Free Kelly sizing tool — see EV%, bankroll fraction and dollar stake in seconds
Reviewed by the OddsGPT Betting Tools editorial team · Updated May 2026
The Kelly Criterion is a bankroll-sizing formula that tells you what fraction of your roll to risk when you have a repeatable edge. Unlike flat staking, Kelly scales bets with confidence: stronger edges warrant larger wagers, while thin edges stay small—protecting you from ruin during variance.
This free Kelly calculator converts your odds format, win probability, and bankroll into expected value (EV%), optimal Kelly fraction, and dollar stake—instantly. Use fractional Kelly (0.25–0.5×) in real play to smooth drawdowns while still compounding long-term growth.
Choose fractional Kelly, then enter odds, win probability and bankroll — results update automatically.
Full Kelly f* at your current odds across win rates 10%–90%. Dot marks your entered probability.
Le calculateur Kelly vous aide à déterminer la taille optimale de mise en fonction du critère de Kelly, qui maximise la croissance à long terme tout en minimisant le risque de ruine.
Ce calculateur vous montrera :
Remarque: Le critère de Kelly suppose que vous pouvez estimer avec précision votre probabilité de victoire. Soyez conservateur dans vos estimations pour éviter de sur-parier.
Kelly maximizes long-term logarithmic growth of bankroll when your win probability is accurate. For net decimal odds b and win probability p (lose probability q = 1 − p), the full Kelly fraction is f* = (b·p − q) / b, equivalent to (b·p − 1) / (b − 1). When f* ≤ 0, there is no +EV bet—staking anyway burns bankroll.
Full Kelly is volatile: a few losses can slash balance sharply. Most bettors use fractional Kelly (multiplying f* by 0.25–0.5) and hard caps (e.g., never more than 5% of roll on one play). Pair Kelly with +EV screening so you only size bets that pass expected value checks first.
The Kelly fraction (before your multiplier) for decimal odds \(O\) and win rate \(p\) is:
Stake = Bankroll × (fractional multiplier) × \(f^*\). Expected value % ≈ \((p \cdot (O-1) - q) \times 100\) where \(q = 1-p\).
The Kelly Criterion was published by Bell Labs researcher John L. Kelly Jr. in 1956 (A New Interpretation of Information Rate, American Mathematical Monthly). Kelly showed how to bet a hidden binary signal when odds are favorable—maximizing the long-run growth rate of capital. Claude Shannon, father of information theory, recognized the link between Kelly sizing and optimal information use; the formula is sometimes called the Kelly–Shannon criterion.
Edward O. Thorp later applied Kelly to blackjack and markets (Beat the Dealer, 1962; Beat the Market, 1967), proving the theory works outside toy models. Leo Breiman (1961) and the edited volume The Kelly Capital Growth Investment Criterion (MacLean, Thorp, Ziemba) formalized why log-utility maximization dominates fixed-stake play when edges are small but repeatable.
Further reading: Kelly (1956) original paper (PDF) · Kelly criterion overview. OddsGPT formulas are cross-checked against these sources.
Kelly sizing is not arbitrary—it maximizes the expected logarithm of wealth over repeated bets. If you risk fraction f of bankroll on a binary wager with net odds b (decimal O − 1) and win probability p, one period later wealth is either (1 + f·b) or (1 − f) times the previous roll. Maximizing E[log W] yields f* = (b·p − q) / b.
The log-utility assumption penalizes ruin heavily: losing 50% requires +100% to recover, so Kelly naturally shrinks stakes when edge is thin. This is why f* hits zero exactly when EV = 0—the growth-optimal strategy is to pass.
Edge (advantage) = your win probability minus break-even probability. At decimal 2.00 (even money), break-even is 50%. If your model says 55%, edge = 5 percentage points. Full Kelly: f* = edge / b = 0.05 / 1.0 = 5% of bankroll. Half Kelly → 2.5%; on a $20,000 roll that is $500.
Full Kelly maximizes long-run growth rate but produces brutal short-term swings. A 25% Kelly stake that loses three times in a row cuts bankroll by roughly 42% (0.75³ ≈ 0.58). Variance scales with f²—doubling Kelly quadruples volatility.
Fractional Kelly (0.25–0.5×) sacrifices a small slice of theoretical CAGR for materially smoother equity curves. Pair with a hard cap (e.g., 5% max per bet) and never increase multiplier after losses—chasing violates the independence assumption.
Scenario: You back an underdog at +150 (decimal 2.50), believe they win 55% of the time, bankroll $10,000, fractional Kelly 0.5×.
| Input | Value | Note |
|---|---|---|
| Decimal odds / p | 2.50 / 55% | +150 American |
| Full Kelly f* | 25% | ×0.5 multiplier → half-Kelly stake |
f* = (2.50·0.55 − 0.45) / 2.50 = 0.25 → 25% of roll at full Kelly (aggressive). Select Half Kelly in the calculator → 12.5% stake → $1,250 on a $10k bankroll.
