Kelly Criterion for Asset Allocation and Money Management

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Jakob Brezigar

Jakob, an experienced specialist in the field of cryptocurrency market making, boasts an extensive international presence. With Orcabay, he has skillfully managed major operations and deals for a wide array of global stakeholders.​

The Kelly Criterion is a mathematical formula used to determine the optimal size of a series of bets. It aims to maximize the logarithm of wealth over the long run while considering both winning and losing probabilities.

It helps bettors and investors optimize their stake size to maximize long-term growth, minimize the risk of ruin, and manage their capital efficiently.

The formula is: f∗=(bp−q)/b where f∗ is the fraction of the bankroll to wager, is the odds received on the bet, is the probability of winning, and is the probability of losing.

It requires precise estimates of winning probabilities, might suggest highly volatile bet sizes, and doesn’t account for personal risk tolerance. Overestimations can lead to significant losses.

Key Takeaways

The Kelly Criterion, established by John Kelly in 1956, is a mathematical strategy originally designed for signal noise optimization but now widely applied in gambling, sports betting, and stock investing. This approach balances potential returns with associated risks, determining the optimal amount to wager or invest. While its mathematical foundation offers a rigorous framework, accurate outcome probability estimation is crucial. Adaptations like the Half and Quarter Kelly provide alternatives for different risk tolerances. Emphasized for long-term growth and disciplined application, the Kelly Criterion stands as a leading method for informed financial decision-making.

Introduction to Kelly Criterion

The Kelly Criterion has gained significant traction as an efficient method for both asset allocation and money management. Established by John Kelly from Bell Labs in 1956, this ingenious system was initially intended to optimize long-distance signal noise issues. However, its applications have significantly expanded, especially in the domain of gambling, casino games, and stock market investing. While conventional alternative methods may focus on mere risk mitigation or expected returns, the Kelly Criterion incorporates both, aiming for optimal growth rate and capital growth.

Using the Kelly Criterion formula, investors, including big names like Warren Buffet, have managed to find an equilibrium between potential returns and risk. This balance has been pivotal in ensuring consistent, long-term gains while effectively minimizing potential losses. This holistic approach towards investment makes the Kelly Criterion stand out as a beacon for those looking to optimize their financial strategies.

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Kelly Criterion Is a Mathematical Formula

The essence of the Kelly Criterion lies in its mathematical robustness. Developed by John Kelly during his tenure at Bell Labs, it’s a groundbreaking approach to risk management and optimal bet sizing. The formula given by: f=(bp−q)bf=b(bpq)​ encompasses various variables, with ff denoting the fraction of the bankroll to wager, bb representing the decimal odds minus one, pp standing for the probability of winning, and qq is the probability of losing or 1−p1−p. This criterion, embedded in the heart of probability theory, offers a rigorous, mathematical guideline for any bet or investment.

Kelly criterion a reflection of Kelly’s genius to draw connections between Shannon’s information theory and the world of gambling. This amalgamation led to the Kelly formula, aiming at the optimal bet size while keeping potential risks at bay. Such a principle is now foundational in both sports betting and the stock market, proving its versatility and applicability.

How to Use Kelly's Criterion

The Kelly Criterion, a significant concept in the world of betting and money management, provides users with a systematic approach to optimizing their bets or investments. The application of Kelly’s Criterion, though mathematically driven, requires a practical understanding of the event or asset in question. This criterion is a mathematical tool to ensure a balanced approach to risk. One begins by deducing the expected probability of a successful outcome or pp. The chance of winning, an essential element to consider, is juxtaposed against the chance of an unfavorable outcome. Subtracting the probability of success from 1 gives you qq or the likelihood of failure.

Using the derived values in the Kelly formula provides insights into how much one should ideally stake, ensuring that potential returns and risks are harmoniously balanced. The real-world implications of this criterion, especially in the spheres of casino games or sports betting, underscore the importance of accurate probability estimation. By diligently comparing the calculated win probability against the odds presented by bookmakers, one can determine the positive expected value of a potential bet. This positive expected value, a cornerstone of the Kelly strategy, ensures that the potential risk is commensurate with the possible returns. Through such rigorous application, the Kelly Criterion promotes a comprehensive approach to money management, strengthening the bettor or investor’s decision-making process.

kelly criterion formula

Modified Quarter and Half Systems

While the full application of the Kelly Criterion has its proponents, there are others who view its recommendations as being overly aggressive. To cater to a broader audience, modified versions like the Half Kelly and Quarter Kelly have emerged. These versions advocate for wagering half or a quarter of the original Kelly recommendation, thereby tempering potential risks.

