Calculation Explanation
The Kelly Criterion uses the following formula:
f* = (bp – q) / b
Where:
- f* = Fraction of bankroll to bet
- b = Decimal odds – 1
- p = Probability of winning
- q = Probability of losing (1 – p)
Warning: The Kelly Criterion suggests a negative bet size, indicating this bet has negative expected value and should be avoided.
Caution: The recommended bet size is quite high. Consider using a fractional Kelly approach (e.g., 25% or 50% of the calculated amount) to reduce risk.
Please fill in all fields with valid values.
Kelly Criterion for Optimal Betting
The Kelly Criterion is a mathematical formula developed by John L. Kelly Jr. in 1956 that determines the optimal bet size to maximize long-term wealth growth while minimizing the risk of ruin. Originally designed for information theory and gambling, this powerful formula has found widespread application in investment portfolio management, sports betting, and financial trading.
The formula calculates the ideal fraction of your bankroll to wager based on the probability of winning and the odds offered. By using the Kelly Criterion, bettors can avoid the common pitfalls of overbetting (which can lead to bankruptcy) and underbetting (which limits potential returns). The strategy aims to achieve the highest possible growth rate of your capital over time.
This calculator implements the classic Kelly formula: f* = (bp – q) / b, where f* represents the fraction of bankroll to bet, b is the net odds received, p is the probability of winning, and q is the probability of losing. The result provides a scientifically-backed approach to position sizing that has been proven effective across various forms of investing and betting.
How to Use the Kelly Criterion Calculator
Step 1: Enter Win Probability
Input your estimated probability of winning the bet as a percentage (0-100%). This should be your honest assessment based on research, analysis, or historical data. For example, if you believe there’s a 60% chance of winning, enter 60.
Step 2: Input Decimal Odds
Enter the decimal odds offered by the bookmaker. Decimal odds represent the total payout per unit wagered, including your original stake. For instance, odds of 2.50 mean you receive $2.50 for every $1 wagered if you win.
Step 3: Specify Your Bankroll
Enter your total available betting capital in dollars. This should represent the maximum amount you’re willing to risk across all your betting activities. The Kelly Criterion will calculate the optimal bet as a percentage of this total amount.
Step 4: Calculate and Review Results
Click the calculate button to generate your optimal bet size. The calculator will display the recommended percentage of your bankroll to wager, the actual dollar amount, potential profit, and expected value. Pay attention to any warnings about negative expected value or high-risk bets.
Step 5: Apply Risk Management
Consider using a fractional Kelly approach by betting only 25-50% of the calculated amount to reduce volatility. The full Kelly can be aggressive, so many professional bettors use a more conservative fraction to balance growth with risk management.
