What is the Kelly criterion calculator?
The Kelly criterion is a formula for the share of a bankroll to stake when you believe a bet has a positive expected value. With a bankroll of 1,000 units, even-money odds (2.00) and a belief that the bet wins 55% of the time, full Kelly says to stake 10% of the bankroll, which is 100 units. Half Kelly stakes 50 units. If the bet has no edge, Kelly says to stake nothing.
This page is not a betting system, and it does not find edges for you. Kelly takes your estimate of the win chance as true, and everything it says depends on that estimate. It is a tool for sizing a stake once an edge is real, and it is just as useful for showing how quickly a small overestimate turns a “good” bet into a bad one. Every casino game has a negative expected value for the player, so the formula returns zero for all of them.
How do you use the Kelly criterion calculator?
- Enter your bankroll. It starts at 1,000 units.
- Enter the odds. Decimal, fractional and American formats work.
- Enter your estimated win chance. Be honest, and if in doubt, enter a lower number.
- Choose the fraction of Kelly. 1 is full Kelly, 0.5 is half Kelly. The default is 0.5.
- Enter how wrong you could be. This is the number of percentage points your chance might be too high. It starts at 2.
- Read the large number. It is the suggested stake in units. The panel compares fractions and shows what happens if the chance is lower than you think.
Example: Bankroll 1,000, odds 2.00, chance 55%, half Kelly. Full Kelly is 0.55 – 0.45 / 1 = 10%. Half of that is 5%, so the stake is 50 units. If your chance is really 53%, full Kelly falls to 6%, so a 10% stake would have been an overbet.
How is the Kelly stake calculated?
Write b for the net odds (decimal odds minus 1), p for the win chance and q for 1 – p. The Kelly fraction is f = p – q / b, which is the same as (b x p – q) / b. The suggested stake is the bankroll x f x the fraction you chose. If f is zero or negative, the bet has no edge and the stake is zero. The formula comes from maximising the long-run growth rate of the bankroll, as set out by John Kelly in 1956 and developed by Edward Thorp.
| Step | Working | Result |
|---|---|---|
| Net odds b | 2.00 – 1 | 1.00 |
| Win and loss chance | p = 0.55, q = 0.45 | 0.55 and 0.45 |
| Full Kelly fraction | 0.55 – 0.45 / 1.00 | 10.0% |
| Half Kelly | 10.0% x 0.5 | 5.0% |
| Stake | 1,000 x 5.0% | 50 units |
What does the Kelly stake look like for different edges?
Kelly grows quickly with the edge. At even money, a 52% chance gives a stake of 4% of the bankroll and a 60% chance gives 20%. Notice that the bet size is set by the edge, not by how confident you feel. A table of full Kelly at odds of 2.00 shows how steeply it climbs.
| Your win chance | Full Kelly stake |
|---|---|
| 50% | 0% (no edge) |
| 52% | 4% |
| 55% | 10% |
| 60% | 20% |
| 65% | 30% |
At 50% there is no edge and Kelly says zero. That is also what it says for every roulette, slot or dice bet at a casino, where the chance of winning is below the break-even chance. The roulette odds and payouts page shows why.
Why do people use half or quarter Kelly?
Full Kelly maximises long-run growth if your win chance is exactly right, but it is bumpy and unforgiving of mistakes. Smaller fractions give up a little growth for a lot of smoothness. The table uses the default 55% bet at 2.00 and a 1,000 bankroll. “Halve before double” is the approximate chance of the bankroll falling to half before it doubles, for small repeated bets with a correct chance.
| Fraction | Stake as % of bankroll | Stake in units | Growth per bet | Halve before double |
|---|---|---|---|---|
| 0.25 of Kelly | 2.5% | 25 | 0.22% | 1 in 129 |
| 0.5 of Kelly | 5.0% | 50 | 0.38% | 1 in 9 |
| 1 of Kelly | 10.0% | 100 | 0.50% | 1 in 3 |
Half Kelly gives up only a quarter of the growth of full Kelly, and cuts the chance of halving the bankroll before doubling from 1 in 3 to 1 in 9. Quarter Kelly cuts it to about 1 in 129.