In realms where uncertainty is high, such as in horse racing or certain casino games, these fractional Kelly systems can be advantageous. They offer a midway point, allowing for potential growth while also hedging against substantial losses. It’s a testament to the adaptability of the Kelly system, where bettors and investors can customize their approach based on their risk tolerance and long-term objectives.

Kelly Criterion Example in Sports Betting

The Kelly Criterion stands as a beacon for many sports betting enthusiasts, offering a structured approach to maximize the potential returns on their bets. To elucidate the workings of the Kelly Criterion in sports betting, consider a scenario in horse racing. Suppose a particular horse has decimal odds of 3.20. Through these odds, the bookmaker implies a win probability of 31.3%. Delving deeper into the mechanics of this, the probability of winning becomes a pivotal aspect that bettors should carefully analyze. Now, if your research and analysis lead you to a personal win probability estimation of 35.7%, the Kelly formula would swing into action. By utilizing the Kelly formula, a bettor can decipher the right stake, and in this case, it would recommend wagering 6.9% of your bankroll on this horse. This “kelly bet” approach showcases the powerful interface of one’s own judgment with the standardized market odds. The precision of the Kelly betting method lies in its ability to hone in on opportunities where the probability of using one’s insights exceeds the implied market probability. It’s this interplay of personal estimation against market odds that’s at the crux of the Kelly-based approach, especially in sports betting. With the Kelly Criterion being applied consistently, bettors can fine-tune their strategies, leading to potentially better outcomes in the long run.

Is the Kelly Criterion System Allowed in Bookmakers?

The beauty of the Kelly Criterion system lies not only in its mathematical precision but also in its adaptability across a variety of betting scenarios. This mathematical formula stands as a testament to the marriage of rigorous analytics and practical betting applications. It doesn’t rely on subjective intuitions or hidden tricks, making it a trusted tool among many sports bettors. Therefore, bookmakers don’t typically impose restrictions on its use, recognizing the integrity and validity of the Kelly Criterion as a general money management system. The underpinnings of the Kelly Criterion are grounded in the keen estimation of accurate probability predictions. This emphasis on accurate forecasting, coupled with the strategic “kelly bet” approach, makes it a cornerstone for informed risk-taking in the betting domain. Bookmakers are acutely aware that any misjudgment in this estimation, despite using the Kelly Criterion, can result in losses. This innate balance of potential reward and risk ensures that while bettors might profit from their insights, bookmakers remain protected and profitable in the long term, maintaining a harmonious ecosystem in the world of sports betting.

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What is Kelly Strategy

Often referred to interchangeably with the Kelly Criterion, the Kelly Strategy is rooted in mathematical formulations designed to guide betting or investing decisions. Its primary objective is to ascertain the optimal amount one should invest or wager, aiming to maximize the expected logarithm of wealth over an extended period. This strategy efficiently counterbalances potential gains against possible setbacks.

The Kelly Strategy, by effectively determining the optimal bet size, ensures that one doesn’t overextend their resources while still capitalizing on favorable opportunities. It’s this calibrated approach, backed by mathematical rigor, that makes the Kelly Strategy a preferred choice for many professional gamblers and astute investors alike.

Can I Bet on Football With the Kelly Criterion Formula?

Certainly! The Kelly Criterion formula’s flexibility and adaptability allow it to transcend various sectors, making it especially applicable to the vibrant and unpredictable world of football betting. Football, as one of the world’s most loved sports, is replete with vast amounts of data, ranging from intricate team tactics to detailed player performances. By employing rigorous analysis, such as evaluating teams’ past results, scrutinizing player fitness levels, considering managerial strategies, and even assessing the impact of home versus away games, bettors can cultivate a more informed perspective on potential match outcomes. Statistical software and football databases have further revolutionized the betting scene, enabling a deeper dive into metrics that might be overlooked in a cursory analysis. By assimilating all this data, the Kelly Criterion formula can then be applied to estimate the most judicious bet size. The overarching goal remains the same: to achieve a betting strategy that’s both potentially profitable over time and rooted in strategic insight.

How Does Kelly Criterion Gambling Work?

