December 4, 2023

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# The Kelly Criterion: A Winning Strategy for Top 1 Smart Bettors

Kelly Criterion calculator

## Introduction to Kelly Criterion

The Kelly Criterion is a mathematical formula that helps bettors determine the optimal amount of money to bet on a given outcome. The criterion is named after its creator, John L. Kelly Jr., who introduced it in his 1956 paper “A New Interpretation of Information Rate”.

The basic idea behind the Kelly Criterion is to maximize the expected value of the logarithm of the wealth. In other words, it tells you how much of your bankroll you should wager on a given bet in order to achieve the highest expected return over the long term. The Kelly Criterion takes into account both the probability of winning and the payoff if you win.

Here’s an example of how the Kelly Criterion works in practice: Let’s say you have a bankroll of 1,000£ and you’re considering placing a bet on a horse race. The odds of your chosen horse winning are 2 to 1 (or, in other words, the payout for a 1£ bet is 3£). According to the Kelly Criterion, you should bet a fraction of your bankroll equal to:

f = (2 x 0.5 – 1) / (2 – 1) = 0.5

So, you should bet 50% of your bankroll, or 500£, on the horse. This is because the formula takes into account both the probability of winning (50%) and the payoff if you win (3£ for every 1£ bet).

Using the Kelly Criterion can help you make more informed betting decisions and avoid common mistakes such as overbetting or underbetting. However, it’s important to note that the Kelly Criterion assumes you have accurate information about the probabilities of winning and the payoffs for each bet. In reality, this is often not the case, and bettors should always use their own judgment and expertise when making betting decisions.

Overall, the Kelly Criterion is a powerful tool for bettors who are looking to maximize their long-term returns while minimizing risk. By using this formula, you can make more strategic bets and improve your overall success rate.

## “The Mathematics Behind Kelly Criterion”:

The Kelly Criterion is based on the concept of maximizing the expected logarithmic growth rate of wealth. This means that the formula aims to maximize the long-term growth of your bankroll, rather than just the immediate return on a single bet.

The formula for the Kelly Criterion is as follows:

f* = (bp – q) / b

where:

• f* is the optimal fraction of your bankroll to bet
• b is the net odds received on the bet (i.e., the payout if you win, minus the amount you bet)
• p is the probability of winning the bet
• q is the probability of losing the bet, which is equal to 1 – p

To understand how this formula works, let’s consider the example of a coin toss. If you bet £10 on heads and the coin is fair (i.e., the probability of heads is 0.5), the payout if you win is £20 (i.e., your original bet plus £10 profit). In this case, the net odds received on the bet (b) are 2.0, since the payout is twice the original bet.

Using the Kelly Criterion formula, we can calculate the optimal fraction of our bankroll to bet:

f* = (0.5 x 2 – 0.5) / 2 = 0.25

This means that we should bet 25% of our bankroll, or £250, on the coin toss. If we bet more than this amount, we are taking on more risk than necessary and may end up losing money over the long term. If we bet less than this amount, we are not taking advantage of the opportunity to maximize our expected growth rate.

The Kelly Criterion is a powerful tool for bettors because it takes into account both the probability of winning and the payoff if you win. By using this formula, you can calculate the optimal bet size for any given scenario and make more informed betting decisions.

However, it’s important to note that the Kelly Criterion assumes that you have accurate information about the probabilities of winning and the payoffs for each bet. In reality, this is often not the case, and bettors should always use their own judgment and expertise when making betting decisions. Additionally, the Kelly Criterion does not take into account other factors such as risk tolerance or bankroll size, so it should be used as a general guide rather than a hard-and-fast rule.

## Calculating Kelly Criterion: A Step-by-Step Guide

Calculating the Kelly Criterion can be a bit daunting at first, but once you understand the formula and the steps involved, it becomes a straightforward process. Here’s a step-by-step guide to calculating the Kelly Criterion:

Step 1: Determine the Net Odds (b) The first step is to determine the net odds (b) for the bet you are considering. This is calculated by subtracting one from the payout ratio. For example, if the payout ratio is 3 to 1, the net odds are 2.

Step 2: Determine the Probability of Winning (p) The next step is to determine the probability of winning (p) for the bet. This can be based on a variety of factors, including historical data, expert opinions, and your own analysis. It’s important to be as accurate as possible when estimating the probability of winning, as this will impact the size of your bet.

