The Kelly Criterion: Optimal Bet Sizing Strategy

The Kelly Criterion is a mathematical formula used to determine the optimal size of a series of bets. It helps bettors maximize long-term growth while minimizing the risk of ruin.

The Formula

The Kelly Criterion formula is:

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)

Why Use Kelly Criterion?

1. Maximizes Growth: Optimizes long-term bankroll growth
2. Manages Risk: Prevents overbetting and potential ruin
3. Mathematical Foundation: Based on solid mathematical principles
4. Adaptable: Adjusts bet size based on edge and odds

Example

Suppose you have a bet with:

• Decimal odds of 2.50 (b = 1.50)
• You estimate a 50% probability of winning (p = 0.50, q = 0.50)

f* = (1.50 × 0.50 - 0.50) / 1.50 = 0.083 or 8.3%

You should bet 8.3% of your bankroll.

Fractional Kelly

Many professional bettors use "fractional Kelly" (e.g., half-Kelly or quarter-Kelly) to reduce variance:

• Half-Kelly: Bet 50% of the Kelly recommendation
• Quarter-Kelly: Bet 25% of the Kelly recommendation

This approach trades some growth potential for reduced volatility.

Important Considerations

• Accurate Probabilities: The formula requires accurate probability estimates
• Bankroll Volatility: Full Kelly can lead to significant swings
• Edge Required: Only bet when you have a positive edge (bp > q)
• Conservative Approach: Consider fractional Kelly for more stability

Using Our Calculator

Try our Kelly Criterion Calculator to quickly determine your optimal bet size based on your edge and bankroll.

Conclusion

The Kelly Criterion is a powerful tool for bankroll management, but it requires discipline and accurate probability assessment. Start conservatively with fractional Kelly and adjust as you gain experience.