Kelly Criterion Calculator
Size a stake against your bankroll to maximise long-run growth rather than a single result.
Kelly Criterion Calculator
Size a stake against your bankroll so that long-run growth is maximised rather than short-run profit.
Your own estimate, not the bookmaker’s
Edge
12.50 %
Full Kelly
8.33 %
Recommended stake
₦2,083.33
Kelly is only as good as your probability estimate. Overstate it by a few points and full Kelly overstakes badly, which is why fractional Kelly is the practical default.
What is the Kelly Criterion?
The Kelly criterion answers a question flat staking ignores: given an edge, how much should you actually bet? It sizes each stake in proportion to the edge and inversely to the odds, which mathematically maximises the long-run growth rate of a bankroll.
It is a bankroll rule, not a selection method. Kelly cannot tell you whether a bet is good — you supply that as your probability estimate — only how much to put behind one you already believe in.
The Formula
- Net odds: b = O − 1
- Kelly fraction: f = (b × P − (1 − P)) ÷ b
- Stake: bankroll × f × your chosen fraction
- If f ≤ 0 there is no edge — do not bet
Example
A price of 2.50 implies a 40 % chance. You rate the outcome at 45 % and your bankroll is ₦100,000.
- b = 1.50
- f = (1.50 × 0.45 − 0.55) ÷ 1.50 = 0.125 · 8.33 % of bankroll
- Full Kelly: ₦8,333
- Quarter Kelly: ₦2,083
Note how large full Kelly is for a five-point edge — over 8 % of the bankroll on one bet. That is the formula working as intended, and also why most people scale it down.
Why Fractional Kelly
Full Kelly is optimal only if your probability is exactly right. In betting it never is: you are estimating, and errors are asymmetric — overestimating your edge leads to overstaking, which compounds against you. Half Kelly captures about three-quarters of the growth with roughly half the volatility; quarter Kelly is the common choice for anyone whose edge is uncertain.
If your probability comes from converting a bookmaker's own price, Kelly will always return zero or less. That is the formula telling you something true: you need an independent estimate for any of this to mean anything.
Frequently Asked Questions
Why is full Kelly dangerous?
Because it assumes your probability estimate is exact. It is not. Overstate your edge by a few points and full Kelly overstakes badly — and the formula is aggressive even when you are right: full-Kelly bankrolls routinely halve before they grow. Half or quarter Kelly gives up a little long-run growth for a far smoother ride, which is why almost everyone who uses it in practice uses a fraction.
What is the Kelly formula?
f = (b × P − (1 − P)) ÷ b, where b is the net odds (decimal odds minus 1) and P is your probability. It reduces to (P × O − 1) ÷ (O − 1) — your edge divided by the net odds. Multiply f by your bankroll for the stake.
What does a negative Kelly figure mean?
That your probability estimate is below what the price implies, so the bet is −EV. The correct stake is zero. The formula technically suggests betting the other side, but at a bookmaker that side is priced with its own margin, so it is rarely a real opportunity.
Where do I get the probability from?
That is the hard part, and no calculator solves it. Common sources are a model of your own, the no-vig price from a sharper bookmaker, or closing prices from a low-margin market. If your estimate is just the same bookmaker’s odds converted back, Kelly will always return zero — correctly.
Related Tools
- Value Bet / EV Calculator — check that the bet has an edge before sizing it.
- No-Vig Calculator — a defensible source for the probability Kelly needs.
- Implied Probability Calculator — convert prices into the percentages you are comparing against.