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Step 3: Determine the Probability of Losing (q) The probability of losing (q) is simply the complement of the probability of winning (p). In other words, if the probability of winning is 0.7, the probability of losing is 0.3.

Step 4: Calculate the Kelly Criterion (f*) Once you have determined the net odds (b), the probability of winning (p), and the probability of losing (q), you can calculate the Kelly Criterion using the following formula:

f* = (bp – q) / b

This will give you the optimal fraction of your bankroll to bet on the given outcome. If the result is negative, it means you should not bet on this outcome.

Step 5: Apply the Kelly Criterion to Your Bankroll Once you have calculated the Kelly Criterion, you can apply it to your bankroll to determine the actual amount of money to bet. For example, if your bankroll is £1,000 and the Kelly Criterion tells you to bet 0.5 (or 50%), you should bet £500 on the outcome.

It’s important to note that the Kelly Criterion is not a one-size-fits-all solution and should be used in conjunction with your own knowledge and expertise. Additionally, the formula assumes that you have accurate information about the probabilities of winning and the payoffs for each bet. In reality, this is often not the case, and bettors should always use their own judgment and analysis when making betting decisions.

## The Kelly Criterion Calculator for Beginners

Enter the probability (in percentage) of your selection winning. For example, if you think there’s a 60% chance of your selection winning, enter 60.

Enter the decimal odds the bookmaker is offering for your selection. For example, if the bookmaker is offering odds of 2.5 (or 3/2 in fractional odds), enter 2.5.

Enter the percentage of your bankroll you’re willing to risk on this bet. For example, if you’re willing to risk 5% of your bankroll on this bet, enter 5.

Enter the total amount of money you have to bet (your bankroll).

Kelly Criterion:
Bet Size:

## Pros and Cons of Kelly Criterion in sports betting

Pros:

1. Maximizes Expected Growth: The Kelly Criterion is a mathematically proven method that maximizes the expected growth rate of your bankroll over the long run, making it an attractive betting strategy.
2. Considers Edge: The Kelly Criterion considers the edge a bettor has over the sportsbook by taking into account the probability of winning and the odds offered by the sportsbook. This allows bettors to bet more when they have an edge and less when they don’t.
3. Balances Risk and Reward: The Kelly Criterion balances risk and reward by ensuring that bettors bet enough to make a profit when they win, but not so much that they risk going broke when they lose.
4. Adaptable: The Kelly Criterion can be adapted to various betting scenarios and bankroll sizes, making it a flexible betting strategy.

Cons:

1. Requires Accurate Probabilities: The Kelly Criterion requires accurate probabilities of winning and losing, which can be difficult to estimate in sports betting. If the probabilities are wrong, the Kelly Criterion can lead to overbetting or underbetting.
2. Can Lead to Large Swings: The Kelly Criterion can lead to large swings in bankroll due to its aggressive betting approach. This can be risky for bettors with smaller bankrolls or those who are risk-averse.
3. Can Be Complex: The Kelly Criterion can be complex to calculate and implement, especially for those who are not familiar with advanced mathematics. This can make it difficult for some bettors to use effectively.
4. Does Not Account for Variance: The Kelly Criterion does not account for variance in sports betting, which can be significant. Even if a bettor has an edge, they can still experience losing streaks that can significantly impact their bankroll.

The Kelly Criterion can be an effective betting strategy for those who can accurately estimate probabilities and are willing to accept the potential swings in bankroll. However, it is not without its drawbacks, and bettors should carefully consider the pros and cons before implementing this strategy in their sports betting.

## Kelly Criterion vs. Other Bankroll management alternatives

The Kelly Criterion is a widely used method for managing risk in sports betting. The principle of the Kelly Criterion is to determine the optimal bet size based on the perceived edge over the bookmaker. This ensures that the bettor can maximize their long-term returns while minimizing their risk of ruin.

One of the main advantages of using the Kelly Criterion is that it is a mathematically proven method for maximizing expected value in the long run. Unlike other betting strategies that rely on gut instinct or arbitrary betting amounts, the Kelly Criterion takes into account the bettor’s edge and the size of their bankroll to determine the optimal bet size.

