Kelly Formula Calculator
Knowing which bet has an edge is only half the game. The other half is how much to stake. The Kelly criterion, published by John Kelly Jr. at Bell Labs in 1956, converts your estimated win probability and the odds on offer into the fraction of your bankroll that maximizes long-run growth. This Kelly formula calculator runs that math: with a 60% win chance at net odds of 1.5 on a $1,000 bankroll, it says stake 33.33% ($333.33), and it shows the half-Kelly and quarter-Kelly figures most professionals actually use, plus the implied probability your estimate has to beat.
One warning belongs up front, because it decides whether the answer means anything. The probability you enter must be your own estimate, not the bookmaker’s implied probability read back off the odds. Enter the implied probability and the formula returns zero by construction, which tells you nothing. Kelly sizes an edge. It cannot create one.
Quick Answer
With a 60% win probability at net odds of 1.5, the Kelly fraction is (1.5 times 0.60 minus 0.40) divided by 1.5, which equals 33.33%. On a $1,000 bankroll that is a $333.33 stake at full Kelly, $166.67 at half Kelly, and $83.33 at quarter Kelly. If your probability matched the odds’ implied 40%, the formula would return zero: no edge, no bet.
Key takeaways
- Kelly maximizes long-run growth rate, not single-bet profit. It optimizes the expected logarithm of wealth, which compounds fastest without courting ruin.
- Full Kelly is aggressive. Most professionals use half or quarter Kelly, trading some growth for a far smoother ride.
- A negative result is an answer. Zero or below means the bet has no edge at the offered odds: the correct stake is nothing.
- The probability estimate is everything. Kelly cannot tell a good estimate from a bad one; overconfident inputs produce overconfident stakes.
- Quick Answer
- What the Kelly criterion optimizes
- The formula, with a real bet
- Why professionals bet half Kelly
- When Kelly says bet nothing
- The estimate is the whole bet
- Kelly beyond sports: position sizing with care
- What other Kelly tools miss
- Frequently asked questions
- Add This Calculator to Your Website
- References
What the Kelly criterion optimizes
John Kelly Jr. derived the criterion in 1956 at Bell Labs while studying information theory, and showed that staking the Kelly fraction maximizes the expected log of wealth: the fastest sustainable compounding rate. The Corporate Finance Institute’s Kelly criterion reference states the practical upshot plainly: no other staking system grows a bankroll faster in the long run without accepting extra risk of ruin. That is why the formula migrated from horse racing to blackjack card counting to options trading floors.
The intuition is geometric. Flat betting grows wealth arithmetically. Kelly-sized betting grows it geometrically, because stakes scale with the bankroll after every result. The cost is volatility: full Kelly stakes swing hard, and a string of losses at 33% stakes cuts deep before the math recovers. Before sizing any leveraged position around these stakes, check margin requirements so a drawdown never becomes a margin call. Kelly is a growth engine, not a risk manager, and it assumes you can keep betting through the losing runs.
The formula, with a real bet
The formula is f* = (b times p minus q) divided by b, where b is net odds (profit per dollar staked), p is your win probability, and q is 1 minus p. Net odds are decimal odds minus 1. A price of 2.50 in decimal odds is net odds of 1.5. A price of 1.91, the usual -110 American line, is net odds of 0.91. If your book shows American odds and you are unsure of the conversion, our odds calculator runs the formats side by side.
The worked example, step by step. First, the edge numerator: b times p minus q equals 1.5 times 0.60 minus 0.40, which equals 0.50. Positive, so an edge exists. Second, scale by odds: 0.50 divided by 1.5 equals 0.3333, the full Kelly fraction. Third, stake it: 33.33% of $1,000 equals $333.33 at full Kelly. Fourth, fraction it: half Kelly is 16.67%, or $166.67, and quarter Kelly is 8.33%, or $83.33.
Note the implied probability check the calculator runs alongside the stake. Net odds of 1.5 mean decimal odds of 2.5, implying a 40% chance, because 1 divided by 2.5 equals 0.40. Your 60% estimate beats the market’s 40% by 20 points, and that gap is the edge being priced. A bet only qualifies when your probability exceeds the implied one. Otherwise Kelly correctly returns zero or negative. For the expected-value side of the same decision, see our expected value of profit calculator, which answers whether a bet is profitable before Kelly answers how much to stake on it.
Why professionals bet half Kelly
Full Kelly is mathematically optimal under perfect estimates, and nobody has perfect estimates. That single fact drives the whole professional practice. The table below compares the three fractions the calculator reports, on the worked example.
| Fraction | Share of bankroll | Stake on $1,000 | What you trade |
|---|---|---|---|
| Full Kelly | 33.33% | $333.33 | Maximum growth, brutal drawdowns |
| Half Kelly | 16.67% | $166.67 | Roughly three quarters of the growth, far smaller swings |
| Quarter Kelly | 8.33% | $83.33 | Smoothest ride, slowest compounding |
The half-Kelly description in that table is how practitioners commonly describe it: about three quarters of the growth with about half the volatility. The deeper reason is the overbetting cliff. Bet double Kelly and the expected growth rate collapses to zero: the same as not betting at all, but with maximum variance. Since an overstated probability pushes you toward overbetting without warning, fractioning is insurance against your own estimation error. When the edge is small, the stakes are small anyway, and fractioning matters less. When the edge looks large, fractioning matters most, because that is when an error costs the most.
When Kelly says bet nothing
Kelly’s most underrated output is zero. Whenever b times p is less than q, the formula returns a negative fraction, which is the mathematics telling you the bet has no edge at the offered price. Treat every negative Kelly result as a filter doing its job, not a formula malfunction. The calculator shows $0 for full, half, and quarter stakes in that case, rather than dressing a negative number up as a smaller stake.
