Estimate a Kelly stake using your bankroll, betting odds and probability estimate.
Kelly calculations are extremely sensitive to the probability estimate entered. Overestimating your edge can produce stakes that are too large.
The Kelly Criterion is a mathematical staking formula designed to calculate what percentage of a bankroll should theoretically be risked when a positive edge is believed to exist.
Unlike a flat staking system, Kelly changes the suggested stake according to three things: your bankroll, the odds being offered and your estimate of the probability that the bet will win.
The larger the calculated edge, the larger the Kelly percentage. If the calculation finds no positive edge, Kelly recommends no stake.
For decimal betting odds, the standard Kelly formula can be written as:
Another equivalent version is:
The result tells you what fraction of the bankroll the Full Kelly calculation would allocate to the bet.
Imagine your bankroll is €1,000, the bookmaker offers decimal odds of 2.30 and you estimate the outcome has a 50% probability of winning.
Full Kelly would therefore allocate approximately €115.38 from a €1,000 bankroll.
Half Kelly would use approximately €57.69, while Quarter Kelly would reduce that again to approximately €28.85.
Full Kelly uses the entire percentage produced by the formula. Fractional Kelly simply reduces that percentage.
Fractional Kelly is commonly discussed because Full Kelly can produce aggressive bankroll swings, particularly when probability estimates are uncertain.
Kelly only produces a positive stake when the probability estimate entered implies that the offered price has positive expected value.
If your estimated probability is too low relative to the bookmaker's odds, the raw Kelly calculation becomes zero or negative. This calculator displays that result as a 0% stake.
For example, if decimal odds are 2.00 and your estimate is only 45%, the price would require a 50% break-even rate while your estimate sits below that threshold.
Fair odds are the decimal price corresponding to the probability estimate that you entered.
A 50% estimate produces fair odds of 2.00. If the market offers 2.30, your estimate implies that the offered price is above your calculated fair price.
The formula can calculate a stake precisely, but that precision does not make the underlying probability estimate accurate.
This is extremely important because Kelly reacts strongly to changes in estimated probability.
If you believe an outcome has a 55% chance when its true probability is much lower, the calculator may suggest a much larger stake than the actual edge would justify.
In other words, the mathematics can be correct while the input is wrong.
Kelly and expected value are closely related but answer different questions.
Expected value asks: Does my probability estimate make this price theoretically positive or negative EV?
Kelly asks: If I believe a positive edge exists, what fraction of the bankroll does the formula allocate to it?
Because of this relationship, Kelly produces no positive stake when the probability and odds entered do not create positive expected value.
The calculator only reacts to the numbers you provide. Entering an unrealistic probability can create a large Kelly stake even when the real betting edge does not exist.
Kelly is therefore better understood as a bankroll mathematics tool than as a system for deciding which bets will win.
The Kelly Criterion shows how probability, price and bankroll interact in a single mathematical model.
It makes the effect of an estimated edge visible and demonstrates why bankroll sizing cannot be separated from the quality of the probability estimate being used.
Comparing Full, Half and Quarter Kelly also makes it easier to see how reducing the Kelly fraction changes the amount of bankroll exposed without changing the underlying probability assumption.