Kelly Criterion Calculator

What is the Kelly Criterion?

The Kelly Criterion is a mathematical formula used to determine the optimal size of a series of bets to maximize long-term growth of your bankroll. It considers both the odds offered and your estimated probability of winning to calculate the ideal stake size as a percentage of your current bankroll.

This formula helps bettors avoid betting too much (which risks significant losses) or too little (which limits potential gains). The Kelly Criterion is particularly useful for professional bettors and those serious about long-term profitability in sports betting.

How to Use This Calculator:

1. Enter the american odds offered by the bookmaker
2. Input your estimated probability of winning (as a percentage)
3. Enter your current bankroll size
4. The calculator will show your optimal bet size and other relevant information

Understanding the Kelly Criterion Formula

The Kelly Criterion formula calculates the optimal bet size as a percentage of your bankroll: f* = (bp - q) / b

Where:

• f* = Fraction of bankroll to bet (Kelly percentage)
• b = Decimal odds minus 1 (e.g., +200 = 2.0, so b = 2.0)
• p = Your estimated probability of winning
• q = Probability of losing (1 - p)

This formula maximizes the expected logarithm of your bankroll, which translates to optimal long-term growth while managing risk.

Real-World Kelly Criterion Example

Scenario: You've found an NBA bet with +200 odds (3.0 decimal), and after thorough analysis, you believe there's a 40% chance of winning.

Calculator Inputs:

• American Odds: +200
• Estimated Win Probability: 40%
• Current Bankroll: $1,000
• Kelly Multiplier: 0.25 (Quarter Kelly for safety)

Calculation:

• Decimal odds (b): 2.0
• Win probability (p): 0.40
• Lose probability (q): 0.60
• Full Kelly: (2.0 × 0.40 - 0.60) / 2.0 = 0.10 or 10%
• Quarter Kelly: 10% × 0.25 = 2.5% of bankroll
• Recommended Bet: $25

This bet size maximizes long-term growth while reducing the volatility that comes with full Kelly staking.

Full Kelly vs Fractional Kelly: Which Should You Use?

Kelly Type	Multiplier	Volatility	Best For
Full Kelly	1.0	Very High	Aggressive bettors with high confidence in probability estimates
Half Kelly	0.5	Moderate	Balanced approach, 75% of full Kelly growth
Quarter Kelly (Recommended)	0.25	Low	Conservative, reduces risk of overestimating edge
Tenth Kelly	0.1	Very Low	Ultra-conservative, beginners

Most professional sports bettors use Quarter Kelly or Half Kelly to account for uncertainty in their probability estimates and reduce bankroll swings.

Benefits of Using Kelly Criterion

• Optimal bankroll growth: Mathematically proven to maximize long-term wealth
• Systematic approach: Removes emotion from bet sizing decisions
• Protection against ruin: Never suggests betting your entire bankroll
• Scales with confidence: Bet more when edge is higher, less when uncertain
• Compound growth: Takes advantage of bankroll growth over time

Important Considerations & Common Mistakes

• Garbage in, garbage out: Kelly assumes your probability estimates are accurate. Overconfidence leads to overbetting.
• Use Fractional Kelly: Most pros use 25-50% of the suggested bet to account for estimation errors
• Don't chase losses: Kelly recalculates based on current bankroll, not original amount
• Requires discipline: You must update your bankroll and recalculate for each bet
• Not for parlays: Kelly is designed for single bets with independent outcomes
• Negative Kelly means don't bet: If the formula returns negative, the bet has no value

When to Use Kelly Criterion

Kelly Criterion is most effective when:

• You have a genuine edge (confirmed through analysis or tools like our Edge Calculator)
• You can accurately estimate win probability (use historical data, models, or market analysis)
• You're betting on independent events (not correlated parlays)
• You have a sufficient bankroll to withstand variance
• You're focused on long-term growth rather than short-term profits

Pro Tip: Combine Kelly Criterion with our Edge Calculator to find value bets, then use our EV Calculator to validate positive expected value before determining your bet size with Kelly.

Note: The Kelly Criterion is a powerful tool for bankroll management, but it requires honest, accurate probability assessment. When in doubt, use a smaller Kelly fraction (Quarter Kelly is recommended for most bettors) to reduce variance and account for estimation errors.