At 55% on −110, full Kelly is 5.50% of the roll — a quarter keeps 44% of the growth.
Bet it — $13.75 is quarter Kelly's 1.38% of $1,000.00 at −110.
Full stake 5.50% · fastest growth, only if your 55.0% is exactly rightPast 11.0% you shrink
- The price implies
- 52.4%
- Your edge over it
- +2.6 pts
- Full stake: (b × p − q) ÷ b
- 5.50%
- The stake you bet at a quarter
- $13.75
Definition
What Kelly staking is
Kelly staking is bankroll-percentage sizing scaled to your edge and your odds.
Bet too little and you leave growth on the table; bet too much and a normal cold streak ruins you before the edge pays off. The Kelly criterion solves for the single bet fraction that maximizes long-run growth of the bankroll — the mathematically optimal middle. It does not care how confident you feel. It cares about exactly two things: how likely you are to win, and how much you collect when you do.
The math
The formula
Three inputs, each plain-English:
- p. your true win probability — your model's honest estimate, not the book's implied number.
- q. the probability you lose, which is simply 1 − p.
- b. the net decimal payout — what you win per 1 staked. A +120 underdog pays b = 1.2; a −110 favorite pays b = 0.909.
The numerator b × p − q is your edge expressed in payout terms. When it is positive you have a bet worth making; when it is zero or negative, Kelly stakes nothing — the formula passes for you. Try it in the curve above: drop your chance to the price’s own implied number and the stake goes to $0.
The discipline
Why sharps bet a fraction of Kelly
Full Kelly is optimal only if your edge estimate is perfect — and it never is.
The formula assumes you know your true win probability exactly. In reality that number is a forecast with error bars, and full Kelly punishes overconfidence brutally: bet full Kelly on an edge you have overestimated by a few points and you are wildly overstaked. On the curve above, a quarter stake keeps 44% of the growth full Kelly would, and double the full stake grows nothing at all. That trade is why serious bettors almost never bet more than half Kelly, and many sit at a quarter.
In practice
Bankroll stages
The right fraction is not just about variance tolerance — it is about what your bankroll and your books will actually let you do. As the roll grows, the binding constraint shifts from survival to book limits and account longevity.
Quarter Kelly
Small bankrolls feel every swing. Quarter Kelly keeps a cold streak from gutting the roll before the edge has a chance to show, and it keeps single-bet limits at recreational books from forcing you off-size.
Quarter to half Kelly
With more cushion you can lean toward half Kelly on your highest-confidence edges while holding quarter on the marginal ones. Spread across more books and the per-bet limit stops dictating your stake.
Half Kelly, multi-book
At scale the binding constraint is rarely the math — it is book limits and account longevity. Half Kelly across many books captures growth while keeping any one account from drawing a limit before you have placed the bet.
The long game
What 300 picks looks like
An edge is not a payday; it is a slope. Below is the textbook expected-growth curve for a modest edge — a 55% win probability on a −110 price — staked at full, half and quarter Kelly across 300 settled bets.
Two lessons. First, even a small edge compounds meaningfully over a few hundred plays — which is why 300 settled bets is the rough horizon where a real edge separates from noise. Second, the steepest paper curve is the most dangerous one to ride, because the model assumes your edge is exactly what you think it is.
Questions
Kelly, answered
4 questions · tap one to unfold the answer
Yes — Kelly staking is a bankroll-sizing rule, not a way to beat a sportsbook, so it is entirely legal to use. The practical catch is that books may limit or close accounts that consistently bet winning numbers, regardless of how you size them, because winning is what triggers a review, not the staking math.
Almost never bet full Kelly — full Kelly is only optimal if your edge estimate is exactly right, and it never is. Because your true probability is itself a guess, full Kelly massively overbets the moment you are slightly too confident, so half-Kelly or quarter-Kelly buys a huge cut in volatility for only a small cut in long-run growth.
You need positive expected value before Kelly stakes anything — when your win probability is below the price's break-even, the formula returns a negative or zero fraction, which is the math telling you to pass. There is no minimum edge to act on, but on thin edges the stake is small by design, because a 1% edge does not justify a 5% bet.
A real edge typically takes several hundred settled bets to separate cleanly from variance — most processes need 300 or more plays before the bankroll curve reflects the edge rather than the noise. Track closing-line value alongside it: positive CLV confirms the edge is real long before the win rate has the sample size to prove it.
Continue reading
Growth curves on stated inputs, not a record. Not a sportsbook — bet legally and within your means.