The Kelly Criterion: How Much Should You Bet?
Finding +EV bets is only half the problem. The Kelly Criterion tells you exactly how much to wager — and why most bettors should use a fraction of it.
The bet sizing problem
You've found a +EV bet. Great. Now how much do you wager?
Bet too little and you're leaving money on the table. Bet too much and a bad streak wipes you out. The Kelly Criterion, developed by John Kelly at Bell Labs in 1956, gives the mathematically optimal answer.
The formula
For a simple two-outcome bet at decimal odds d with a win probability p:
Kelly % = p - (1 - p) / (d - 1)
Or equivalently: Kelly % = (p x d - 1) / (d - 1)
This gives you the fraction of your bankroll to wager.
A worked example
You estimate a 55% chance on a bet priced at +120 (decimal 2.20).
Kelly % = (0.55 x 2.20 - 1) / (2.20 - 1) = (1.21 - 1) / 1.20 = 0.175
Kelly says bet 17.5% of your bankroll. On a $10,000 bankroll, that's $1,750.
Does that feel aggressive? It should.
Why full Kelly is dangerous
Full Kelly maximizes long-term growth rate. That's the theory. In practice, it has two serious problems:
- Your edge estimate is noisy. If you think you have 55% but you actually have 51%, full Kelly oversizes dramatically. The formula is extremely sensitive to probability inputs.
- The variance is brutal. Full Kelly has an expected drawdown of 50% of your bankroll at some point. Most humans can't stomach that.
Simulations consistently show that full Kelly produces the highest long-term growth, but also the wildest swings. A single overestimated edge can set you back months.
Fractional Kelly: the practical answer
Almost every serious bettor uses a fraction of Kelly:
- Half Kelly — bets half the Kelly amount. Captures ~75% of the growth rate with dramatically lower variance. This is the most common choice among professional bettors.
- Quarter Kelly — very conservative. Captures ~50% of the growth rate. Good when you're uncertain about your edge or working with a smaller bankroll.
The tradeoff is always the same: less growth in exchange for less risk. Since most of us overestimate our edge, fractional Kelly acts as a built-in correction.
When Kelly says don't bet
If the Kelly formula returns zero or negative, the bet is -EV. Don't take it. Kelly will never tell you to bet on a losing proposition.
This is a useful sanity check. Run your numbers through the Kelly Criterion calculator alongside the EV calculator. If both tools agree the bet has an edge, size it with fractional Kelly and move on.
Kelly and turnover
Kelly tells you how much to bet, but how often you bet matters just as much. A smaller edge bet more frequently can outperform a larger edge bet rarely. Read why bankroll turnover matters more than edge size for the full math.
The rule of thumb
Find the edge with expected value analysis. Size it with half Kelly. Repeat a thousand times. That's the entire strategy.