Another advantage of the Kelly Criterion is that it can help bettors avoid the pitfalls of overbetting or underbetting. Overbetting, or betting too much of your bankroll on a single event, can lead to ruin even if you have a positive expected value. Underbetting, on the other hand, can limit your potential long-term returns. The Kelly Criterion helps you find the optimal bet size to balance these risks.

However, there are also some drawbacks to using the Kelly Criterion for sports betting. One of the main criticisms is that it assumes the bettor has accurate estimates of their edge over the bookmaker. In reality, it can be difficult to accurately quantify your edge in a given event, and small errors in estimation can have a big impact on your long-term returns.

Another drawback of the Kelly Criterion is that it can lead to aggressive betting in some cases. The Kelly Criterion is designed to maximize expected value, which means that it may recommend larger bets than some bettors are comfortable with. This can lead to increased risk and volatility, which may not be suitable for all bettors.

Finally, it’s worth noting that there are other investment strategies that can be effective for sports betting, such as flat betting or using a percentage of bankroll. These strategies are simpler to implement and can be more suitable for bettors who prefer a more conservative approach.

Here’s a comparison between the Kelly Criterion and other popular betting strategies in sports betting:

1. Flat Betting: This is the simplest betting strategy, where a bettor places the same amount of money on every bet, regardless of the odds. While this strategy is easy to follow, it doesn’t take into account the probability of winning and can lead to losses in the long run.
2. Martingale Betting: This is a progressive betting strategy, where a bettor doubles their bet after every loss until they win, at which point they revert back to their original bet. While this strategy can lead to big wins, it can also lead to big losses and requires a large bankroll to execute.
3. Fibonacci Betting: This is another progressive betting strategy, where a bettor increases their bet after every loss according to the Fibonacci sequence. This strategy is less risky than the Martingale, but still requires a large bankroll and can lead to losses in the long run.
4. Proportional Betting: This strategy involves betting a fixed percentage of your bankroll on each bet, depending on the odds and your estimated probability of winning. This strategy is similar to the Kelly Criterion, but doesn’t take into account the size of the bankroll and can lead to underbetting or overbetting.

Compared to these strategies, the Kelly Criterion takes into account both the probability of winning and the size of the bankroll, making it a more effective and efficient strategy in the long run. However, it requires accurate estimates of both the probability of winning and the odds, which can be difficult to obtain in practice. It is also important to note that the Kelly Criterion is not a guarantee of success and can still lead to losses in certain situations. As with any betting strategy, it is important to manage your bankroll wisely and stay disciplined in your betting approach.

## Real-Life Examples of Kelly Criterion in Action

Here are some real-life examples of Kelly Criterion in action in the sports betting world:

1. Billy Walters: Billy Walters is a well-known sports bettor who has used the Kelly Criterion to great effect. He has been able to achieve a long-term winning percentage of around 57% while using the Kelly Criterion to determine his bet sizes.
2. Z-Code System: The Z-Code System is a popular sports betting software that utilizes the Kelly Criterion to help users make betting decisions. The software analyzes various factors, such as player injuries and team performance, to come up with a recommended bet size based on the Kelly Criterion.
3. Ed Thorp: Ed Thorp is a famous mathematician who used the Kelly Criterion to great effect in both investing and sports betting. He was able to achieve a long-term win rate of around 60% in sports betting while using the Kelly Criterion to determine his bet sizes.
4. Warren Buffett: While Warren Buffett is not known for his sports betting prowess, he is a well-known investor who has used the Kelly Criterion in his investment strategy. He has stated that he uses the Kelly Criterion to determine the size of his investments, although he adjusts the formula to take into account the uncertainty inherent in investing.

These are just a few examples of the Kelly Criterion in action in the sports betting world. While the Kelly Criterion is not a foolproof strategy, it has been shown to be effective over the long term when used correctly. It is important to remember that no betting strategy is 100% effective, and that there is always a risk involved in sports betting.

