Kelly Criterion Betting - Get Mathematics on Your Side

You may not have heard of scientific researcher J.L.Kelly, but this relatively obscure academic is responsible for producing one of the world’s best known and most successful staking strategies. The beauty of the Kelly Criterion is that it is both simple yet powerful and can be used with any type of sports betting. In fact, Kelly Criterion investing has also been applied by experts who trade the financial markets. So just what is the Kelly Criterion?

Topics on this page

The Basics and the Kelly Criterion Formula

The principle of the Kelly Criterion is that you can use a mathematical formula to work out exactly how much money to stake on a particular bet. This formula calculates the stake based on the probability of the bet being successful.

This sounds simple, but it is worth noting at this stage that there is a degree of complication associated with the Kelly Criterion betting. The greater the probability that a particular bet will be successful, the higher the stake that the Kelly Criterion recommends, but in order to apply it properly, you need to be reasonably accurate at estimating true probabilities.

  • In-Play betting sports
  • Exclusive offers
  • Game Winner option
£30Matched Free Bet if your first Acca loses Claim Offer
Betway Review
  • Unibet TV
  • Stats & Livescore
  • Horse racing
£40money back Claim Offer
Unibet Review
  • Betting Exchange
  • Live results
  • Live Streaming
£100in free bets Claim Offer
Betfair Review
*18+ T&Cs Apply!

Kelly Criterion Example

Let’s say that you have been looking at a football match between Chelsea and Stoke City. Your estimate of Stoke City’s chances of winning the game is 35 per cent and the current odds quoted by a bookmaker on a Stoke City win are 3/1.

Knowing this detail, you can use the Kelly Criterion to establish your stake size with this formula:

  • (B*W – L) / B = F

It looks a little complicated, but once you know what the letters stand for, it is a straightforward equation. ‘B’ stands for the odds of the bet in question minus 1, which in this case, are 3/1 or 4.0 (B=3.0). The letters ‘W’ and ‘L’ in this equation are the probabilities of a winning and losing bet. Here, you have calculated the probability of a Stoke City win to be 35 per cent, so ‘W’ will be 0.35, and ‘L’ will be 0.65. The last letter in the equation, ‘F’ is the answer you are seeking, which is what fraction of your bankroll should you use to make the bet.

In the case of the Stoke City bet mentioned above, we can add the figures that we know to the equation to produce the following calculation:

  • ((3*0.35)-0.65) / 3 = 0.1333

In this bet, if you are using the Kelly Criterion, you would therefore bet 13 per cent of your bankroll on Stoke City beating Chelsea.

The Ability to Spot Value

Kelly Criterion - the ability to spot value

No sports punter can afford to ignore value, and if every bet you make is a value bet, you will be in profit in the long term. A value bet is a bet where the probability of winning is greater than the price from the bookmaker would suggest.

For example, in the case of the bet above, the odds on a Stoke City win are 3/1, which equates to a probability of 25 per cent. But we think that Stoke’s chances are actually more like 35 per cent, making this a value bet.

In this case, the Kelly Criterion formula has produced a positive number (0.13 or 13 per cent). This means that, if your assessment of the probabilities is correct, you have found a value bet. But if the formula throws up a negative number, this would mean that the bet did not have a positive expectation, as the chances of the bet winning were smaller than the probability implied by the bookmaker’s betting odds. When this happens, by producing a negative number, the Kelly Criterion is telling you that you have not found value, and therefore should not bet.

The Advantages and Disadvantages of Kelly Criterion Investing or Betting


The first is that this formula is a mathematically precise method of striking the right balance when it comes to choosing your stake size. In theory, increasing your stake according to the extent of the expected value is the most effective way to make the most of your betting edge, and if you are skilled at assessing an outcome’s probability, you will be able to maximise your profit.

Yet despite being a mathematically sound method, the Kelly Criterion is also easy to apply. Once you have gone through the calculations a few times, you will find that applying it becomes almost second nature, and should you need a little help, there are plenty of online Kelly Criterion calculators available to assist.

Finally, as we have seen above, the Kelly Criterion can help you to identify bets that don’t provide value. So, when the formula produces an answer that has a negative number, you can avoid making a bet that has a negative value expectation.


As with any staking system, the Kelly Criterion has its drawbacks. The most obvious is the fact that it depends entirely on your ability to accurately estimate the true probabilities of a bet and to be able to do so consistently. If your probability estimates are not accurate, then you will end up staking amounts that are not appropriate, and your betting will be inefficient.

The other downside of the Kelly Criterion is that it is a risk-heavy staking system that can often lead punters to stake more of their bankroll than might normally be the case. For example, in the Stoke City bet mentioned above, the Kelly Criterion recommends betting 13 per cent of your bankroll. This is a relatively high figure, and if you have a run of bad results, your bankroll could deteriorate quickly. For this reason, many punters adjust the stake recommended by the Kelly Criterion, by a half or more, to reduce the risk.


Punters are often tempted to employ a variety of exotic staking methods, many of which have no solid basis. That is not the case the with Kelly Criterion, which is rooted in mathematics and for punters who are confident in their ability to work out true probabilities, the Kelly Criterion is the most efficient and effective of all other betting types.

Other Betting Types