Navigating the intricate world of gambling, the Kelly Criterion emerges as a reliable lighthouse, illuminating the path for bettors towards enlightened betting choices. Its primary focus revolves around calculating the most suitable bet size. This is not merely an arbitrary number but is meticulously derived by juxtaposing the odds provided by bookmakers against the bet’s intrinsic expected value. It’s imperative to note that the Kelly Criterion doesn’t offer a magic wand; its strength is rooted in the union of mathematical principles and the bettor’s forecasting prowess. In games of chance, like roulette or blackjack, the player’s predictions might be based on statistical probabilities. But in scenarios like sports betting, elements such as team dynamics, individual player form, recent performance trends, and even factors like weather conditions or player morale become part of the prediction matrix. Thus, while the Kelly Criterion provides the algorithmic framework, the bettor’s insights and predictions breathe life into the strategy.

Is Kelly's Criterion a Safe Method for Betting?

Defining “safety” within the volatile domain of betting is always a nuanced affair. Nonetheless, from a standpoint of mathematical consistency and logic, the Kelly’s Criterion earns a commendable rank. Instead of allowing emotions or hunches to dictate bet sizes, it mandates decision-making rooted in both the allure of potential gains and the caution of inherent risks. While this approach is structured to reduce the chances of debilitating losses, it’s quintessential to remember that no system, including the Kelly’s Criterion, can guarantee unerring success. The linchpin of its effectiveness remains the bettor’s adeptness at crafting accurate probability estimates. By marrying disciplined betting with precise probability assessments, bettors can elevate their chances of long-term profitability.

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Is the Kelly Criterion Betting Strategy Illegal?

Clearing the air around this, the Kelly Criterion betting strategy operates entirely within the legal boundaries. It’s fundamentally a systematic, mathematical approach designed to guide decision-making in wagering. There’s no element of deceit, manipulation, or any clandestine tactics. Its legitimacy is unwavering, and its sole demand is for the user to have a discerning eye in gauging the real probabilities of an event. Many seasoned bettors and even financial market experts vouch for its efficacy, underscoring its reputable and legal status.

Alternative Betting Systems to the Kelly Criterion

While the Kelly Criterion garners significant praise, the world of betting teems with myriad strategies, each with its unique flair and methodology.

  • Negative Progression Systems: Embodied by strategies like the Martingale system, these revolve around the principle of increasing bets after a loss. The objective is to recoup previous losses in one successful bet, but it can lead to escalating stakes that might be unsustainable in extended losing streaks.

  • Positive Progression Systems: Exemplified by tactics like the Paroli, they advocate for amplifying wagers after a win. This is based on the belief that wins and losses come in streaks, and by leveraging a winning streak, one can optimize returns.

Each of these systems, including the Kelly Criterion, offers its unique blend of risk and reward. Selecting the right one hinges on individual preferences, risk tolerance, and specific betting goals. For those who cherish a structured approach, aiming to harmonize potential growth with prudent risk management, the Kelly Criterion frequently stands out as the gold standard.

The Kelly Criterion, conceived by John Kelly in 1956, offers a strategic balance between maximizing potential returns and minimizing risks. Grounded in mathematical principles, this system determines the optimal fraction of capital to invest or wager. It is revered in diverse domains like gambling, sports betting, and stock market investing. The methodology’s efficiency is determined by the user’s ability to estimate accurate probabilities. With modifications like Half and Quarter Kelly, bettors can tailor the system to their risk preferences. Emphasizing long-term growth, disciplined application, and continual learning, the Kelly Criterion emerges as a robust strategy for informed decision-making in betting and investing.

What is the Kelly Criterion?

The Kelly Criterion is a mathematical formula used to determine the optimal size of a series of bets. It aims to maximize the logarithm of wealth over the long run while considering both winning and losing probabilities.

Why is the Kelly Criterion important in gambling and investing?

It helps bettors and investors optimize their stake size to maximize long-term growth, minimize the risk of ruin, and manage their capital efficiently.

How is the Kelly bet size calculated?

The formula is: f∗=(bp−q)/b where f∗ is the fraction of the bankroll to wager, is the odds received on the bet, is the probability of winning, and is the probability of losing.

What are the drawbacks of using the Kelly Criterion?

It requires precise estimates of winning probabilities, might suggest highly volatile bet sizes, and doesn’t account for personal risk tolerance. Overestimations can lead to significant losses.

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