Kelly Criterion Calculator
The Kelly criterion is a staking formula: given the odds and your estimate of the chance of winning, it gives the share of your bankroll that maximises long-run growth. Enter the price, your probability and your bankroll to see the full, half or quarter Kelly stake, the edge the formula assumes, and the risk that comes with it.
The formula: Kelly % = (b × p − q) ÷ b, with b = decimal odds − 1, p = your probability, q = 1 − p. At 2.50 with a 45% estimate: (1.5 × 0.45 − 0.55) ÷ 1.5 = 8.33%. At the bookmaker's own implied chance, 40%, the answer is 0%: no edge, no bet.
The bankroll is money set aside for betting that you can afford to lose in full, not your savings. Fractional prices can be converted with the odds converter.
Result
How the Kelly Stake Is Worked Out
John Kelly published the formula in 1956 for a problem in information theory; the mathematician Edward Thorp later applied it to blackjack and to investing. It answers one question: if a bet has a positive expected value, what fixed share of the bankroll should go on it so that the bankroll grows as fast as possible over many bets? Bet less and growth is slower; bet more and the swings eventually shrink the bankroll even though every bet is favourable.
The formula needs two inputs and only one of them is known. The odds come from the bookmaker. The probability is yours, and the whole result depends on it. Here is the same price of 2.50 with four different estimates:
| Your estimate | Edge per £1 | Full Kelly | Half Kelly | Quarter Kelly |
|---|---|---|---|---|
| 40% (= 1 ÷ 2.50) | 0p | 0% | 0% | 0% |
| 42% | +5p | 3.33% | 1.67% | 0.83% |
| 45% | +12.5p | 8.33% | 4.17% | 2.08% |
| 50% | +25p | 16.67% | 8.33% | 4.17% |
Two lessons sit in that table. First, at the bookmaker's own implied probability the stake is zero, and since every price includes a margin (the margin calculator shows how much), the honest Kelly stake on a typical bet is nothing at all. The formula only says "bet" when you believe you know better than the price. Second, the stake rises steeply with the estimate: if the true chance is 42% and you believe 45%, you stake 8.33% of the bankroll instead of 3.33%, two and a half times too much.
Why fractional Kelly exists
Full Kelly is aggressive even when the estimate is right. In the continuous-time approximation used by Thorp, the chance that a bankroll staked at a fraction c of Kelly ever falls to a share x of its starting value is x raised to the power (2 ÷ c − 1). For a halving, x = 0.5:
- Full Kelly: 0.5¹ = 50% chance of halving at some point.
- Half Kelly: 0.5³ = 12.5%, for about three quarters of the growth rate.
- Quarter Kelly: 0.5⁷ = 0.78%.
That is why most people who use Kelly at all use a fraction of it, and why a fraction also protects against the estimate being too high. With a £1,000 bankroll, the 45% example above means £83.33 at full Kelly and £41.67 at half Kelly.
Where the probability comes from
The calculator does not supply the probability and neither does Verdecto: we do not give tips. The starting point is the price itself, converted to a percentage (see how betting odds work), with the margin removed. Any estimate above that figure is a claim that you know something the market does not. If you cannot say what that is, the right Kelly stake is the one the formula gives at the market price: zero.
Related Calculators
Kelly assumes your probability estimates are right. The only way to check that is a large sample of results, and the betting ROI calculatorturns those results into a yield.
When the prices at two bookmakers guarantee a profit whatever happens, staking is a different problem: you split the stakes so every outcome pays the same. The arbitrage calculatordoes that split.
On a betting exchange, a lay bet risks its liability, not its stake: liability = lay stake × (odds − 1). Size a lay from the liability, which the lay liability calculatorworks out.
Frequently Asked Questions
What is the Kelly criterion formula?
Kelly stake as a share of your bankroll = (b × p − q) ÷ b, where b is the decimal odds minus 1, p is your estimate of the chance of winning and q is 1 − p. At odds of 2.50 with a 45% estimate: (1.5 × 0.45 − 0.55) ÷ 1.5 = 0.0833, so full Kelly is 8.33% of the bankroll.
What does it mean when the Kelly stake is zero or negative?
It means the bet has no edge at your estimate: the price does not pay enough for the chance you give it. Kelly's answer is to bet nothing. If your estimate equals the bookmaker's implied probability, 1 ÷ odds, the stake is exactly zero, and because bookmaker prices include a margin, that is the answer for most bets.
What is half Kelly and why do people use it?
Half Kelly stakes half the full Kelly amount. It gives up about a quarter of the long-run growth rate but cuts the swings sharply: in the standard continuous approximation, the chance of the bankroll ever halving falls from 50% under full Kelly to 12.5% under half Kelly. It also limits the damage when the probability estimate is too high.
Does the Kelly criterion work for sports betting?
The mathematics works for any bet with known odds and a known probability. The weak point in betting is the probability: it is an estimate, and Kelly stakes grow quickly with small errors. At odds of 2.50, believing 45% when the true chance is 42% leads to a stake 2.5 times the correct one.
Should I use Kelly on accumulators or several bets at once?
The basic formula is for one bet at a time. For an accumulator, p is the chance of every leg winning together, which multiplies each leg's estimate error. For several simultaneous bets the stakes have to be reduced so that the total does not exceed what the single-bet formula allows; staking full Kelly on each separately overbets the bankroll.
No staking plan turns bets with a negative expected value into winning ones, and a bankroll should only ever be money you can afford to lose. Set deposit limits with your bookmaker before you start. 18+. If gambling stops being fun, see our responsible gambling resources.