What Is the Kelly Criterion?
The Kelly Criterion is a mathematical bankroll-management formula used to calculate a theoretical proportion of available capital to allocate to a wager.
In betting, the calculation uses two important inputs: the odds available and your estimated probability of the outcome occurring. The resulting fraction is applied to your bankroll.
Kelly Criterion Formula
For decimal odds, the standard Kelly calculation can be written as:
Kelly fraction = (b × p − q) ÷ b
b = net decimal odds
p = estimated probability of winning
q = probability of losing, or 1 − p
Kelly Criterion Betting Example
Suppose a football selection is available at decimal odds of 2.00 and you estimate its probability of winning at 55%. Your bankroll is 1,000.
Decimal odds
2.00
Estimated probability
55%
Bankroll
1,000
With these inputs, the Kelly fraction is 10%. A full Kelly calculation therefore produces a theoretical stake of 100, while half Kelly produces 50.
Implied Probability vs Your Estimated Probability
Decimal odds of 2.00 imply a probability of 50% before considering bookmaker margin or other market factors. If your estimated probability is 55%, your estimate is higher than the probability implied by those odds.
The Kelly calculation uses the relationship between these values to determine whether the inputs produce a positive theoretical Kelly fraction.
What Is Half Kelly?
Half Kelly means using 50% of the full Kelly stake. If full Kelly produces a theoretical stake of 100, half Kelly produces 50.
The calculator displays both values so you can compare the full theoretical Kelly allocation with a smaller half-Kelly allocation.
Why the Probability Estimate Matters
The Kelly Criterion does not predict the probability of an event for you. You provide that probability estimate.
Because the calculated stake depends directly on the probability entered, an inaccurate estimate can produce a very different stake from one based on a more accurate probability estimate.
When Kelly Produces a Zero Stake
If your estimated probability does not produce a positive mathematical edge at the available odds, the Kelly calculation produces a non-positive fraction.
This calculator displays a zero theoretical Kelly stake in that situation rather than suggesting a negative wager.
Kelly Criterion Calculator FAQ
What is the Kelly Criterion?
It is a mathematical formula used to calculate a theoretical fraction of a bankroll based on odds and estimated probability.
What is Full Kelly?
Full Kelly refers to the complete stake fraction produced by the Kelly formula.
What is Half Kelly?
Half Kelly is half of the stake calculated by the full Kelly formula.
What probability should I enter?
Enter your own estimated probability that the selection will win. The accuracy of that estimate has a direct effect on the calculation.