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Kelly Criterion

The Kelly criterion is a formula for optimal bet sizing given your edge and the odds offered. It maximizes long-run bankroll growth — at the cost of vicious short-term variance. Used carefully it's the sharpest staking tool available. Used naively it's a fast track to ruin.

The Formula

Kelly fraction f = (bp − q) / b

  • f = fraction of your bankroll to bet
  • b = net decimal odds minus 1 (e.g., +150 = decimal 2.50, b = 1.50)
  • p = your estimated probability of winning
  • q = 1 − p (probability of losing)

Worked Example

You estimate the Rangers have a 55% chance to beat the Devils. The book is offering Rangers at +110 (decimal 2.10).

  • b = 1.10
  • p = 0.55
  • q = 0.45
  • f = (1.10 × 0.55 − 0.45) / 1.10 = (0.605 − 0.45) / 1.10 = 0.155 / 1.10 = 0.141

Full Kelly says bet 14.1% of your bankroll on this game. On a $2,000 bankroll, that's $282.

Why Full Kelly Is Dangerous

Two reasons.

First, your edge estimates are wrong. If you think Rangers are 55% but they're actually 52%, Kelly tells you to bet too much. Edge estimation error is the #1 hidden risk in Kelly sizing.

Second, variance. Even with a correct edge, full Kelly produces drawdowns of 50%+ regularly. A correct full-Kelly bettor with a 5% edge will experience a 50% bankroll drawdown about once every 50 bets. Most humans cannot psychologically tolerate that.

Half-Kelly and Quarter-Kelly

Practical sharps use a fractional Kelly — typically half (0.5x) or quarter (0.25x). Fractional Kelly:

  • Reduces expected long-run growth by ~25% (half) or ~50% (quarter)
  • Reduces variance dramatically — max drawdowns shrink to manageable levels
  • Provides cushion against your edge estimate being wrong

The earlier $282 full-Kelly bet becomes $141 at half-Kelly or $70 at quarter-Kelly. Most disciplined sports bettors use quarter-Kelly or simply use flat 1-2% staking, which is similar to quarter-Kelly for typical small edges.

When NOT to Use Kelly

  • You don't have a model. Kelly requires a probability estimate. "It feels like a lock" is not p = 0.65. If you can't justify your number, don't size with Kelly — use flat 1%.
  • Tiny edges. When p is close to the book's implied probability, Kelly tells you to bet trivial amounts. The variance overhead and tracking cost may not be worth it.
  • Correlated bets. Kelly assumes independent outcomes. Parlays violate independence (multiple legs in one game). Same-game parlays violate it severely. Don't Kelly-size SGPs.
  • Negative edge. If f comes out negative, the formula is telling you not to bet. Skip the wager.

Kelly and Bankroll Management

Kelly assumes you can resize your bankroll continuously. In practice, recalculate Kelly weekly or after meaningful P/L moves. Treat Kelly output as the upper bound — pair it with a hard 5% cap per bet regardless of what Kelly says.

See bankroll management for the broader framework Kelly fits inside.

Practical Recipe

  1. Build a probability estimate for the game (model, research, or systematic process).
  2. Convert the book's odds to implied probability. See odds explained.
  3. If your p exceeds implied probability by enough to clear the vig, calculate Kelly.
  4. Apply 0.25x multiplier. Cap at 3% of bankroll regardless.
  5. Bet. Track. Recalibrate.

The Honest Truth

For 95% of recreational bettors, Kelly is mathematical theater. Without a real probability model, your edge estimates are guesses, and Kelly will systematically over-stake your bad picks. Flat 1-2% staking captures most of Kelly's benefit at a fraction of the risk. Use Kelly when you have actual modeling. Use flat staking when you don't.

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