Enter your bankroll, American odds, and estimated win probability to find the mathematically optimal bet size. Supports Full Kelly, Half Kelly, and Quarter Kelly.
The hardest part of Kelly sizing is getting an accurate probability estimate. If you want help with that, we recommend Juice, an iOS app that uses three AI models (ChatGPT, Claude, and Gemini) to estimate probability and calculate EV for any sports bet. It also compares odds across 18 sportsbooks.
The Kelly Criterion is a mathematical formula for determining the optimal fraction of your bankroll to wager on a bet with a known edge. It was developed by Bell Labs scientist John L. Kelly Jr. in 1956, originally as a method for maximizing the long-term growth rate of a portfolio with a positive expected return. It has since been adopted by professional gamblers, hedge funds, and quantitative traders who need a principled approach to position sizing.
The power of Kelly is that it answers a question most bettors never think to ask: given that this is a +EV bet, exactly how much should I wager? Bet too little and you leave profits on the table. Bet too much and you expose yourself to ruin risk even when your edge is real. Kelly finds the mathematically optimal balance between growth and protection.
Bankroll: $2,000. Odds: -110. Estimated win probability: 57%.
Full Kelly f = (0.909 × 0.57 - 0.43) / 0.909 = (0.518 - 0.43) / 0.909 = 0.088 / 0.909 = 9.68%
Half Kelly = 9.68% × 0.5 = 4.84% of bankroll = $96.80
This is the conservative, recommended approach for most bettors using Kelly sizing.
The Kelly formula provides the theoretically optimal bet size, but only when your probability estimate is perfectly accurate. In practice, estimates are uncertain, so most bettors apply a fraction of the full Kelly recommendation to reduce variance while preserving most of the long-run growth benefit.
| Kelly Fraction | Bet Size | Risk Level | Best For |
|---|---|---|---|
| Full Kelly (1.0x) | 100% of formula output | Aggressive | Perfectly calibrated models with very high confidence in probability estimates |
| Half Kelly (0.5x) | 50% of formula output | Moderate | Most serious bettors; captures ~75% of Full Kelly's long-run growth with much lower variance |
| Quarter Kelly (0.25x) | 25% of formula output | Conservative | Recreational bettors, early-stage bankrolls, or markets where probability estimation is uncertain |
Research by Thorp and others suggests that Half Kelly produces approximately 75% of the geometric growth rate of Full Kelly while cutting variance by about 50%. For most sports bettors whose probability estimates carry meaningful uncertainty, Half Kelly is the rational default.
The Kelly Criterion only works when you have a genuine positive edge. If your estimated win probability does not exceed the implied probability embedded in the odds (after accounting for vig), the formula returns a zero or negative value, which means: do not bet.
This is one of Kelly's most useful properties as a discipline tool. It forces you to honestly assess whether a bet is +EV before sizing it. If Kelly returns a negative number, that is a mathematical signal that the bet should be passed regardless of how confident you feel about the outcome.
Before using the Kelly Calculator, use our EV Calculator to confirm the bet is +EV. Then bring those same probability and odds inputs here to size the bet. If your odds are in decimal or fractional format, convert them to American using our Odds Converter before entering them into either calculator.
Kelly maximizes the expected logarithm of wealth, which corresponds to maximizing the long-run geometric growth rate of your bankroll. A bettor following Full Kelly will, in theory, outperform any other fixed-fraction strategy over a long enough time horizon.
However, Full Kelly also produces severe drawdowns. A common scenario: a bettor with a 5% edge using Full Kelly can expect to see their bankroll drop to 50% of peak value at some point during a long betting career. Half Kelly roughly cuts that maximum drawdown to 25%. For bettors with real bankrolls and emotional constraints, the reduced variance of Half or Quarter Kelly is usually worth the modest growth rate sacrifice.
This calculator includes a risk assessment based on the Kelly percentage recommended. Here is how to interpret each level:
Professional sports bettors and quantitative hedge funds both use Kelly-based sizing, though most apply fractional variants. Ed Thorp, the mathematician and hedge fund pioneer who wrote "Beat the Dealer" and "Beat the Market," advocated for Half Kelly as the practical standard for most real-world applications. Thorp demonstrated mathematically that overbetting Kelly reduces long-run geometric growth, while underbetting (even significantly) still outperforms fixed-fraction approaches in the long run.
