Betting with the Kelly Formula

What is the goal of betting with the Kelly Formula?

The goal of this betting strategy is to find the optimal wager for your bets in order to grow your betting budget to the maximum extent possible. The underlying betting principle involved in the Kelly Formula is based on work done by American mathematician John Larry Kelly Jr., who, back in 1956, defined the so-called Kelly Criterion. Originally, this ingenious strategy intended to maximize betting winnings was not focused on the world of sports betting. Why? Without immersing ourselves in the intricacies of mathematics, let us simply say this: Betting with the Kelly Strategy is based on win probabilities that remain constant and must be repeated multiple times in order to guarantee long-term winnings. Naturally, in the world of sports betting this isn’t possible – after all, we are not sitting at a roulette table or rolling poker dice, nor can we precisely calculate the probability of certain results occurring. As a sports tipster, all we can do is try to calculate the probabilities better and more precisely than the bookie in question – which means, discovering those so-called “value bets”! Of course, this now poses the question: How can we apply this mathematical theory to the practice of sports betting? More on this topic in the following section.

How can the Kelly Formula be used in sports betting?

As we explained previously, the Kelly Formula was not originally intended for sports betting. Nevertheless, this strategy can be applied to the sporting arena and provide valuable help. With respect to betting strategies, the focus is generally on odds along with risk minimization. Especially with regards to money management strategies, a very important point is frequently overlooked: the question as to an appropriate and/or ideal level of wager for individual bets. And it is precisely here that the Kelly Formula comes into its own. The key to this approach: The basis for the Kelly Strategy is your total available betting budget! The second factor: your own calculation of the probabilities of winning. Precisely how that works can be read in our article on value bets. It goes without saying that calculations of your personal chances of winning are associated with a certain degree of risk.

Example of calculating wagers with the Kelly Formula

Now let us go one step further: Here, we present to you the concrete application of the Kelly Formula. As an example, we will look at a 3-way bet. Let us assume that a bookie is offering the following odds:

You decide to place a bet on a home victory. Whilst the betting provider calculates the probability of this happening at 41.6% (=100 / 2.4), you personally assess the probability – based on your own experience or calculations – at 50%. In other words, you see value in this bet! For the purposes of our example, your betting budget is €1000. In the next step, you will turn to the Kelly Formula to establish the ideal amount of your bet! This goes as follows:

With a betting budget totaling 1,000 $ and factoring in the bookie’s odds as well as the probabilities you have calculated for yourself, your actual wager would then be 142.86 $. As you can see, when you bet using the Kelly Formula, you quickly find yourself playing with big sums of money! And it soon becomes apparent: the higher your total budget and the greater the discrepancy between calculated probabilities, the bigger the size of your wager. If we assume you win this bet, your next bet involving the Kelly Formula would have to take into account your updated betting budget, which in this case would now be 1,142 $.

Our Recommendation: the “defused” Kelly Strategy

According to the Kelly Formula: the bigger your betting budget, the bigger your wagers. Furthermore, the Kelly Strategy might require you to wager a high proportion of your available budget on a single bet! You cannot exclude a scenario where, if you have a bankroll of 1,000 $, this formula might not require you to bet 300 $ or more. Clearly, we do not recommend placing such bets – so be sure to keep a safe distance! Our tip: You should never wager more than 20% of your total budget per bet. That said, this is still significantly higher than the standard figure of 1-2% suggested under normal circumstances. A popularly used alternative is the so-called “Fractal Kelly Strategy”: Here, you only use a fraction of the wager that the Kelly Formula suggests.

For example, one option would be the “Half Kelly”, in other words, you would bet half of the suggested amount. Similarly, your actual bet might represent only 1/4, 1/8 or 1/10 of the Kelly number. This makes particularly good sense if you have a very big budget, avoiding losses that are too severe. Using our aforementioned example, this would result in the following amounts:

In addition, we note that betting with the Kelly Formula can prove very time-intensive and risky. The best option is to use a pared-down version of the Kelly Strategy (e.g. 1/4 of the calculated wager), up to a predetermined point that must be adhered to. This point may be dictated by time or budget. You should always keep at the back of your mind that, with the Kelly Strategy, everything is based on a value you have calculated for yourself – ultimately, the win probabilities you personally calculate are the be-all and end-all. And it is precisely here that small mistakes and inaccurate calculations can have serious consequences.