Kelly Criterion Betting: How Much to Stake

By MakeItBigToday Editorial Team · Published 2026-10-28

Short answer: the Kelly stake is f* = (p × d − 1) / (d − 1), where p is your estimated probability of winning and d is the decimal odds. If f* comes out zero or negative, you have no edge and the right stake is nothing.

That second sentence is the part people skip. Kelly is not a way to find good bets. It only answers “how much?” after you already believe a bet is priced in your favor, and its answer is only as good as your probability estimate. Every number in this guide is hypothetical, and none of it is a promise of profit.

The formula comes from John L. Kelly Jr.’s 1956 paper “A New Interpretation of Information Rate” in the Bell System Technical Journal, written about information theory rather than sports betting. Bettors and investors adopted it later because it describes the stake size that maximizes long-run growth of a bankroll when the edge is known.

The formula in one line

f* = (p × d − 1) / (d − 1)

• p is your estimated chance of winning, as a decimal.
• d is the decimal odds, the total return per unit staked including the stake.
• f* is the fraction of your current bankroll to bet.

The top of the fraction, p × d − 1, is your expected profit per unit staked. If you are unsure how to read or convert odds, my guide to sports betting odds covers decimal, fractional and American formats. The idea of a positive expected value is the same one behind value betting and expected value in poker.

Worked example (hypothetical numbers)

Assume a $1,000 bankroll and a bet at decimal odds of 2.10. You estimate the chance of winning at 52%.

• Expected profit per unit: 0.52 × 2.10 − 1 = 0.092
• Net odds: 2.10 − 1 = 1.10
• f* = 0.092 / 1.10 ≈ 0.084, or about 8.4% of the bankroll

Full Kelly says stake about $84. Because Kelly uses your current bankroll, the next stake is recalculated after each result: smaller after a loss, larger after a win.

Now change one input. If your honest estimate is 47% instead of 52%, then 0.47 × 2.10 − 1 = −0.013. The result is negative, so Kelly says do not bet at those odds.

Full vs half vs quarter Kelly

Using the same hypothetical $1,000 bankroll and 52% estimate at odds of 2.10:

Full Kelly is the theoretical growth-maximizing stake only if p is exactly right. In practice it produces deep drawdowns along the way, and a small overestimate of p pushes you into overbetting. Fractional Kelly trades some growth for a smoother ride and a buffer against your own estimation error. That is the main reason half Kelly is so common, and why cautious bettors go lower still.

Estimating p without fooling yourself

Since everything rides on p, the practical work is in estimating it. Start from the price: decimal odds of 2.10 imply roughly a 47.6% chance (1 ÷ 2.10) before you account for the bookmaker margin. Your estimate needs a reason to differ from that number, such as a model you have tested on past results or information the market has not priced. If you cannot explain why your 52% beats the market’s 47.6%, treat the gap as zero and do not bet.

Keep a record of every estimate next to the outcome. Over a large hypothetical sample, events you rated at 60% should win close to 60% of the time. If they win less, your estimates run hot, and the honest fix is to lower p or move to a smaller fraction of Kelly until your record says otherwise.

When Kelly breaks

Kelly is a sizing rule built on assumptions, and it stops being useful when they fail:

• Your probability is a guess. If p comes from gut feel rather than a tested model, the output is just that guess multiplied.
• The edge is not there. Against a bookmaker margin, many bets have negative expected value. Kelly sized correctly on a wrong p is still a losing plan.
• Multiple bets at once. Stacking several simultaneous Kelly stakes can commit far more of the bankroll than any single one suggests. Combined bets like parlays compound this; see my breakdown of parlay math.
• Bankroll is money you need. Kelly treats the bankroll as a pool you can afford to see shrink a lot. Rent money is not a bankroll.

Kelly for traders

Some traders use Kelly thinking as a cap on position size: the stronger and more reliable the edge, the larger the position can be, and with no edge the position is zero. The simple formula assumes fixed win and loss payoffs, which trades rarely have, so a direct plug-in can mislead. A fixed-risk approach like the one in my position sizing calculator guide is easier to apply, with Kelly used as a sanity check that you are not sizing beyond any plausible edge.

Responsible gambling

Gambling is for adults 18+ (21+ in some places), and only with money you can afford to lose. No staking method removes the house edge or guarantees a win. Set limits before you start and stop if betting stops being entertainment. If gambling is causing problems for you or someone close to you, the National Council on Problem Gambling lists confidential help, including the 1-800-GAMBLER helpline in the US. In the UK, BeGambleAware offers free, confidential support; other countries have their own local services.

This article is for education only. All figures are hypothetical, and nothing here is betting, investment or financial advice.

MakeItBigToday Editorial Team — MakeItBigToday staff, who are members of BYDFi's business development team. Guides are drafted with AI writing tools and the math is checked before publishing. The guides do not describe a personal trading history.