, we can then use the Kelly Criterion to calculate the stake, by working out the following simple formula:

(bp – q) / b = f

In this equation, ‘b’ refers to the multiple of the available odds on the bet in question. For example, if the decimal odds for a bet are 4.0, then ‘b’ is 3. The letters ‘p’ and ‘q’ refer to the probability of the bet winning and losing respectively. So if a bet has a 55% chance of being successful, then p will be 0.55 and q will be 0.45. Finally, ‘f’ is the answer to the equation and refers to the fraction of your total betting bank that you should use in this bet.

If we take an example of a bet where the decimal odds are 4.0 and the probability of the bet winning are 35%, we can apply the relevant figures to the equation as follows:

((3*0.35)-0.65) / 2 = 0.4

Based on the Kelly Criterion, for this bet, although the probability of losing is higher than the probability of winning, you should be staking 40% of your betting bank.

kelly criterion equation

The importance of value

An important aspect of the Kelly Criterion is that it can also tell you when a bet offers value. Value is a vital concept in sports betting. Broadly speaking, you have found a value bet when the probability of its being successful is higher than the implied probability of the odds for that bet. For example, if the decimal odds of a bet are 4.0, then the implied probability of that bet is 25% or 0.25. If you think that the likelihood of the bet being successful is greater than 25%, then you have identified a bet with a positive expected value.

In the example above, the answer to the Kelly Criterion formula is a positive number. This tells you that you have identified a bet with value. If the answer to the equation had been a negative number, this would show that the bet did not have positive expected value, or in other words, that the likelihood of the bet being successful was smaller than the implied probability of the odds. Since it is a fundamental rule of betting that you should only bet when there is a positive value expectation, when it throws up a negative number, the Kelly Criterion is effectively telling you that you shouldn’t bet.

value importance

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The main advantage of the Kelly Criterion is that it helps a bettor to strike the right balance between risk and safety, between growing a betting bank and safeguarding it. By increasing the size of the wager in proportion to the expected value, you are maximising your edge, and for those who are adept at calculating the probability of a bet being successful, the Kelly Criterion offers the most effective way to profit from their skill.

Another advantage of the Kelly Criterion is that the system is relatively easy to use. Once you have carried out the calculations a few times, it becomes familiar, and if you do need help, there are a number of free Kelly Criterion calculators online. The system also helps you to spot bets that don’t offer value. When the formula throws up an answer with a negative number, you have a useful warning not to bet.

kelly criterion advantages


There are two main disadvantages associated with the Kelly Criterion. The first is that it depends entirely on your ability to accurately and consistently work out the real probabilities of bets. If your estimates are inaccurate, then using the formula will lead to incorrect stake size recommendations and an inefficient use of your betting bank.

The second disadvantage is that this system is inherently aggressive. It can lead to the bettor using significant fractions of their betting bank. In the example used above, the formula suggested using 40% of your betting bank. This is a very high figure, given that many successful bettors will rarely bet more than 5% of their bank at any time. As a result, it is common for those using this system to half or quarter the suggested stake, in order to offer more protection for their betting bank.

kelly criterion disadvantages


The Kelly Criterion is based on solid mathematics and has a lot to recommend it. For those adept at calculating true probabilities, it offers a dynamic way of maximising their rewards. It is important to remember, however, that the Kelly Criterion is essentially a staking system. It will not identify potential bets and is not an automatic route to profit. It should therefore be used with caution, particularly by those new to betting.