Glossary · Staking
Kelly Criterion
The mathematically optimal stake size given your edge and the odds — maximises long-run bankroll growth.
The Kelly Criterion tells you the fraction of your bankroll to stake on a bet so that, over the long run, your bankroll grows as fast as possible without going broke.
It rewards edge and punishes uncertainty. If you have no edge, Kelly stakes zero. If your edge is huge, Kelly stakes aggressively. Most professional bettors stake a fraction of full Kelly — commonly half-Kelly or quarter-Kelly — because real-world probability estimates are imperfect and full Kelly is brutally volatile.
Formula
f* = (bp - q) / b where: f* = fraction of bankroll to stake b = decimal odds - 1 (the net amount won per 1 unit staked) p = your estimated probability the bet wins q = 1 - p (probability the bet loses) Equivalent form using decimal odds (d): f* = (p · d - 1) / (d - 1) Fractional Kelly: stake = bankroll · f* · k where k is your Kelly fraction (e.g. 0.5 for half-Kelly).
Worked example
Bankroll: $1,000. Decimal odds: 2.10. Your model probability: 52%.
b = 2.10 - 1 = 1.10
p = 0.52
q = 0.48
f* = (1.10 · 0.52 - 0.48) / 1.10
= (0.572 - 0.48) / 1.10
= 0.0836 → 8.36% of bankroll on full Kelly
Full-Kelly stake: $83.60
Half-Kelly stake: $41.80 (recommended in practice)Related
- Expected Value (EV)— The average profit (or loss) per unit staked if the same bet were repeated infinitely.
- Edge— How much better your estimated probability is than the market's implied probability.
- Bankroll— The pool of money set aside exclusively for betting. Never your rent.
- Variance— The natural swings around your true expected value. Bigger edges have smaller swings; longshots have huge ones.
- Fractional Kelly— Staking a fixed fraction (e.g. 0.5×) of full Kelly to reduce variance.