Kelly criterion calculator
Kelly sizes a bet from your edge. Enter the odds and the chance you think the bet has; the calculator shows the stake and whether there is an edge at all.
19+ in most of Canada (18+ in Alberta, Manitoba and Quebec), 21+ in most US states. A calculator shows what a bet pays, not how likely it is to win. Free help: 1-800-GAMBLER (US), ConnexOntario 1-866-531-2600 (Ontario), 211 (Alberta). More help.
The formula
f = (b × p − q) ÷ b, with b = decimal odds − 1, p your win probability and q = 1 − p. Stake = f × bankroll × multiplier.
Worked example
A +120 bet you think wins 50% of the time: b = 1.2, f = (1.2 × 0.5 − 0.5) ÷ 1.2 = 8.33% of the bankroll. With $1,000, full Kelly stakes $83.33 and half Kelly $41.67. Expected profit: $10.00 per $100 staked.
Kelly stake at +120 by win probability
| Your win probability | Edge | Full Kelly | Half Kelly |
|---|---|---|---|
| 45% | -0.45 pts | no bet | no bet |
| 48% | 2.55 pts | 4.67% | 2.33% |
| 50% | 4.55 pts | 8.33% | 4.17% |
| 52% | 6.55 pts | 12.00% | 6.00% |
| 55% | 9.55 pts | 17.50% | 8.75% |
| 60% | 14.55 pts | 26.67% | 13.33% |
+120 breaks even at 45.5%. Below that, Kelly says not to bet. Fair odds from the no-vig calculator are a common way to estimate p.
Questions
What is the Kelly criterion?
A staking formula that sizes each bet by your edge: the stake, as a share of bankroll, that maximises long-run bankroll growth if your win probability is right.
What is the Kelly formula?
f = (b × p − q) ÷ b, where b is the decimal odds minus 1, p your win probability and q = 1 − p. A negative result means no bet.
Why do people bet half Kelly?
Full Kelly swings hard and over-stakes when the probability estimate is too high. Half or quarter Kelly gives up some growth for much smaller drawdowns.
Does Kelly work if I have no edge?
No. Without an edge the formula returns zero or less: the right Kelly stake is nothing.