Bookmakers set odds with a margin baked in, so most casual bets fail this test. Our bookmaker margin calculator shows how that margin is built into a set of odds. The practical decision rule is simple: only bet when your estimated probability exceeds the odds’ implied probability, by enough to survive being wrong about the size of the gap. A 41% estimate against 40% implied odds is technically an edge, and it is far too thin to stake real money on with confidence.
The estimate is the whole bet
Run the sensitivity check before trusting any Kelly number. If your true probability were 50% instead of the 60% you entered, the fraction would be (1.5 times 0.50 minus 0.50) divided by 1.5, which equals 16.67%, or $166.67 on $1,000. A ten-point estimation error halves the stake. If your true probability were 40%, the fraction would be zero. Kelly amplifies whatever you feed it, including error, and it has no way to know which input is the honest one.
That is why serious users keep a record. Log the probability you estimated, the odds you took, and the outcome, and check over time whether your 60% bets actually win about 60% of the time. If they win 50%, your stakes have been roughly double what they should have been. Calibration, not cleverness, is what makes Kelly safe to use. A model with a documented track record earns a full or half-Kelly stake. A gut feeling earns quarter Kelly at most, and usually earns a pass.
Kelly beyond sports: position sizing with care
Traders adapt Kelly by treating the expected gain and loss as the odds and sizing positions fractionally. The catch is that stock and crypto edges are harder to estimate than bet probabilities, so fractional Kelly (quarter or less) is the norm, and it complements rather than replaces risk management. Correlated positions break the single-bet assumption too: five positions that all fall together are not five independent Kelly bets, and sizing each at its standalone fraction overbets the portfolio.
Two limits apply everywhere Kelly is used. First, Kelly assumes repeatable bets with stable edges. A one-off illiquid wager with a wide spread fits the assumptions poorly. Second, Kelly assumes fractional betting and no transaction costs. Real books have minimums, fees, and limits that bend the math at the edges. None of this makes the formula useless. It makes the fraction a starting point for judgment, not a substitute for it. This calculator is an educational tool, not financial advice, and no stake it reports should be taken as a recommendation.
What other Kelly tools miss
Most Kelly tools compute the fraction and stop. They never show the dollar stake, the fractional alternatives, or the implied probability to compare against, so the user still has to finish the job by hand. Many accept the bookmaker’s implied probability as the win probability input, which guarantees a zero edge and a useless answer, without warning that the two numbers must come from different sources. Few explain that Kelly assumes repeatable bets with stable edges, and almost none mention the overbetting cliff.
This calculator shows full, half, and quarter stakes in dollars, flags the no-edge case explicitly with $0 stakes, and states the assumptions up front. It also keeps the odds format honest: net odds in, not decimal odds mislabeled as net odds, which is a quiet error in several competing tools that shifts every answer. One more distinction matters for multi-leg bets. A parlay is not one Kelly bet, and its legs are not independent edges to be sized together. Our bet parlay calculator prices the combined ticket separately, and Kelly should be applied to single, repeatable edges, not to a parlay treated as one wager.
Frequently asked questions
f* = (b times p minus q) divided by b. f* is the fraction of bankroll to stake, b is net odds (profit per dollar risked), p is your estimated win probability, and q = 1 minus p. Example: b = 1.5, p = 0.60 gives (0.90 minus 0.40) divided by 1.5 = 33.33%.
Betting half the full Kelly fraction: 16.67% instead of 33.33% in the worked example, or $166.67 on a $1,000 bankroll. It sacrifices some growth rate for much lower volatility, and it is what most professionals actually stake.
The bet has no edge at the offered odds. The mathematics is telling you not to bet, not to size a smaller stake. Only wager when your probability estimate exceeds the odds’ implied probability.
Yes, with care. Traders adapt it by treating the expected gain and loss as the odds and sizing positions fractionally. The catch is that stock edges are harder to estimate than bet probabilities, so fractional Kelly (quarter or less) is the norm, and it complements rather than replaces risk management.
Long-run growth falls while volatility rises. At exactly 2 times Kelly the expected growth rate drops to zero: the same as not betting at all, but with maximum variance. Overbetting is the fastest way to turn an edge into ruin.
John L. Kelly Jr., a researcher at Bell Labs, published it in 1956 in the Bell System Technical Journal in the context of information theory. It was later popularized for gambling by Edward Thorp and adopted across trading and investing.
Add This Calculator to Your Website
References
- Corporate Finance Institute. Kelly Criterion. Accessed Oct 25, 2026.
- BetLegendPicks. Kelly Criterion Calculator. Accessed Oct 25, 2026.
- BonusFinder. Kelly Criterion Calculator. Accessed Oct 25, 2026.
- Ryan O'Connell Finance. Kelly Criterion Calculator: Optimal Bet Sizing Tool. Accessed Oct 25, 2026.
- Phemex Academy. Crypto EV Calculator: Using Probability and Kelly Criterion for Position Sizing. Accessed Oct 25, 2026.
- DG3. Kelly Criterion Calculator: Sizing in Cents, Not Odds. Accessed Oct 25, 2026.
- MyBookie. Kelly Criterion Sports Betting Guide: Formula, Examples and Calculator. Accessed Oct 25, 2026.
- Prevayo. Kelly Criterion Mastery: Complete Position Sizing Guide. Accessed Oct 25, 2026.
- Horise. Smarter Betting with the Kelly Criterion. Accessed Oct 25, 2026.
- BettorEdge. Using Kelly Criterion with Prediction Markets. Accessed Oct 25, 2026.