The Kelly Criterion

The Kelly Criterion formula was developed in 1956 by John Kelly, a mathematician fond of betting on horse racing.

The Kelly Criterion is used to calculate the percentage of bankroll that we can allocate to a certain bet based on its quota, with the double aim of avoiding unnecessary risks and achieving the highest return.

The formula includes concepts that you already know, such as the bank and the odds, and new ones, such as the estimation of the probability of victory of the player or the team you are going to bet on (expressed in percentage):

% bank = [((odds *% probability) – 1) / (odds – 1)] * 100

Let’s look at an example.

You have a bank of 1,000 euros and you decide to bet on the R. Madrid-Barcelona match, which will be held. R. Madrid has a share of 1.7 and Barcelona have been assigned another of 2.1. Perhaps the antecedents of the confrontations of both have influenced in the favoritism of R. Madrid. But Barcelona is in better shape. Therefore, you value that Barsa has a probability of victory of at least 50% (higher than that assigned by the house: 1 / 2.1 = 47.62%). You decide to bet, considering the pick a value bet or value bet.

If you apply the Kelly method, you get that your optimal bet is the following:

% banking = [((2.1 * 50%) – 1) / (2.1 – 1)] * 100 = [(1.05 – 1) / 1.1] * 100 = (0.05 / 1 , 1) * 100 = 4.54%.

Therefore, if you have a bankroll of 1,000 euros, your bet in favor of Barcelona would be [1,000 * 4.54% =] 45.4 euros.

The use of the Kelly Criterion has several drawbacks:

The calculation depends directly on your ability to estimate the probability of victory of the competitor chosen for the bet.
The percentage of bankroll to invest grows the greater the difference between the probability defined by the couta and the one you assign to the event. For example, if instead of estimating Barcelona a 50% probability of victory, you had put it at a 60% victory, the banking percentage to invest would be 23.64% (236.36 euros), which would be above an aggressive full stake of 10% of the bankroll.