## How to Implement Kelly Criterion in Your Betting Strategy

Implementing the Kelly Criterion in your betting strategy can be a great way to manage your bankroll and potentially increase your profits over the long run. Here are some steps you can take to implement the Kelly Criterion:

1. Determine your edge: Before you can use the Kelly Criterion, you need to have a good idea of what your winning percentage is in a particular market. You can do this by analyzing past data or using statistical models to estimate your edge.
2. Choose your bet sizing percentage: The Kelly Criterion suggests that you should bet a certain percentage of your bankroll based on the size of your edge. A common percentage is 1-2% of your bankroll per bet, although you can adjust this based on your risk tolerance.
3. Calculate your Kelly bet size: Once you know your edge and your bet sizing percentage, you can calculate your Kelly bet size using the following formula: (Edge * Odds – (1 – Edge)) / (Odds – 1). This will give you the percentage of your bankroll that you should bet on a particular outcome.
4. Monitor your results: The Kelly Criterion is designed to maximize long-term growth, but there will be ups and downs along the way. It’s important to track your results over time and adjust your bet sizing as necessary based on changes in your edge or risk tolerance.

Keep in mind that the Kelly Criterion is just one tool in your betting toolbox, and it may not be appropriate for every situation. It’s important to consider other factors such as market liquidity, odds movement, and bankroll management when making betting decisions.

## Common Mistakes to Avoid When Using Kelly Criterion

Using Kelly Criterion can be a powerful tool for sports bettors, but it’s important to use it correctly to avoid making costly mistakes. Here are some common mistakes to avoid when using Kelly Criterion:

1. Overestimating your edge: Kelly Criterion assumes that you have an accurate estimate of your probability of winning. If you overestimate your edge, you may end up placing larger bets than you should, leading to potential losses.
2. Underestimating your risk: Kelly Criterion also assumes that you have an accurate estimate of your risk. If you underestimate your risk, you may end up placing larger bets than you should, leading to potential losses.
3. Failing to adjust for changing probabilities: As probabilities change over time, it’s important to adjust your bets accordingly. Failing to adjust for changing probabilities can lead to placing bets that are too large or too small.
4. Placing too many bets: Kelly Criterion can be a powerful tool, but it’s important to use it selectively. Placing too many bets can increase your risk and lead to potential losses.
5. Ignoring transaction costs: When placing bets, there are often transaction costs associated with them. Ignoring these costs can lead to placing bets that are too large and ultimately lead to losses.
6. Focusing too much on short-term gains: Kelly Criterion is a long-term strategy, and it’s important to focus on long-term gains rather than short-term gains. Focusing too much on short-term gains can lead to taking on unnecessary risk and ultimately lead to losses.

By avoiding these common mistakes, sports bettors can use Kelly Criterion effectively and increase their chances of long-term success.

## Here are some tips for maximizing your returns when using the Kelly Criterion in sports betting:

1. Use accurate probability estimates: The Kelly Criterion relies heavily on accurate probability estimates. It is important to have a deep understanding of the sports or events you are betting on and the factors that could affect the outcome. The more accurate your probability estimates, the more successful your betting strategy will be.
2. Limit your bets to the optimal Kelly percentage: It is important to stick to the optimal Kelly percentage recommended by the formula. This will ensure that you are betting the optimal amount to maximize your returns while minimizing risk.
3. Avoid large variations in bet size: It is important to avoid large variations in bet size when using the Kelly Criterion. While it may be tempting to increase your bet size after a big win, this can lead to excessive risk and may ultimately result in losses.
4. Consider bankroll management: The Kelly Criterion does not take into account your overall bankroll or your ability to absorb losses. It is important to consider bankroll management strategies and set limits on your bets to avoid losing your entire bankroll.
5. Use the Kelly Criterion in conjunction with other betting strategies: The Kelly Criterion can be a useful tool when used in conjunction with other betting strategies. It is important to diversify your betting portfolio and use multiple strategies to maximize your returns and minimize risk.

By following these tips, you can maximize your returns with the Kelly Criterion and build a successful sports betting strategy.

## Conclusion: Is Kelly Criterion Right for You?

Kelly Criterion can be a useful tool for sports bettors who want to maximize their returns. By using this formula, bettors can calculate the optimal amount of money to bet on each wager based on their perceived edge and the odds offered by the sportsbook.

However, it is important to note that the Kelly Criterion is not a foolproof strategy and should not be used as the sole basis for making betting decisions. It is also important to carefully consider the risks involved and to manage your bankroll accordingly.

Before implementing the Kelly Criterion into your betting strategy, make sure to carefully assess your own risk tolerance, experience level, and overall betting goals. If used correctly, the Kelly Criterion can be a powerful tool to help you make informed and profitable betting decisions.