What happens if your estimate is wrong?
This is the check the calculator does for you with the “how wrong could I be” box. Take the default bet. Suppose you stake full Kelly (10%) because you think the chance is 55%, but the true chance is 53%. True Kelly for 53% is 6%, so you are staking about 1.7 times the correct amount. The table shows what happens to long-run growth when you stake a multiple of the correct Kelly stake.
| Stake relative to Kelly | Stake as % of bankroll | Growth per bet if the 55% chance is right |
|---|---|---|
| 0.5x Kelly | 5% | +0.38% |
| 1x Kelly | 10% | +0.50% |
| 1.5x Kelly | 15% | +0.37% |
| 2x Kelly | 20% | -0.01% |
| 3x Kelly | 30% | -1.62% |
At twice Kelly the growth rate is about zero, and beyond it growth is negative even though every bet has a positive EV. With a true chance of 53% and a stake of 10%, growth per bet is only 0.10% against 0.18% at the correct 6% stake, and a 5% stake (about the correct half of the mistaken amount) gives 0.18%. A small overestimate of the edge turns full Kelly into an overbet, which is why fractions of Kelly are standard.
What does the calculator leave out?
- The estimate. Kelly cannot tell you if your chance is right. Most perceived edges are not real.
- Fixed odds. It assumes the same odds for every bet and bets that are independent.
- Simultaneous bets. It sizes one bet at a time, not several at once.
- Limits and fees. Maximum stakes, commission and withdrawal costs are not modelled.
- Your tolerance for swings. Even half Kelly can fall a long way before it recovers.
- Casino games. There is no player edge, so there is no Kelly stake.
What mistakes do people make with Kelly?
- Treating it as a system. It sizes a stake for an edge you already have. It does not create one.
- Using the price as the win chance. That gives a zero edge and a zero stake every time.
- Rounding the edge up. Because Kelly is so sensitive, a small overestimate is the most common way to overbet.
- Forgetting to recompute. As the bankroll changes, so does the stake.
- Ignoring the downswings. Full Kelly regularly loses half the bankroll before recovering.
What should you try next?
Set the win chance to the break-even chance (100 divided by the decimal odds) and see the stake fall to zero. Then try lowering your chance by one point at a time. If you want the average result of a single bet, use the expected value calculator. To see how likely a losing run is for a given stake, use the risk of ruin calculator. If you are setting limits before you play, start with the Safer play toolkit.
How to read the result
The large number is the suggested stake in units, which is your bankroll x the Kelly fraction x the fraction of Kelly you chose. The line under it gives the stake as a percentage of the bankroll and the expected growth per bet if your chance is right. The panel compares full, half and quarter Kelly, with the approximate chance of the bankroll halving before it doubles. It also shows the effect of your chance being lower than you entered. If the stake is zero, the bet has no edge at your estimate.
How it is calculated
Net odds b = decimal odds - 1. Kelly fraction f = p - q / b, where p is your win chance and q = 1 - p. Stake = bankroll x f x fraction chosen. If f is zero or negative, the stake is zero. Growth per bet = p x ln(1 + stake share x b) + q x ln(1 - stake share). Halve before double = (1 - 2^-g) / (2^g - 2^-g) with g = 2 / fraction - 1, an approximation for small repeated bets.
Worked example
Worked example
Bankroll 1,000, odds 2.00, chance 55%, half Kelly. b = 1.00, f = 0.55 - 0.45 / 1.00 = 10%. Stake = 1,000 x 10% x 0.5 = 50 units, which is 5% of the bankroll. Expected growth if the chance is right is about 0.38% per bet. If the true chance is 53%, full Kelly falls to 6%, so a 10% stake would be an overbet.
Limits
Kelly assumes your win chance is exactly right, the odds are fixed, the bets are independent and you can bet any amount. In practice the chance is an estimate, and a small overestimate turns an edge into an overbet. It sizes one bet at a time, ignores limits, fees, bonuses and tax, and says nothing about whether an edge exists. No casino game gives the player an edge, so the Kelly stake for them is zero. Results are estimates, not predictions.