What is the Kelly Criterion?

If you've been betting for a while, you've probably wondered: "What's the perfect bet size?" Too small and you're missing out on profits. Too big and you risk going broke. The Kelly Criterion provides a mathematical answer to this age-old question.

Developed by Bell Labs scientist John Kelly in 1956, the Kelly Criterion calculates the optimal fraction of your bankroll to bet based on your edge and the odds offered. It's used by professional gamblers, hedge funds, and investment managers worldwide.

The Formula

Kelly % = (bp - q) / b

Where:

• b = decimal odds - 1 (the profit multiplier)
• p = your estimated probability of winning
• q = probability of losing (1 - p)

Don't worry if this looks intimidating – it's simpler than it appears.

Step-by-Step Example

Let's say Melbourne Storm are playing Parramatta Eels, and you find these odds:

• Melbourne Storm to win: 2.40
• Your estimated probability: Storm have a 50% chance of winning

1. Calculate the Variables

• b = 2.40 - 1 = 1.40
• p = 0.50 (50%)
• q = 1 - 0.50 = 0.50 (50%)

2. Apply the Formula

• Kelly % = (1.40 × 0.50 - 0.50) / 1.40
• Kelly % = (0.70 - 0.50) / 1.40
• Kelly % = 0.20 / 1.40 = 0.143
• Kelly suggests betting 14.3% of your bankroll.

What Kelly Tells You

The Kelly percentage reveals important information:

• Positive result: You have an edge – bet this percentage
• Zero result: No edge – don't bet
• Negative result: You're at a disadvantage – definitely don't bet

In our example, 14.3% suggests you have a significant edge worth betting on.

The Problem with Full Kelly

While mathematically optimal for long-term growth, full Kelly can be aggressive:

• Our 14.3% example means betting $143 on a $1,000 bankroll
• Kelly assumes perfect probability estimation (rarely realistic)
• It can suggest very large bets during hot streaks
• Volatility can be stomach-churning

Fractional Kelly: The Practical Solution

Most professional bettors use "fractional Kelly" – betting a fraction of what full Kelly suggests:

• Quarter Kelly (25%): Conservative approach
• Half Kelly (50%): Moderate approach
• Three-Quarter Kelly (75%): Aggressive approach

Using our example from earlier:

• Full Kelly: 14.3%
• Half Kelly: 7.15%
• Quarter Kelly: 3.6%