What is The Kelly Criterion?

John Alesia
John Alesia

The Kelly criterion is a mathematical formula used to determine the optimal size of a bet or investment in a situation where the potential for gain and loss is known. It is based on the idea of maximizing the long-term growth rate of an investment portfolio(bankroll), while also taking into account the potential risk of ruin.

The Kelly criterion can be expressed as follows:

Fraction of bankroll to bet = W – [(1 – W) / R

Where:

  • Fraction of bankroll to bet is the percentage of the bankroll that should be placed on a given bet.

  • W is the probability of winning the bet.

  • R is the expected return on the bet, expressed as a multiple of the original stake.

The Kelly criterion can be used in various situations, such as stock investing, sports betting, and gambling. It is based on the assumption that the investor or gambler has a reliable estimate of the probability of winning and the expected return on the bet or investment. It is important to note that the Kelly criterion is a theoretical model and may not always produce optimal results in practice due to the limitations of real-world data and the complexity of financial markets.

Here is an example of using the Kelly criterion to determine the optimal size of a sports bet:

Suppose you are considering making a bet on a soccer match, and you believe that the probability of your team winning is 60%. The sportsbook offers odds of +200, which means that if you win the bet, you will receive a return of 2 times your original stake.

To use the Kelly criterion, we can plug these values into the formula like this:

Fraction of bankroll to bet = 0.6 – [(1 – 0.6) / 2] = 0.2

According to the Kelly criterion, you should bet 20% of your bankroll on this game. So if you have a bankroll of $1,000, you should place a bet of $200 on your team to maximize your long-term growth potential.


The Dangers


One of the main dangers of using the Kelly criterion is that it assumes that the bettor has a precise and accurate estimate of the probability of winning a particular bet. In reality, however, it is often difficult to estimate the probability of a sports event with any degree of accuracy. This can lead to overconfidence in one's predictions, leading to excessive betting and potentially significant losses.

Another danger of the Kelly criterion is that it assumes that the bettor has an unlimited bankroll and that their betting strategy can be adjusted based on the size of their bankroll. In practice, however, most sports bettors have limited funds, and betting too aggressively can lead to financial ruin.

Finally, the Kelly criterion does not account for the psychological factors influencing betting behavior, such as the desire to recoup losses or the temptation to chase after wins. These factors can lead to irrational betting decisions, which can undermine the effectiveness of the Kelly criterion and result in even larger losses.

In conclusion, while the Kelly criterion can be a useful tool for sports bettors, it is important to use it with caution and consider the formula's limitations. Betting too aggressively can lead to significant losses, and it is essential always to maintain discipline and to bet within one's means.