Kelly formula

Kelly’s Formula was created by scientist John Larry Kelly. According to the formula, there is always an ideal bet to be made, depending on the odds and the probability of a hit. This guide provides the necessary prerequisites for the Kelly Formula to work and explains its advantages and disadvantages.

What is Kelly’s formula?

How to use Kelly’s formula?

Three disadvantages of Kelly’s formula

Kelly’s fractional method

With Kelly’s Formula, you can calculate the exact amount to be bet on a game, depending on the relevance of the bet. This helps to optimize your chances of winning and minimize your chances of losing. However, this is easier in theory than in practice.


Kelly’s formula is a mathematical formula that helps determine the value of your bets. The formula is often used when trading stocks, playing in casinos or placing sports bets. Many successful investors use the Kelly Formula to generate more profit.

Many believe that the Kelly Formula is the most successful system currently available on the betting market. However, there may be circumstances where this theory is not so successful in reality.

Many believe that the Kelly Formula is the most successful system currently available on the betting market.

The formula can only be used if you know that your investment or bet is worth it. If your bet is not promising, you should not use this formula. There are two main reasons for using Kelly’s Formula:

Maximize your earnings

Reduce your risk of losing all money


At first, Kelly’s formula is very simple. The formula says that the value of your bet must be as big as the probability of winning minus the probability of losing. If you have a 55% chance of winning and a 45% chance of losing, you must bet 10% of your bankroll (55-45 = 10). As we mentioned earlier, the formula prevents you from placing a bet when the value is zero or less. The system reduces the possibility of you losing all your money, since it assumes that you always bet a percentage of your bankroll.

Kelly’s Formula:

bp-q / b

b = odds -1
p = chance of winning (you calculate)
q = chance of losing (which is 1 – p)

(Chance to win x odds – 1) / (odds – 1) = stake


You thought about betting on Team A to beat Team B. According to your analysis, Team A has a 50% chance of winning. This means that there is a 50% chance that the game will end in a draw or that Team B will win, which would be a loss for you. The bookmaker offers odds of 2.10 for Team A to win. Using this data in the formula would look like:

(0.50 x 2.10 – 1) / (2.10 – 1) = 0.045

According to Kelly’s Formula, you must bet 4.5% of your bankroll on this game, as this is the advantage you have over the bookmaker.


Kelly’s formula expects a probability to be estimated as an exact percentage. The problem arises when you bet on several games at the same time.

Kelly’s formula can lead to big losses because:

1. It is very difficult to find exact values ​​to bet. In addition, it is even more difficult to define the precise probability of the different results of a game. You need to have a lot of knowledge to find out if the probability of a team winning is 52% or 54%, for example. This knowledge is an essential requirement for Kelly’s Formula.

2. The second disadvantage of Kelly’s formula is the problem that arises when you bet on several games at the same time. If you use the same account for all bets, you will end up having to bet large amounts. For example, if you find four games and bet on all of those games at the same time.

The first game is worth 35% of your bankroll

The second game is worth 25% of your bankroll

The third game is worth 18% of your bankroll

The fourth game is worth 27% of your bankroll

If you use Kelly’s formula for all of these bets, it means that you must bet 105% of your account, which is impossible.

3. Another problem with Kelly’s formula is that you can change your bankroll value a lot, increasing or decreasing your money quickly. If you find a 50% value, you will need to wager 50% of your account. If you lose this bet, it means that you will lose half of your money with that bet. Although Kelly’s formula has a mathematical basis, there are still few who take this risk on just one bet.


Many variations of the system were invented due to the uncertainties and risks associated with it. The best known variant is called Kelly’s Fractional Method. According to this variant, you must bet only a certain percentage of the main system. You can cut the percentage in half or more. It is important that the percentage reduction is constant and used in all your bets. Kelly’s fractional method is a much less risky variant than Kelly’s formula.


You compared the chances of winning and losing a game and found the value of 10%. According to Kelly’s Formula, you must bet 10% of your bankroll. However, if you prefer to use the “half Kelly” system, you will cut the bet in half. In this case, your bet will be only 5% of your bankroll.

Although the profit is lower, you minimize the risk of losing large amounts on a single bet. The chances of long-term success increase, although this happens more slowly. If you know you have a long-term advantage in the market, there is no need to take a chance to profit quickly. Online betting should be seen as a marathon and not a sprint.

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