The Kelly criterion
The mathematically correct answer to 'how much should I bet.' Full Kelly, fractional Kelly, why pros use the latter, and what happens when you overbet.
The Kelly criterion answers a precise question: given my edge on a bet and the odds offered, what fraction of my bankroll should I risk to maximize the long-run growth rate of my bankroll? It is the closed-form solution. Most professional bettors size around it.
The formula
For a binary bet with two outcomes, Kelly returns the fraction of bankroll to risk.
f = (bp - q) / b Where: f = fraction of bankroll to bet b = decimal odds - 1 (i.e. profit per unit risked) p = your estimated probability of winning q = 1 - p
An example. You have a $10,000 bankroll. You estimate a 55% probability of winning a bet offered at +110 (decimal 2.10).
BANKROLL $10,000 PRICE +110 (b = 1.10) YOUR PROB 55% (p = 0.55, q = 0.45) f = (1.10 × 0.55 - 0.45) / 1.10 = (0.605 - 0.45) / 1.10 = 0.141 FULL KELLY STAKE $10,000 × 0.141 = $1,410
Full Kelly says risk 14.1% of bankroll on this bet. Most working bettors will read that and immediately wonder if it is too much. They are right to wonder.
Kelly Sizing
// WB://TOOLS/KELLYRecommended sizing
Full Kelly maximizes long-run growth assuming you know the probability exactly. In practice, most operators bet quarter or half Kelly to dampen drawdowns. Negative Kelly means the bet is negative EV; do not bet.
Why full Kelly is too aggressive in practice
Full Kelly maximizes the long-run logarithmic growth of bankroll under one specific assumption: that you know the probabilities exactly. If your probability estimate is wrong, even by a little, full Kelly massively overbets.
Most real-world probability estimates are noisy. A model with 53% confidence might be a 51% true probability event. A 'lock' you think is 70% might actually be 60%. Full Kelly does not forgive that uncertainty. The penalty for overbetting is substantially worse than the penalty for underbetting.
Fractional Kelly
Most professionals bet a fixed fraction of full Kelly: half-Kelly, quarter-Kelly, or even one-eighth Kelly. The math says you give up some of the long-run growth in exchange for a much smoother equity curve and far lower ruin risk.
| Sizing | Long-run growth | Typical drawdown |
|---|---|---|
| Full Kelly (1.0x) | Maximum (theoretical) | Severe. 50%+ peak-to-trough is normal. |
| Half Kelly (0.5x) | ~75% of full | Around 25% peak-to-trough. |
| Quarter Kelly (0.25x) | ~44% of full | Around 12% peak-to-trough. |
| Eighth Kelly (0.125x) | ~23% of full | Around 6% peak-to-trough. |
Quarter Kelly is the most common professional setting. It captures a meaningful fraction of full Kelly's growth with drawdowns that operators can stomach without abandoning the strategy mid-streak.
Why drawdowns matter so much
The math of Kelly is built on the assumption that you keep betting the strategy. The strategy needs to survive its drawdowns. A 50% drawdown does not just hurt your bankroll; it hurts your conviction in the strategy. Most bettors abandon their approach somewhere on the descent. The next 1,000 bets that would have recovered the drawdown never get placed.
Quarter or half Kelly is the sizing that lets you keep playing. Full Kelly is the sizing that maximizes growth assuming nothing breaks. In practice, things break.
Kelly when probabilities are uncertain
If you are not confident in your probability estimates, treat the formula's output as an upper bound and discount accordingly. A simple rule of thumb: if your edge could plausibly be off by 50% in either direction, bet quarter Kelly.
If your edge is verified by a long-running CLV record (see closing line value), you can bet closer to full Kelly. If your edge is your gut feel about which team will win, you should not be using Kelly at all.
Kelly across multiple bets
When you have multiple positive-EV bets available simultaneously, Kelly does not simply scale. The proper version (multivariate Kelly) accounts for correlation between bets and total exposure. A simple approximation: cap total exposure across all open bets at one full Kelly, allocated across bets in proportion to their individual Kelly recommendations.
Two Kelly bets at 5% each (10% combined exposure) is fine. Ten Kelly bets at 5% each (50% combined exposure) is overbetting catastrophically. The portfolio matters, not the bets in isolation.
When Kelly is the wrong tool
- When your bankroll is tiny relative to minimum bet sizes. The math assumes you can size continuously. If the smallest bet is 5% of your bankroll, Kelly is moot.
- When you cannot tolerate the implied drawdowns. Personal psychology matters. A risk-averse bettor sizing eighth Kelly is making a sound choice.
- When your edge is poorly measured. Garbage in, garbage out. Kelly amplifies the cost of bad probability estimates.
What to read next
Variance and drawdown goes deeper on what to expect from any sizing strategy over a long sample. Conviction-proportional sizing is how WagerBird's confidence model translates into bet size in practice.