TJ Sep 1, 2023

# Kelly Criterion: Using Mathematics to Win in Online Betting

If you want to get an edge over opponents, using the Kelly Criterion can amp up your chances of success.

There is always a mathematical way to approach everything—even gambling. That is where the Kelly Criterion comes to play.

Interested? Read this blog to learn how to become a successful winner!

## The Development of the Kelly Criterion

The technique was developed by John L. Kelly Jr. in the 1950s while working at Bell Labs. His primary focus was information theory, specifically coding theory and communication systems. However, he became interested in applying probability theory and statistics to gambling and investment.

Kelly’s motivation was to find an optimal betting strategy that maximized the growth rate of a bankroll. He wanted to address how much to bet when an edge or advantage exists in a particular wager. Kelly believed that the traditional methods of betting, which involved arbitrary bet sizes, did not exploit the full potential of a favorable situation.

He drew upon information and statistical decision theory concepts to develop the Kelly Criterion. He aimed to find a formula that could mathematically determine the ideal fraction of the bankroll to bet to achieve maximum growth in the long run.

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His breakthrough came when he realized the problem could be framed as a logarithmic utility maximization problem. By considering the logarithm of wealth as the utility function, Kelly sought to maximize the expected logarithmic growth rate of the bankroll.

Through his research, Kelly derived the formula we now know as the Kelly Criterion. This formula considers the probability of winning, the odds offered by the bookmaker, and the bankroll size to calculate the optimal fraction of the bankroll to bet. The result is a percentage that indicates how much to wager to maximize long-term growth while balancing risk and reward.

## Understanding the Kelly Criterion

The Kelly Criterion considers the probability of winning and the offered odds to calculate the ideal wager size that maximizes long-term growth. The formula is as follows:

f* = (p * b – q) / b

In this formula:

“f*” represents the fraction of the bankroll to bet.

“p” represents the probability of winning.

“q” represents the probability of losing (1 – p).

“b” represents the odds received on the bet.

## Applying the Kelly Criterion:

To illustrate the application of the Kelly Criterion, let’s consider a simplified example. Suppose you are betting on a coin toss, and the bookmaker offers 2:1 odds (b = 2). You estimate the probability of the coin landing on your chosen side to be 0.6 (p = 0.6).

Using the formula, we can calculate the optimal fraction of your bankroll to wager:

f* = (0.6 * 2 – 0.4) / 2

f* = 0.2

In this case, the Kelly Criterion suggests that you should wager 20% of your bankroll to maximize long-term growth. By betting too little, you might miss out on potential profits. Conversely, betting too much could put your bankroll at risk in case of a losing streak.

## Advantages of the Kelly Criterion

The Kelly Criterion is a powerful tool in betting, offering distinct advantages that can enhance your wagering strategy. By harnessing the mathematical precision of this formula, you can optimize your betting decisions and unlock the potential for long-term growth. Here are its advantages:

### Optimal Bankroll Growth

The Kelly Criterion’s primary goal is to maximize long-term growth. By properly allocating your bets based on your perceived edge, you can enhance your chances of increasing your bankroll over time.

### Customization to Edge

The technique considers your estimation of the probability of winning, allowing you to tailor your bets according to your confidence level. The more accurate your estimation, the more precise your wager size will be.

### Risk Management

The formula incorporates the odds the bookmaker offers and adjusts the bet size accordingly. This helps manage risk by avoiding excessive bets on unfavorable odds and capitalizing on favorable ones.

## Limitations and Considerations

### Assumptions and Estimations

The accuracy of the Kelly Criterion relies on your ability to estimate the probability of winning accurately. Biases, emotional influences, or insufficient information can lead to inaccurate estimations and potentially impact the formula’s effectiveness.

### Variability and Bankroll Volatility

The Kelly Criterion can result in significant swings in your bankroll due to its aggressive nature. It’s essential to carefully balance the desire for growth with the need for bankroll stability to withstand losing streaks.

### Practical Constraints

The Kelly Criterion assumes that fractional bets are feasible, which may not always be true in practical betting scenarios. Additionally, it doesn’t consider external factors such as transaction costs, bet size limits, or potential odds changes.

## Is the Kelly Criterion Effective in Online Gambling?

The Kelly Criterion can be effectively applied to online gambling, leveraging its advantages in optimizing betting decisions. Online platforms like OKBet provide access to vast information, real-time odds, and diverse betting options. Utilizing these resources lets you make informed decisions and allocate your bankroll optimally.

However, it is crucial to maintain discipline in adhering to the recommended wager sizes and utilize account management tools provided by online platforms for effective bankroll management. Additionally, considering market efficiency and accurately assessing probabilities and odds are key factors in using the Kelly Criterion effectively in online gambling.

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