Free tool
Kelly Criterion Calculator
Work out the optimal stake as a fraction of your bankroll based on your edge.
The Kelly criterion calculates the stake that maximises long-term bankroll growth, expressed as a fraction of your bankroll. It uses your odds and your estimate of the true win probability. Because full Kelly can be volatile, many bettors use half-Kelly to reduce swings.
Your bet
Recommended stake
- Kelly fraction
- 10.00%
- Full Kelly stake
- 100.00
- Half Kelly stake
- 50.00
How it works
The Kelly criterion calculates the optimal fraction of your bankroll to stake on a bet, given the odds and your own estimate of the probability of winning. From your bankroll, the decimal odds and your estimated win probability, it returns the Kelly fraction, the recommended stake, and a more conservative half-Kelly stake. The formula is f = (b·p − q) / b, where b is the decimal odds minus one, p is your estimated probability of winning, and q is 1 − p. The result, f, is the proportion of your bankroll to wager. If f is zero or negative, you have no mathematical edge and the calculator advises against betting. Kelly is designed to maximise the long-term growth of your bankroll while protecting it from ruin. By sizing each stake in proportion to your perceived edge, it bets more when value is greater and less when it is slim, which is why many professional bettors use it, almost always at a reduced fraction, as a disciplined staking framework.
Worked example
Suppose your bankroll is £1,000, the decimal odds are 2.00, and you estimate your probability of winning at 0.55. b = odds - 1 = 2.00 - 1 = 1 p = 0.55 q = 1 - p = 0.45 f = (b·p - q) / b = (1 x 0.55 - 0.45) / 1 = (0.55 - 0.45) / 1 = 0.10 Full Kelly stake = 10% of £1,000 = £100 Half-Kelly stake = 5% of £1,000 = £50 The positive fraction confirms an edge, so full Kelly suggests staking £100, while the safer half-Kelly suggests £50.
Kelly assumes your win probability is accurate; overestimating your edge causes the formula to overbet and can rapidly erode a bankroll. Most experienced bettors stake a fraction such as half or quarter Kelly to reduce volatility and protect against estimation error.
Frequently asked questions
What is the difference between full and half Kelly?
Full Kelly stakes the exact fraction the formula recommends and maximises theoretical growth, but it is highly volatile. Half Kelly stakes half that amount, sacrificing a little long-term growth for a much smoother ride and greater protection against overestimating your edge.
What does a negative Kelly fraction mean?
A fraction of zero or below means the odds do not compensate for your estimated probability, so you have no edge. In that case the correct stake is nothing and the bet should be avoided.
Why do most bettors use a fraction of Kelly?
Full Kelly is mathematically optimal only if your probability estimate is exactly right, which is rarely the case. Betting a fraction such as half or quarter Kelly cushions the impact of estimation errors and significantly reduces bankroll swings.
Does Kelly guarantee I will make money?
No. Kelly only optimises stake sizing when you genuinely have an edge and your probabilities are accurate; it cannot turn a losing system into a winning one. If your estimates are wrong, even careful Kelly staking will lose money over time.
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