Advanced Lesson 9 of 12

Kelly Criterion

Key Takeaways

  • Kelly % = (bp - q) / b, where b=odds-1, p=win prob, q=lose prob
  • Full Kelly is aggressive; most use fractional Kelly (25-50%)
  • Kelly only works if your probability estimates are accurate

What Is the Kelly Criterion?

The Kelly Criterion is a mathematical formula that determines the optimal bet size to maximize bankroll growth while minimizing risk of ruin.

Unlike flat betting (same stake every bet), Kelly adjusts your stake based on your edge. Bigger edge = bigger bet. No edge = no bet.

The formula was developed by John Kelly at Bell Labs in 1956 and has been adopted by professional gamblers and investors worldwide.

The Kelly Formula

Kelly % = (bp - q) / b. Where: b = decimal odds - 1, p = probability of winning, q = probability of losing (1 - p).

Example: Odds of 3.00 (b=2), you estimate 40% win probability (p=0.4, q=0.6). Kelly = (2×0.4 - 0.6) / 2 = (0.8 - 0.6) / 2 = 0.1 = 10% of bankroll.

If Kelly outputs zero or negative, the bet has no value - don't place it. Kelly automatically tells you which bets to make and how much to stake.

Fractional Kelly in Practice

Full Kelly is mathematically optimal but volatile. Most bettors use fractional Kelly - typically 25-50% of the suggested stake - to reduce variance.

Quarter Kelly (25%) significantly smooths your equity curve while sacrificing only a small amount of long-term growth. It's a good balance for most bettors.

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Test Your Knowledge

Answer these questions to complete the lesson and track your progress.

1. What does the Kelly Criterion determine?

2. Why do most bettors use fractional Kelly?

3. If Kelly outputs a negative number, you should: