Kelly Criterion Calculator
Size a bet from your win probability, decimal odds, and bankroll with the Kelly criterion.
What it does
The Kelly criterion answers a narrow question: given a bankroll, a known payoff, and an honest estimate of the win probability, what share of the bankroll should go on the bet? The answer is the fraction that maximizes the expected logarithm of wealth, which is the same as maximizing long-run growth without risking ruin.
The inputs are three numbers. Win probability is your own estimate, not the implied probability hidden in the odds. Decimal odds state the total return per unit staked, so even money is 2.00 and a 3.00 quote pays two units of profit for each unit risked. The bankroll is the total amount you are willing to dedicate to the betting account.
The formula first converts decimal odds to net odds, b = decimal odds - 1. It then multiplies b by the win probability p, subtracts the loss probability q, and divides by b. A positive result is the Kelly fraction. A zero or negative result means the wager has no edge at those odds and should be skipped.
For example, a 55 percent chance at decimal odds of 2.00 gives b = 1.00, so the fraction is 1.00 x 0.55 minus 0.45, which is 0.10. On a $1,000 bankroll that is a $100 stake. The edge per bet is 10 percent, and the expected log growth is about 0.50 percent per bet.
Full Kelly is mathematically optimal only when the probability is exactly right and the bet can be repeated without limits. Real estimates carry error, and full Kelly produces large swings even when the edge is genuine. Half Kelly cuts the growth rate by roughly a quarter but also cuts volatility by about half, which is why many practical bettors stop short of the full fraction.
How to use
- Enter your own estimated probability of winning, from 0 to 100 percent.
- Enter the decimal odds offered by the bookmaker, such as 2.00 or 3.50.
- Enter the bankroll dedicated to betting, not your total savings.
- Read the Kelly fraction and the stake it implies.
- Check the edge: a negative edge means the tool recommends no bet.
- Decide whether to use the full fraction or a smaller share such as half Kelly.
Formula
- p
- Your estimated probability of winning, as a decimal from 0 to 1.
- q
- Probability of losing, equal to 1 - p.
- b
- Net odds: decimal odds minus 1, the profit per unit staked.
- f
- Kelly fraction of the bankroll, floored at zero when the edge is negative.
The fraction is capped at zero in the output, so a losing proposition shows a 0.0 percent stake rather than a negative one. Growth is the expected log of wealth, p x ln(1 + b f) + q x ln(1 - f), which is zero when no bet is made. The formula assumes the bet resolves win or lose with no push, and that the same edge can be bet repeatedly.
Worked example
Example: 55 percent at decimal odds 2.00 with a $1,000 bankroll
You estimate a 55 percent chance to win, the bookmaker offers decimal odds of 2.00, and your bankroll is $1,000.
- Convert the probability: 55 percent is p = 0.55, so q = 1 - 0.55 = 0.45.
- Convert the odds: b = 2.00 - 1 = 1.00.
- Kelly fraction: (1.00 x 0.55 - 0.45) / 1.00 = 0.10, which is 10.0 %.
- Stake: 0.10 x $1,000 = $100.00.
- Edge: 0.55 x 2.00 - 1 = 0.10, which is 10.0 %.
- Growth: 0.55 x ln(1.10) + 0.45 x ln(0.90) = 0.0050, which is 0.50 % per bet.
Reference table
| Decimal odds | Break-even probability | Kelly fraction at 55 percent | Decision |
|---|---|---|---|
| 1.50 | 66.7 % | 0.0 % | No bet, negative edge |
| 2.00 | 50.0 % | 10.0 % | Bet 10 percent of bankroll |
| 3.00 | 33.3 % | 32.5 % | Bet 32.5 percent of bankroll |
| 4.00 | 25.0 % | 40.0 % | Bet 40 percent of bankroll |
Limits
- Assumes your win probability is accurate; small errors produce large stake errors because the formula is sensitive near the edge.
- Covers a single binary bet with no push, cash-out, or partial settlement.
- Does not model simultaneous bets, correlated outcomes, or limits on how much the bookmaker will accept.
- Full Kelly can draw down deeply even when the edge is real, so the raw fraction is not a risk recommendation.
Common mistakes
- Using the bookmaker's implied probability instead of your own estimate, which always produces a zero edge.
- Entering American odds such as +100 or -150 in the decimal odds field.
- Treating the Kelly fraction as a safe amount rather than a growth-maximizing amount with large swings.
- Sizing against total savings instead of a bankroll you can afford to lose.
- Forgetting that a negative fraction is floored to zero, then reading the zero stake as a formula error.
Try it yourself
Quick checks. Answers sit tucked under each question.
Win probability 60 percent, decimal odds 2.00, bankroll $500. What is the stake?
20.0 percent of $500, which is $100.00.
Win probability 50 percent, decimal odds 2.50, bankroll $200. What is the stake?
16.7 percent of $200, which is $33.33.
Win probability 45 percent, decimal odds 2.00, bankroll $1,000. What does Kelly say?
The edge is -10.0 percent, so the stake is $0.00.
Questions
What is the Kelly criterion in one sentence?
It is a formula that gives the bankroll fraction which maximizes expected long-run growth for a bet with known odds and a known win probability.
Should I always bet the full Kelly amount?
No. Full Kelly is volatile and depends on an accurate probability. Half Kelly or quarter Kelly is common when the estimate is uncertain.
What decimal odds should I enter?
The total return per unit staked, including the stake. Even money is 2.00, a 50 percent profit is 1.50, and a 200 percent profit is 3.00.
Why is the recommended stake zero?
At those odds your estimated probability does not beat the break-even point, so the formula returns a negative fraction, which the tool floors at zero.
Does Kelly guarantee a profit?
No. It maximizes expected log growth over many repetitions, but any single bet can lose and a run of losses can still be severe.
Can I use Kelly for investing?
The math applies to any binary payoff with a known probability, but stock returns are not binary and their probabilities are not known, so the raw formula needs adaptation.
Sources
- Princeton: A New Interpretation of Information Rate (Kelly, 1956)
- Stony Brook: The Kelly Criterion lecture notes