The Kelly Criterion
Knowing a bet is positive-EV tells you to make it. The Kelly Criterion tells you how much, the stake that grows a bankroll fastest without blowing it up.
The Kelly Criterion is a formula that tells you how much of your bankroll to bet based on your edge and the odds. It sizes bets bigger when your edge is larger, aiming to grow a bankroll fast without risking ruin.
The problem Kelly solves
Say you've found a real edge. How much of your bankroll should ride on it? Bet too little and you leave growth on the table. Bet too much and one bad run wipes you out. The Kelly Criterion is a formula that answers this exactly: the fraction of your bankroll that, bet over and over, grows it the fastest.
The formula
In betting terms, the Kelly fraction is:
f = (b × p minus q) / b
where b is the profit per $1 staked (decimal odds minus 1), p is your estimated win probability, and q is your chance of losing (1 minus p). The answer is the share of your bankroll to bet. It's driven entirely by your edge. The bigger the gap between your probability and the price, the more Kelly tells you to bet.
A bet at +100 (decimal 2.00, so b = 1) that you think wins 55% of the time. p = 0.55, q = 0.45.
f = (1 × 0.55 minus 0.45) / 1 = 0.10. Kelly says bet 10% of your bankroll. Shrink the edge to a 52% win rate and it drops to about 4%. No edge at all (50%) and Kelly says bet zero. The formula flat refuses to bet when you've got no advantage.
Put your own price, probability and bankroll into the Kelly calculator to see the fraction and the stake it suggests.
Why almost everyone bets fractional Kelly
Full Kelly is mathematically perfect but wild. It fires off big bets and stomach-churning swings, and it's merciless about one thing: if your probability estimate is off, it overbets and can gut your bankroll. Since nobody's estimates are perfect, most serious bettors use half Kelly or quarter Kelly. Same formula, then bet half or a quarter of what it says. You give up a little growth for a lot less volatility and a big cushion for being wrong.
The catch, one more time
Kelly is only as good as the probability you feed it. Garbage in, ruin out. It's a powerful tool once you can estimate real edges, and a dangerous one if you're kidding yourself about how sharp your reads are. Pair it with honest records and closing line value to confirm your edges are real before you let Kelly size them.
Common questions
How does the Kelly Criterion work?
It takes your estimated win probability and the odds, and outputs the fraction of your bankroll to stake. More edge means a bigger bet; no edge means no bet. Our Kelly calculator runs the formula for you.
What is fractional Kelly?
Betting a set fraction of what full Kelly suggests, like half or a quarter. Because your edge estimate is never perfect, most bettors use fractional Kelly to smooth out the swings while keeping most of the growth.
Why not just bet full Kelly?
Full Kelly assumes you know your true edge exactly, which you do not. Overestimate it and full Kelly overbets and can crush your bankroll. Half Kelly is the common, safer compromise.
Key takeaways
- Kelly answers 'how much,' sizing bets to your edge for the fastest long-run growth.
- f = (b times p minus q) / b. Bigger edges mean bigger bets, and no edge means bet nothing.
- Full Kelly is optimal but wild and unforgiving of bad estimates, so most people bet half or quarter Kelly.
- It's only as good as your probability estimate. Confirm your edges are real before sizing with it.