Direct Answer
The Kelly Criterion gives the bet size that maximizes the long-run logarithmic growth of a bankroll. The formula is f = (bp − q) / b, where b is decimal odds minus one, p is win probability, and q is 1 − p. Most professionals use fractional Kelly because full Kelly is mathematically optimal but practically too volatile.
Key Takeaways
- Kelly maximizes geometric growth under known edge.
- Real edges are uncertain — use fractional Kelly.
- ¼ to ½ Kelly is the professional range.
- Above 2× Kelly, growth turns negative.
Worked example
A +120 underdog you believe wins 50% of the time: b = 1.20, p = 0.50, q = 0.50. Kelly = (1.20 × 0.50 − 0.50) / 1.20 ≈ 8.3% of bankroll. That is enormous — a $10,000 roll would stake $833 on one bet. Even with positive EV, drawdowns of 40–60% are normal.
Why fractional Kelly wins
Full Kelly assumes your edge estimate is exact. Real edges are uncertain. Half-Kelly recovers ~75% of long-run growth with ~50% of the variance. Past 2× Kelly, long-run growth becomes negative even with positive-EV bets.
What Kelly does not do
It does not protect against estimation error, correlated bets, liquidity limits, or withdrawal needs. Treating it as a magic formula has bankrupted skilled bettors with genuine edges.
Frequently asked questions
Why not bet full Kelly if it's optimal?+
Because it's optimal only when your probability estimate is exact. Any overestimate of edge causes outsized losses, and small errors compound badly.
Does Kelly handle multiple simultaneous bets?+
Yes, but the math requires accounting for correlation. Independent bets can be sized near individual Kelly; correlated bets need reduced exposure.
Educational only. Not wagering, financial, or legal advice. See our editorial policy.