In sports betting specifically, the challenge is that probability estimates are inherently uncertain in a way that casino card counting probabilities are not. A card counter knows the exact probabilities from deck composition. A sports bettor is working with models, injury data, and qualitative judgment. This estimation uncertainty is the primary argument for using Half or Quarter Kelly rather than Full Kelly. Building better inputs through thorough research, including systematic player props research, directly improves the quality of your Kelly calculations.
The complete professional betting workflow combines EV analysis with Kelly sizing:
For deeper background on why this framework works and how to build the probability estimation skills required, read our complete Kelly Criterion guide and our expected value guide.
The Kelly Criterion originated in information theory and was quickly adopted by both professional gamblers and investors because the underlying math is identical. Both use the same formula, but the inputs come from very different places.
In investing, edge comes from the expected return of an asset relative to its risk. A stock with an expected annual return of 12% and a risk-free rate of 5% has an edge of 7%. The "odds" are the ratio of potential gain to potential loss. Kelly-based portfolio managers like Ed Thorp applied this to options and equities with remarkable success over decades.
In sports betting, edge comes from the gap between your estimated true probability and the implied probability embedded in the sportsbook's odds. A bet at -110 (52.38% implied) where you estimate 57% true probability has an edge of roughly 4.6 percentage points. That edge, combined with the payout odds, produces the Kelly fraction.
The key practical difference is certainty. In a casino card counting scenario, probabilities are mathematically precise from deck composition. In sports betting, probabilities are estimates based on imperfect information. In investing, expected returns are forward-looking projections subject to model error. Both environments carry estimation uncertainty that argues for fractional Kelly rather than Full Kelly.
One important distinction: investing Kelly often needs to account for correlation between positions (a tech portfolio is not 20 independent bets). Sports betting Kelly faces a similar issue when making multiple bets on the same game. In both contexts, treating correlated positions as independent and sizing each with full Kelly will lead to systematic overbetting.
The Kelly Criterion is a mathematical formula that determines the optimal fraction of your bankroll to wager on a bet with a positive expected edge. It was developed by Bell Labs scientist John L. Kelly Jr. in 1956 and maximizes the long-run geometric growth rate of your bankroll.
Kelly f = (b x p - q) / b, where b is the decimal profit per unit wagered (e.g., 0.909 for -110 odds), p is your estimated win probability, and q is 1 minus p. The result is the fraction of your bankroll to wager.
For almost all sports bettors, fractional Kelly is the right choice. Full Kelly is mathematically optimal only if your probability estimate is perfectly accurate, which is essentially never the case in sports betting. Half Kelly captures approximately 75% of the long-run growth rate of Full Kelly while cutting variance roughly in half. Quarter Kelly is appropriate for new bettors, volatile markets, or any situation where your confidence in the probability estimate is limited. Start with Half Kelly and consider Quarter Kelly during early stages of building a track record.
This is the central risk of Kelly sizing. If you estimate 60% probability but the true probability is 52%, you will be overbetting significantly. Over time, this overbetting causes your bankroll to decline even if you are placing technically "positive" bets by your own estimates. The solution is to use fractional Kelly (which provides a buffer against estimation error), track your actual results against your probability estimates to identify calibration bias, and be genuinely conservative with probability estimates rather than optimistic. Overconfidence is the most common cause of Kelly-related bankroll blowups.
Yes, but you need to treat the parlay as a single bet. Multiply the individual leg probabilities to get the combined win probability, use the actual parlay payout odds, and apply the formula once. Do not apply Kelly to each leg individually and then combine them. Most parlays will produce a negative Kelly result (indicating -EV) because sportsbooks shave each leg's odds before combining them. If the full parlay Kelly is negative, skip the bet. If it is positive, apply Half or Quarter Kelly to the combined parlay bet as a single position.
A negative Kelly result means the bet has negative expected value at the given odds and probability. The formula is telling you to skip the bet entirely. Do not force a Kelly calculation on -EV situations.
Most real sports betting edges produce Full Kelly percentages between 2 and 15%. After applying Half Kelly, optimal bet sizes typically land between 1 and 7.5% of bankroll. Percentages above 15% (Full Kelly) warrant skepticism about the probability estimate unless you have a strong, validated model.
Kelly bet sizes should be recalculated based on your current bankroll before each bet. After wins, your bankroll grows and Kelly amounts increase proportionally. After losses, they decrease. This self-adjusting property is one of Kelly's most valuable features for bankroll preservation.