Criterio de Kelly

Kelly Criterion

Developed by John Kelly in 1956, this formula determines the optimal bet size to maximize bankroll growth.

The Formula

Kelly % = (bp - q) / b

Where:

• b = decimal odds - 1
• p = probability of winning
• q = probability of losing (1 - p)

Example Calculation

You assess a team has 60% chance to win at odds of 2.00:

• b = 2.00 - 1 = 1
• p = 0.60
• q = 0.40

Kelly % = (1 × 0.60 - 0.40) / 1 = 0.20 (20% of bankroll)

Key Principles

Only Bet with an Edge

If Kelly % is negative or zero, don't bet!

Proportional Betting

Bet size adjusts with bankroll:

• Bankroll grows → larger bets
• Bankroll shrinks → smaller bets

Maximizes Growth

Optimal for long-term bankroll growth, but:

• High variance
• Can be psychologically difficult

Fractional Kelly

Most professionals use a fraction of Kelly:

Half Kelly: Divide result by 2

• Reduces variance
• Slower growth
• Much safer

Quarter Kelly: Divide by 4

• Very conservative
• Minimal risk of ruin
• Steady growth

Practical Application

Step 1: Assess True Probability

Critical skill - must be accurate!

Step 2: Calculate Edge

Compare your probability to bookmaker's odds

Step 3: Apply Formula

Determine bet size as % of bankroll

Step 4: Execute

Place bet and track results

Real-World Challenges

Probability Assessment

• Hardest part of Kelly
• Requires extensive knowledge
• Small errors = big impact

Variance

• Full Kelly has high variance
• Can lose 50%+ of bankroll
• Psychologically challenging

Discipline Required

• Must recalculate for each bet
• No emotional betting
• Strict bankroll tracking

Sports Betting Application

Best For:

• Professional bettors
• Long-term investors
• Value betting

Requirements:

• Accurate probability assessment
• Detailed record keeping
• Large sample size

Example Strategy

Setup

• Starting bankroll: $1,000
• Use Half Kelly
• Track all bets in spreadsheet

Bet 1

You assess 55% win probability at 2.00 odds:

• Full Kelly: 10%
• Half Kelly: 5%
• Bet: $50

Bet 2

New bankroll: $1,050 (after win) You assess 52% at 2.10 odds:

• Half Kelly: 2.5%
• Bet: $26.25

Professional Insights

Advantages

• Mathematically optimal
• Self-correcting (adjusts with bankroll)
• Prevents over-betting
• Maximizes long-term growth

Disadvantages

• Requires accurate probability estimates
• High variance
• Psychologically difficult
• Complex calculations

Tools & Resources

• Kelly Criterion calculators online
• Spreadsheet templates
• Bankroll tracking apps
• Statistical analysis software

Conclusion

The Kelly Criterion is the gold standard for serious bettors. While complex, it provides a mathematically sound approach to bankroll management. Use fractional Kelly for safety.