Using the Kelly Criterion for Optimal Bets and Maximum Profits

Kosta Tiodorovic 1 month ago
Using the Kelly Criterion for Optimal Bets and Maximum Profits

The Kelly Criterion is a mathematical formula that can be used to make the most of your bets, whether in gambling or investing. In this blog post, we provide you with all the necessary information to understand this concept. We’ll go over the basic principles and origins and give you simple examples to see how you can apply the Kelly Criterion to your betting tactics. 

The Math Behind It 

Using the Kelly Criterion is a strategy that balances the risk of losing with the potential for profitability, guiding you to bet a portion of your funds that corresponds to the probability of winning. It was formulated in 1956 by John L. Kelly Jr., a researcher at Bell Labs. Kelly, originally focusing on long-distance telephone signal noise, unexpectedly created a system that found its most significant applications in sports betting and finance. 

The core of the Kelly Criterion is its formula, which can be expressed as:

f*= bp-qb

  • f*represents the fraction of your bankroll to bet
  • b is the net odds received on the bet (expressed as b:1)
  • p is the probability of winning
  • q is the probability of losing, which is 1-p

Simply put, the formula can be expressed as the given odds multiplied by the probability of winning, subtracting the probability of a loss and that total divided by the odds. 

Can Kelly Criterion Be Used in Casino Games?

The essence of the Kelly Criterion betting is to wager a portion of your bankroll based on your edge in a given wager. However, in casino games, this becomes impractical due to the inherent house edge present in these games. Unlike skill-based betting, where the player can have an edge, online casino games are designed to give the house an advantage. This means that the return to player (RTP) is never 100%, leading to a situation where the Kelly Criterion would consistently suggest a negative betting percentage.

Using the Formula in Sports Betting

This approach is especially well-suited to making sports bets. If you manage to properly provide values needed for applying the Kelly Criterion formula, you should always get an optimal percentage of your bankroll needed for the bet to be profitable. Here are some examples of how you can use it in different sports. 

Kelly Criterion in Football Betting

When betting on football, the odds and probabilities can vary significantly depending on the matchup, league, and other factors such as team form, injuries, and historical performance. Let’s consider a hypothetical scenario where you’re betting on a team with odds of 3:1 (meaning b = 3) and you estimate the probability of your team winning at 50% (p = 0.5). The probability of losing (q) would be 50% (1-p = 0.5). 

Plugging these values into the Kelly formula would look like this:

f*= (30.5) – 0.53 = 1.5-0.53 = 0.333

This result suggests that you should bet approximately 33.3% of your bankroll on this football match to optimize your bankroll growth.

Kelly in Basketball Betting

Basketball betting, with its dynamic odds and frequent scoring, presents unique opportunities for applying the Kelly Criterion. Suppose you find a game where the odds are 2.5:1 ( b = 2.5) and you believe the probability of your chosen team winning is 55% (p = 0.55). Consequently, the probability of losing (q) is 45% (1 – p = 0.45).

In application, it would look like this:

f*= (2.50.55) – 0.452.5 = 1.375-0.452.5 = 0.37

This calculation indicates that you should allocate 37% of your bankroll to this bet.

Applying the Formula in Tennis Betting

Let’s say you’re betting on a tennis match. You have odds of 2:1 (so b=2), and you believe the probability of your chosen player winning is 60% (p=0.6). Therefore, the probability of losing (q) is 40% (1 – 0.6 = 0.4). If we use these numbers for the Kelly formula, we get:

f*= (20.6) – 0.42 = 1.2-0.42 = 0.4

This result suggests that you should bet 40% of your bankroll on this match for optimal profit growth.

Half, Third, and Quarter Kelly

Adjusting the Kelly Criterion by betting a fraction of the recommended amount, like half (½), a third (⅓), or a quarter (¼) Kelly, is a common strategy to manage further risks. These variations help in smoothing the volatility in your bankroll while still adhering to the principles of the Kelly Criterion. Here are a couple of reasons why bettors choose to employ this strategy. 

  1. Reduced volatility: By betting a fraction (like half) of what Kelly suggests, you reduce the fluctuations in your bankroll, leading to a more stable growth pattern.
  2. Less aggressive betting: This approach involves fewer initial bets and can be more suitable for those who are risk-averse or new to using the Kelly Criterion.
  3. Balance between growth and safety: Fractional Kelly strategies are the sweet spot between maximizing growth and protecting your bankroll from significant drops.

What are Kelly Criterion Calculators? 

For those looking to get serious about this strategy, Kelly Criterion calculators are a valuable tool. They simplify the process of determining the optimal bet size, eliminating the need for complex manual calculations. To use a Kelly Criterion betting calculator, you typically need to input the odds of the bet, your estimated probability of winning, and sometimes the total bankroll you are willing to bet. The calculator then uses the Kelly formula to determine the optimal bet size as a percentage of your bankroll.

A key feature in many of these calculators is the Kelly multiplier. This is an adjustable factor that allows you to bet a fraction of the amount suggested by the pure Kelly Criterion, often used as a way to reduce risk. As mentioned above, this multiplier can be half, a third, or a quarter. For the full Kelly Criterion number, use a multiplier of 1. 

Pros and Cons 

The method is primarily aimed at enhancing the long-term growth of your betting bankroll, simultaneously working to reduce the risk of depleting all your betting funds. By using this criterion, bettors make informed decisions and align their betting strategies with the goal of long-term profitability while avoiding the pursuit of immediate, high-risk gains.

There are several advantages to using the Kelly Criterion:

  • Guides optimal bet sizing: This is crucial for maximizing the growth of your bankroll over an extended period.
  • Emphasizes risk management: By recommending that only a portion of your bankroll should be placed on any given bet, it mitigates the likelihood of significant losses.
  • Focus on long-term strategy: This makes it an ideal approach for disciplined bettors who are in it for sustainable gains rather than quick, risky wins.

However, the Kelly Criterion is not without its drawbacks:

  • Challenging to estimate winning probabilities accurately: Overestimation, for instance, can lead to overly aggressive betting and potential financial setbacks.
  • Complex calculations: This is particularly the case in dynamic betting scenarios, and might demotivate some bettors.

Understanding the percentages in Kelly Criterion betting is crucial for effective application. The formula’s result, expressed as a percentage, indicates the recommended portion of your bankroll to wager. A positive value implies favorable odds and suggests that a bet is advisable. The higher the percentage, the stronger your edge is perceived, indicating a larger bet. Conversely, a negative or zero value signifies unfavorable odds, advising against placing the bet. 

Minimize Your Betting Risk with Kelly Criterion Formula

The Kelly Criterion betting approach stands as a beacon for bettors seeking a balanced method of managing their bankroll. This formula is not just about maximizing returns; it’s equally focused on minimizing risk, ensuring you don’t put your entire bankroll at stake. Its application in betting scenarios, especially in sports betting, is relatively straightforward, making it accessible even for those who are new to this concept. 

So, if you’re looking to optimize your betting strategy while keeping risks in check, consider implementing the Kelly Criterion to your next wager. It’s a step toward more disciplined, calculated, and potentially profitable betting experiences.

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