Estimation error is the silent killer: if you think p = 55% but true p is 50%, full Kelly oversizes and increases risk of ruin. Halving Kelly cuts variance roughly in half while sacrificing only a fraction of theoretical growth—an excellent trade for real markets.
Combine fractional Kelly with flat caps, stop-loss rules, and CLV tracking. Never chase losses by cranking the multiplier after a bad beat—the math assumes independent, identically modeled edges.
Kelly maximizes the <strong>geometric mean</strong> of wealth, not the arithmetic average. Log utility U(W) = log(W) is concave: a 50% loss hurts more than a 50% gain helps, so full Kelly is already aggressive. Research cited by Thorp and Ziemba shows <strong>half Kelly</strong> captures ~75% of the maximum growth rate while cutting variance roughly in half—often the best real-world compromise when p is estimated, not known.
Quarter Kelly (~0.25×) is common among sports bettors with noisy models; it sacrifices more CAGR but keeps drawdowns survivable through losing streaks. Our calculator exposes full, half, quarter, and custom multipliers so you can stress-test sizing before committing real money.
Overconfident probability estimates. If you input p = 58% but true p is 52%, Kelly oversizes dramatically. A 6-point error on a −110 line can turn a +EV bet into negative growth at full Kelly. Always sanity-check p against closing line and no-vig fair odds.
Over-Kelly and ignoring caps. Betting above Kelly ("double Kelly") amplifies ruin risk even with a real edge. Never raise stakes after losses to "recover"—that is martingale behavior, not Kelly. Cap any single wager (many pros use 5% max) regardless of formula output.
Treating correlated bets as independent. Same-game parlays, correlated player props, or stacking multiple lines on one match inflate true risk. Kelly assumes each bet is an independent draw—violating that assumption is how disciplined bettors still go broke.
Screen plays for +EV first with our expected value calculator—Kelly only sizes bets that already clear value.
Derive fair win probability from any price using the implied probability calculator before you enter p here.
When books diverge, test arbitrage scenarios for risk-free locks—then use Kelly only on discretionary +EV spots.
You find a basketball underdog at decimal 2.10 and model 52% win chance (implied 47.6%). EV ≈ +9.2%. Full Kelly f* ≈ 8.4% of bankroll; half Kelly → 4.2% on a $5,000 roll = $210.
Your Poisson model says BTTS Yes is 58% but the book offers 1.85 (54.1% implied). f* ≈ 7.3% full Kelly. Use our Poisson calculator for fair probability, then size here with quarter Kelly if the fixture is correlated with other open bets.
True arbitrage has f* → ∞ in theory—you should stake to capture the lock, not apply Kelly. Use the arbitrage calculator for guaranteed profit splits; reserve Kelly for discretionary +EV where your probability estimate matters.
Kelly applies beyond sports: if an asset has 60% chance of +20% and 40% of −10%, treat net odds b = 0.20 and p = 0.60 → f* ≈ 40% (aggressive; fractional Kelly essential). The same math warns against over-leveraging when edge estimates are noisy.
Crypto spot or perp trades map to Kelly when you assign win probability and payoff ratio. Example: 55% chance of +20% move, 45% of −15% → treat b = 0.20, p = 0.55. Full Kelly can suggest large allocation—use quarter Kelly or lower because tail risk and estimation error dwarf sports-betting variance. Never apply Kelly to leveraged positions without modeling liquidation risk separately.
Stock and options traders use Kelly-like sizing when backtests show repeatable edge. Convert expected return and loss size into equivalent b and p, then apply fractional Kelly. Portfolio managers often run half Kelly or less because correlation across positions breaks the single-bet independence assumption—aggregate exposure caps matter more than per-trade formula output.
Most Kelly tools accept only one odds format and output a bare percentage. OddsGPT adds: (1) <strong>six odds formats</strong> synced with your site preference; (2) <strong>fractional Kelly presets</strong> plus custom multiplier; (3) live <strong>EV%, full Kelly, applied fraction, and dollar stake</strong>; (4) interactive <strong>f* vs win-rate chart</strong> and full/half/quarter comparison bars.
We integrate Kelly into a full betting-math stack—pair with our EV, implied probability, and Poisson tools so you screen +EV first, derive fair p, then size. No signup, no paywall, instant results in the browser.
Only size bets that are +EV after honest probability work. Use fractional Kelly (0.25–0.5×), cap any single wager (often 5% of bankroll max), and track CLV to verify your model. When Kelly fraction is zero or negative, pass—forcing action on -EV prices is how bankrolls die.
Kelly sizing is educational—not financial advice. Sports betting carries risk of loss and addiction. Never bet money you cannot afford to lose. Overestimating win probability is the fastest path to ruin.
Resources: BeGambleAware, NCPG (US), GamCare (UK).
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