The Kelly Criterion Calculator helps bettors calculate the optimal percentage of their bankroll to stake based on their odds of winning and their confidence level. To use it, input your Kelly Multiplier, the decimal odds of your bet, and your estimated win percentage. The calculator will display both the expected value (EV%) and the recommended percentage of your bankroll to stake.
Detailed Instructions for Using the Kelly Criterion Calculator
- Enter the Kelly Multiplier: The Kelly Multiplier allows you to adjust the aggressiveness of your bet. By default, the multiplier is set to 1, meaning you're applying the full Kelly Criterion. If you want to be more conservative, enter a value less than 1 (e.g., 0.5), which will reduce the suggested stake.
- Input the Decimal Odds: In the "Decimal Odds" field, enter the odds for your bet in decimal format. For example, if the odds are 2.50, input that number.
- Enter Win Percentage: Input your estimated probability of winning in the "Win Percentage" field. This is your best estimation of how likely the bet is to succeed. The value should be entered as a percentage (e.g., 60%).
- View Results:The Expected Value (%) field will show the percentage profit or loss expected from your bet.The Percentage of Bankroll to Stake displays the recommended percentage of your total bankroll that should be staked according to the Kelly Criterion formula.
What is the Kelly Criterion?
The Kelly Criterion is a mathematical formula used to determine the optimal size of a series of bets, in order to maximize the long-term growth of your bankroll or investment. It was initially developed in the 1950s by John L. Kelly, Jr., a researcher at Bell Labs, as a way to maximize the growth rate of communication signals. However, the formula soon found its way into the world of gambling and finance, where it is used to manage risk while seeking optimal returns.
The Mathematics Behind the Kelly Criterion
The Kelly Criterion is expressed as:
\[f∗=bp−qbf^* = \frac{bp - q}{b}f∗=bbp−q\]
Where:
- f* represents the fraction of the bankroll to wager
- b is the decimal odds minus 1 (i.e., the net gain per unit bet)
- p is the probability of winning
- q is the probability of losing (1 - p)
To adapt this to common use:
\[ f^* = \frac{\text{Win Probability} \times (\text{Decimal Odds} - 1) - (1 - \text{Win Probability})}{\text{Decimal Odds} - 1} \]
The expected value (EV) in percentage terms is calculated as:
\[ EV\% = (\text{Win Probability} \times (\text{Odds} - 1)) - (1 - \text{Win Probability}) \]
Real-World Example
Imagine you are betting with odds of 3.00 and estimate a 40% chance of winning (p = 0.40). Here’s how the Kelly Criterion would calculate the optimal percentage of your bankroll to stake:
Step 1: Calculate the EV%:
\[ \begin{aligned} f^* &= \frac{0.40 \times (3.00 - 1) - (1 - 0.40)}{3.00 - 1} \\ &= \frac{0.80 - 0.60}{2.00} \\ &= 0.10 \end{aligned} \]
The expected value is 20%, meaning, over time, you expect a 20% return on your stake.
Step 2: Calculate the Kelly Percentage:
\[ \begin{aligned} f^* &= \frac{0.40 \times (3.00 - 1) - (1 - 0.40)}{3.00 - 1} \\ &= \frac{0.80 - 0.60}{2.00} \\ &= 0.10 \end{aligned} \]
The Kelly Criterion recommends that you bet 10% of your total bankroll on this particular bet.
Using the Kelly Multiplier
The Kelly Multiplier allows bettors and investors to scale their risk. A full Kelly stake (multiplier = 1) maximizes growth but also introduces more volatility. Reducing the multiplier to 0.5 (half Kelly) cuts the stake in half, lowering both risk and reward. This is often advised in high-volatility environments or when the bettor feels less certain about their win percentage.
For example, if the Kelly Criterion recommends betting 10% of your bankroll, but you choose a multiplier of 0.5, you would bet 5% instead. This strategy helps mitigate the risk of large losses during losing streaks while still benefiting from the positive expected value over the long term.
The History of the Kelly Criterion in Gambling and Finance
The Kelly Criterion was first introduced by John L. Kelly, Jr. in 1956 in his paper "A New Interpretation of Information Rate." Kelly's work was initially aimed at improving signal clarity in telecommunications, but its applications in risk management and decision-making became apparent to gamblers and investors alike.
Application in Gambling
In the gambling world, professional bettors, including horse racing punters and sports bettors, quickly adopted the Kelly Criterion as a way to optimise their bankroll management. The formula offered a scientific approach to betting that minimised the risk of going bankrupt while maximising long-term gains.
Historically, the Kelly Criterion has been particularly effective in sports betting markets where a bettor can gain an edge by accurately assessing probabilities. It allows bettors to dynamically adjust their stake based on their perceived advantage (i.e., win probability). This method contrasts sharply with flat staking or proportional betting strategies, where the same percentage is bet regardless of the odds or edge.
Application in Finance
Beyond gambling, the Kelly Criterion has also been widely used in finance and investing. Traders and investors use the formula to determine the optimal portion of their capital to allocate to individual trades or investments based on their estimated probability of success and the potential returns. Some of the world's top hedge funds, including those run by investors like Warren Buffett and Ed Thorp, have employed variations of the Kelly Criterion to inform their risk management strategies.
In finance, however, the full Kelly strategy can sometimes be too aggressive due to market volatility. As a result, many financial investors use fractional Kelly strategies (e.g., half or quarter Kelly) to reduce the potential downside during market drawdowns.
Why the Kelly Criterion Matters
The Kelly Criterion stands out as one of the most important concepts in both gambling and investing because it maximizes the rate of wealth growth while controlling risk. While it’s more complex than other betting systems, it offers an unparalleled balance between risk and reward, making it a valuable tool for anyone serious about growing their bankroll or investments over the long term.
Whether you're betting on sports, trading stocks, or making long-term investments, the Kelly Criterion Calculator is a powerful tool to ensure you're putting the right amount of your capital to work while managing risk effectively.
Issues with the Kelly Criterion
The Kelly Criterion assumes that gamblers can accurately assess the percentage chance of an outcome occurring and that they can always get their bets on.
In reality neither of these are possible. At Sharp Betting we prefer to use Sharp Stakes to determine stake level. This is based on a maximum stake the gambler feels comfortable per bet. The actual stake is determined by the price available rather than the percentage chance the gambler thinks an outcome has.
In our experience if we calculate an outcome at a 50% chance and the odds suggest it has a 10% chance the reality is far closer to 10% than 50%. The Kelly Criterion would suggest staking 45% of the bank on the bet whereas Sharp Stakes would be 10% of the our maximum bet.
