The Kelly Criterion

While flat betting is simple and effective, there's a more sophisticated approach to bet sizing that has been mathematically proven to maximize long-term growth: the Kelly Criterion.

Developed by John Kelly at Bell Labs in 1956, the Kelly Criterion calculates the optimal bet size based on your edge and the odds you're getting. It's used by professional gamblers, hedge funds, and anyone serious about optimal capital allocation.

The Kelly Formula

Where:

• p = your estimated probability of winning (as a decimal)
• q = probability of losing = 1 - p
• b = decimal odds you're receiving (win_profit / risk)

Kelly Example 1: Even Money Bet (+100)

Let's start simple. You find an even-money bet (+100 odds) where you estimate a 55% chance of winning.

Setup:

• p = 0.55 (55% win probability)
• q = 0.45 (45% loss probability)
• b = 1.0 (even money: win $100 on a $100 bet)

Calculation:

Kelly % = (b × p - q) / b
Kelly % = (1.0 × 0.55 - 0.45) / 1.0
Kelly % = (0.55 - 0.45) / 1.0
Kelly % = 0.10 / 1.0
Kelly % = 10%

Result: Bet 10% of your bankroll. On a $5,000 bankroll, that's $500.

Kelly Example 2: Betting on a Favorite (-110)

Now let's look at the most common scenario: betting at -110 odds with a 58% estimated win probability.

Setup:

• p = 0.58
• q = 0.42
• Odds: -110 → Decimal = 1 + (100/110) ≈ 1.909
• b = 1.909 - 1 ≈ 0.909

Calculation:

Kelly % = (0.909 × 0.58 - 0.42) / 0.909
Kelly % = (0.527 - 0.42) / 0.909
Kelly % = 0.107 / 0.909
Kelly % = 11.8%

Result: Bet 11.8% of your bankroll—about $590 on a $5,000 bankroll.

Kelly Example 3: Betting on an Underdog (+150)

For underdogs, you win less often but the payout is bigger. Let's say you estimate a 45% chance at +150 odds.

Setup:

• p = 0.45
• q = 0.55
• Odds: +150 → Decimal = 1 + (150/100) = 2.5
• b = 2.5 - 1 = 1.5

Calculation:

Kelly % = (1.5 × 0.45 - 0.55) / 1.5
Kelly % = (0.675 - 0.55) / 1.5
Kelly % = 0.125 / 1.5
Kelly % = 8.3%

Result: Bet 8.3% of your bankroll—about $415 on a $5,000 bankroll.

Why Kelly Works

The Kelly Criterion is mathematically optimal for several reasons:

1. Maximizes Long-Term Growth Rate

No other bet sizing strategy will grow your bankroll faster over the long run, assuming your edge estimates are accurate. This has been proven mathematically and validated empirically by decades of professional gambling and investing.

2. Prevents Overbetting

If you bet more than Kelly, your risk of ruin increases dramatically. Betting 2x Kelly doesn't give you 2x the growth—it gives you massive volatility and a real chance of going broke.

3. Scales with Your Edge

Bigger edges mean bigger bets. Smaller edges mean smaller bets. This is intuitive and mathematically sound.

4. Accounts for Odds

A 5% profit edge at +200 is different from a 5% profit edge at -200. Kelly adjusts for this automatically.

The Volatility Trap: Why Kelly Bets More on Favorites

Here's something counterintuitive: Kelly recommends betting more on favorites than underdogs, even with the same profit edge.

Why? Because underdogs carry higher variance.

With a 5% edge at -200, you win approximately 70% of the time. Long losing streaks are rare. Your bankroll can safely handle larger bets.

With a 5% edge at +200, you win only 35% of the time. It's perfectly normal to go on 10-12 bet losing streaks. Larger bets would devastate your bankroll during these expected cold streaks.

When Kelly Says "Don't Bet"

If your Kelly calculation gives a negative number, that means you don't have an edge—or worse, you have negative expected value. Don't place the bet.

Example: You estimate 48% win probability at -110 odds.

Kelly % = (0.909 × 0.48 - 0.52) / 0.909
Kelly % = (0.436 - 0.52) / 0.909
Kelly % = -0.084 / 0.909
Kelly % = -9.2%

A negative Kelly means this bet has negative expected value. Pass.