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Kelly Criterion
generalA mathematical formula for determining the optimal bet size based on your perceived edge and the odds offered.
Key Takeaways
- 1Kelly Criterion calculates optimal bet size based on edge
- 2Most pros use fractional Kelly (25-50%) to reduce variance
- 3Over-betting is more costly than under-betting
- 4Requires accurate probability estimation to work properly
What is the Kelly Criterion?
The Kelly Criterion is a formula developed by John Kelly at Bell Labs in 1956. It calculates the optimal percentage of your bankroll to wager based on your edge and the odds.
The Formula
f = (bp - q) / b**
Where:
- f* = fraction of bankroll to wager
- b = decimal odds - 1 (net odds)
- p = probability of winning
- q = probability of losing (1 - p)*
Example
You believe a team has a 55% chance of winning at +100 (decimal 2.0):
- b = 2.0 - 1 = 1
- p = 0.55
- q = 0.45
- f* = (1 × 0.55 - 0.45) / 1 = 0.10 = 10% of bankroll*
Fractional Kelly
Most professionals use fractional Kelly (typically 25-50% of the full Kelly recommendation) because:
- It reduces variance significantly
- It protects against errors in probability estimation
- The cost of over-betting is much higher than under-betting
Key Insight
The Kelly Criterion assumes you know the true probability. In practice, your probability estimates are imperfect, which is why fractional Kelly is preferred.