Fractional Kelly: The Practical Solution
Full Kelly is mathematically optimal, but it has a major flaw: it's extremely aggressive, and it assumes you know your exact edge.
In the previous lesson, Kelly recommended betting 11.8% of your bankroll on a single bet. If you're making multiple bets per day, you could easily have 30-50% of your bankroll in action at once. This leads to massive swings.
The Problem with Full Kelly
Let's see what happens with full Kelly in practice:
Scenario: You have a $10,000 bankroll and make 10 bets at full Kelly, averaging 10% per bet. You're now risking $10,000 (100% of your bankroll) across those bets.
If you go 4-6 on those bets, you could be down 20-30% despite having an edge on every single bet.
Warning
Psychologically Brutal: Most bettors can't handle the swings of full Kelly. They start questioning their models. They tilt. They make emotional decisions. The math says full Kelly is optimal, but psychology says it's unsustainable for most people.
The Edge Estimation Problem
Full Kelly assumes your edge estimate is perfect. In reality, it never is.
If you think you have a 10% edge but actually have a 7% edge, you're now significantly overbetting. Even a 2-3% overestimate puts you at serious risk of ruin.
This is why virtually no professional bettor uses full Kelly.
The Fractional Kelly Solution
The solution is to bet a fraction of what Kelly recommends. This dramatically reduces volatility while still capturing most of the growth.
Fractional Kelly
Bet Size = Kelly % × Fraction=A1*0.25Common Kelly Fractions
| Fraction | Description | Volatility | Growth Rate |
|---|---|---|---|
| Full Kelly (100%) | Maximum growth | Very High | 100% of optimal |
| Half Kelly (50%) | Balanced approach | Moderate | ~75% of optimal |
| One-Third Kelly (33%) | Conservative growth | Low-Moderate | ~56% of optimal |
| Quarter Kelly (25%) | Safety-first | Low | ~50% of optimal |
Key Insight
If you use Half Kelly, you capture about 75% of the growth rate of full Kelly, but you reduce your volatility by 50%. That's an incredible trade-off: give up 25% of growth to cut swings in half.
Full Kelly vs. Fractional Kelly Comparison
Let's compare bet sizes for the same bet using different Kelly fractions:
Bet Assumptions:
- Odds: -110 (b ≈ 0.909)
- Win Probability: 58% (~10.7% EV edge)
- Bankroll: $5,000
| Kelly Fraction | Recommended Bet | Volatility | Practical Note |
|---|---|---|---|
| Full Kelly (1.00x) | $590 | Very High | Max long-run growth, large drawdowns |
| Half Kelly (0.50x) | $295 | Moderate | Cuts risk while retaining strong growth |
| One-Third Kelly (0.33x) | $197 | Low-Moderate | Reduces volatility; smoother equity curve |
| Quarter Kelly (0.25x) | $148 | Low | Smaller risk exposure with slower growth |
Tip
Notice how Quarter Kelly wagers $148 instead of $590. That's a 75% reduction in bet size—and a 75% reduction in the emotional rollercoaster.
Monte Carlo Simulation: The Visual Proof
Professional bettors use Monte Carlo simulations to visualize the difference between Kelly fractions. Here's what 1000 bets at -110 with a 55% win rate looks like:
Full Kelly: Grows fastest but with extreme volatility. Bankroll might swing from $10,000 to $25,000 to $8,000 to $40,000.
Half Kelly: Still strong growth with much smoother path. Typical range: $10,000 to $20,000 with fewer scary drops.
Quarter Kelly: Slowest growth but most consistent. Steady climb from $10,000 to $15,000+ with minimal drawdowns.
Most professional bettors use Quarter to Half Kelly because the psychological sustainability outweighs the theoretical growth sacrifice.
Which Fraction Should You Use?
The right fraction depends on your experience, confidence, risk tolerance, and betting volume.
Use Quarter Kelly (25%) If:
- You're new to prop betting
- You're not confident in your edge estimates
- You have low risk tolerance
- You're betting on many games simultaneously
Tip
Quarter Kelly is my recommendation for most readers of this book. It's conservative, sustainable, and will keep you in the game long enough to learn and improve.
Use One-Third Kelly (33%) If:
- You have moderate experience (6+ months of validated results)
- You're confident in your models
- You can handle moderate swings
- You want balanced growth and safety
Use Half Kelly (50%) If:
- You're experienced and confident
- Your models have a proven track record
- You can handle significant volatility
- You're betting selectively (not high volume)
Warning
Half Kelly is for advanced bettors only. Even then, most professionals cap at this level.
Avoid Full Kelly Unless:
- You're a professional with years of experience
- You have ironclad confidence in your edges
- You can psychologically handle 30-40% drawdowns
- Even then, most professionals don't use full Kelly
The Progression Path
Here's a sensible timeline for adjusting your Kelly fraction:
| Timeline | Fraction | Why |
|---|---|---|
| Months 1-6 | Quarter Kelly | Learning, validating edge, building confidence |
| Months 6-12 | Quarter to One-Third | Validated edge, growing experience |
| Year 2+ | One-Third to Half | Proven track record, comfortable with variance |
| Expert | Half (rarely more) | Years of success, deep understanding |
Key Insight
Start with Quarter Kelly. As you gain experience and confidence over 6-12 months, consider moving to One-Third Kelly. Very few bettors should ever use Half Kelly or Full Kelly.
Kelly Criterion Calculator
Try the interactive calculator for this concept
📝 Exercise
Instructions
Fractional Kelly Comparison: You have an $8,000 bankroll and find a bet at -120 odds (b ≈ 0.833) with a 57% estimated win probability.
Full Kelly calculation: Kelly % = (0.833 × 0.57 - 0.43) / 0.833 ≈ 5.4%
Compare the bet sizes for different Kelly fractions.
You're a beginner with moderate risk tolerance. Which betting approach makes the most sense?