Kelly Criterion Calculator
Determine the optimal fraction of your bankroll to wager on a bet or investment. Enter the win probability and the odds (or decimal odds) to get the Kelly percentage, expected growth rate, and a visual comparison of different betting fractions.
What Is the Kelly Criterion?
The Kelly Criterion is a mathematical formula developed by John L. Kelly Jr. that calculates the optimal size of a series of bets or investments to maximize the logarithm of wealth. It balances risk and reward by determining the fraction of your bankroll to wager to achieve the highest expected geometric growth.
The formula is widely used in gambling, investing, and sports betting. It helps you avoid over-betting (which can lead to ruin) and under-betting (which leaves growth on the table).
How Does the Kelly Criterion Calculator Work?
The calculator uses the following formula for full Kelly:
f = (p × b − q) / b
Where:
f = fraction of bankroll to bet
p = probability of winning (as a decimal)
q = probability of losing (1 − p)
b = net odds received (decimal odds − 1, e.g., for odds 2.0, b = 1)
If the result is negative, the bet has no edge and you should not wager.
The calculator also supports fractional Kelly (e.g., half-Kelly), which reduces volatility and is often recommended for conservative investors. The chart displays the expected log-growth for various betting fractions, allowing you to visualize the optimal point.
Why Use This Kelly Criterion Calculator?
- Accurate Optimal Bet Sizing: Computes the exact fraction based on your inputs.
- Multiple Odds Formats: Supports decimal, American, and fractional odds.
- Visual Growth Curve: See how different bet sizes affect your expected growth.
- Fractional Kelly Support: Apply a fraction of the full Kelly for lower risk.
- Free & Private: No registration, all calculations in your browser.
Understanding the Results
- Optimal Kelly Fraction: The percentage of your bankroll you should bet for maximum long-term growth.
- Recommended Bet Size: The actual dollar amount based on your bankroll.
- Expected Growth Rate: The expected log-growth per bet (the rate at which your bankroll grows).
- Edge: Your expected return per dollar wagered (positive if you have an advantage).
Important Considerations
- Over-betting risk: Betting more than the Kelly fraction increases the chance of ruin.
- Assumptions: The formula assumes you can reinvest profits and that outcomes are independent.
- Volatility: Full Kelly can cause large drawdowns; many practitioners use half-Kelly or less.
❓ Kelly Criterion FAQ
What is the Kelly Criterion?
The Kelly Criterion is a formula that calculates the optimal fraction of your bankroll to bet on a given opportunity, maximizing the expected logarithm of wealth. It's used in gambling, investing, and sports betting.
How do I calculate the Kelly fraction?
f = (p × b − q) / b, where p is win probability, q is loss probability (1-p), and b is the net odds (decimal odds minus 1). If f ≤ 0, you have no edge and should not bet.
What do decimal odds mean?
Decimal odds represent the total return for a $1 bet, including your stake. For example, odds of 2.0 mean you get $2 for every $1 bet (profit of $1). Net odds (b) = decimal odds − 1.
How do American odds work?
American odds are shown as positive or negative numbers. Positive odds (e.g., +150) indicate profit on a $100 bet ($150 profit). Negative odds (e.g., -200) indicate how much you need to bet to win $100 ($200 bet to win $100). The calculator converts them to decimal for you.
What is fractional Kelly?
Fractional Kelly means betting a fraction of the full Kelly percentage. For example, half-Kelly (0.5) reduces volatility and drawdowns while still providing good growth. Many investors prefer fractional Kelly for lower risk.
What is a good Kelly fraction?
A fraction between 0.25 and 0.5 (quarter- to half-Kelly) is often recommended for conservative investors. Full Kelly can be too volatile for many. The optimal fraction depends on your risk tolerance.
What if the Kelly fraction is negative?
A negative Kelly fraction means the bet has a negative expected value (no edge). You should not make the bet if you aim to maximize long-term growth.
Is the Kelly Criterion only for gambling?
No, it's also used in investment portfolio allocation, option trading, and any situation where you have a probabilistic edge and want to size your position optimally.
What is the expected growth rate?
The expected growth rate is the expected logarithmic increase in your bankroll per bet. It's the rate at which your wealth grows if you repeatedly make the same bet with the same edge.
Can I use this calculator for stocks?
Yes, you can treat a stock investment as a bet with a win probability and potential return. However, stock outcomes are not binary and have continuous returns; the Kelly formula can be adapted for such cases.
What is the difference between Kelly and risk of ruin?
Kelly focuses on maximizing long-term growth. Risk of ruin is the probability of losing a certain percentage of your bankroll. Full Kelly has a higher risk of ruin than fractional Kelly.
Is the Kelly Criterion guaranteed to make money?
No, it's a mathematical optimum based on your inputs. If your probability estimates or odds are inaccurate, the results will be suboptimal. The formula maximizes expected log-growth, not certainty.