Kelly Criterion Calculator
18+ · Gambling can be addictive. The house edge means you lose over time.
- Full Kelly
- $83.64
- 8.36% of your bankroll
- Half Kelly
- $41.82
- 4.18% of your bankroll
- Quarter Kelly
- $20.91
- 2.09% of your bankroll
Your edge: 9.20% expected profit per $1 staked (52.00% chance against 47.62% implied by the odds). Kelly is only as good as that 52%: if your real chance is lower, every stake below is too big.
Growth and risk over
| Stake size | Of bankroll | Growth per bet | Median after 100 | Behind after 100 | Ever halved |
|---|---|---|---|---|---|
| Quarter Kelly | 2.09% | 0.168% | $1,183.14 | 24.2% | 0.0% |
| Half Kelly | 4.18% | 0.289% | $1,333.98 | 24.2% | 3.0% |
| Full Kelly | 8.36% | 0.385% | $1,468.36 | 30.8% | 25.7% |
| Double Kelly | 16.73% | -0.004% | $996.37 | 53.9% | 66.2% |
Growth per bet is the typical (geometric) change, exp(G) - 1. Median, behind and ever halved are exact for your inputs: computed over every possible sequence of wins and losses, not simulated.
How to use it
- Pick your odds format and enter the odds you can get.
- Enter your bankroll: the money set aside for betting, not your savings.
- Enter your honest estimate of the win probability. The break-even probability under the field is what the odds imply.
- Read the full, half and quarter Kelly stakes. If the calculator says bet $0, you have no edge at that price.
- Check the growth and risk table to pick a fraction you can live with. The URL keeps your inputs for sharing.
The Kelly formula
Stake a fraction f of your bankroll at decimal odds d with win chance p. A win multiplies the bankroll by 1 + (d - 1) × f, a loss by 1 - f. Over many bets your bankroll grows at the average of the log of those multipliers, and Kelly picks the f that maximises it:
G'(f) = 0 gives f* = (p × d - 1) ÷ (d - 1)
The top of the fraction, p × d - 1, is your expected profit per $1 staked. If it's zero or negative, so is f*, and the best stake is nothing. This is the result in J. L. Kelly Jr.'s 1956 paper; the calculator also shows G itself, so you can see what each stake size gives up.
Example: 52% at +110 (decimal 2.10). f* = (0.52 × 2.10 - 1) ÷ 1.10 = 8.36% of the bankroll.
Why fractional Kelly
Same example, 100 bets, re-staking the same fraction of the current bankroll every time. Exact figures over every possible run of wins and losses:
| Stake | Of bankroll | Growth per bet | Behind after 100 | Ever halved in 100 |
|---|---|---|---|---|
| Quarter Kelly | 2.09% | 0.168% | 24.2% | 0.0% |
| Half Kelly | 4.18% | 0.289% | 24.2% | 3.0% |
| Full Kelly | 8.36% | 0.385% | 30.8% | 25.7% |
| Double Kelly | 16.73% | -0.004% | 53.9% | 66.2% |
Full Kelly grows fastest in the long run, but a bankroll cut in half along the way is routine. Half Kelly gives up a quarter of the growth and much of the drawdown. Double Kelly takes all the risk for roughly no growth. The shape is the same for any small edge: betting a fraction k of full Kelly gives close to k × (2 - k) of the maximum growth, so about 75% at half Kelly and about 44% at quarter Kelly.
The bigger reason is that p is an estimate. Kelly with an overestimated p is overbetting, and the table shows how quickly that turns bad. Betting a fraction is a margin of safety for being wrong about your edge.
No edge, no bet
Kelly never tells you to bet on a game with a house edge. Every casino bet has p × d below 1 by design, so f* is negative and the stake is $0. The odds calculator shows the edge of any bet, and the house edge page explains how sites set it. In sports betting an edge is possible but rare: it means your probability is better than the bookmaker's price, margin included.
What other Kelly calculators get wrong
- Calling the expected value per bet the "edge" in one place and the probability gap in another.
- Formulas with an extra odds term in the numerator, which oversize every stake.
- Showing a negative stake, or saying in one place that a negative edge returns zero and in another that it returns a negative number.
- Growth and drawdown tables with round numbers and no working. Ours are computed from your inputs.
Source: J. L. Kelly Jr., "A New Interpretation of Information Rate", Bell System Technical Journal 35(4), 1956. The growth, median, behind and halving figures are our own exact calculations.
Where to use it
Compare esports and CS2 bookmakers on our CS2 betting sites list, or crypto sportsbooks and casinos on crypto casinos. Check what a game keeps with the house edge calculator. Set a budget first, and see our responsible gambling page if it stops being fun.
FAQ
- What is the Kelly criterion formula?
- f = (p x d - 1) / (d - 1), where p is your chance of winning and d the decimal odds. It's the share of your bankroll to stake. The same thing written with net odds b = d - 1 is f = (b x p - q) / b, with q = 1 - p.
- Why do bettors use half or quarter Kelly?
- Full Kelly swings hard and assumes your win probability is exactly right. Half Kelly keeps about three quarters of the growth for much less risk: in our example the chance of halving your bankroll within 100 bets drops from 26% to 3%. If you overestimate your edge, a fraction also keeps you from overbetting.
- What does a negative Kelly number mean?
- That you have no edge at those odds: your win chance is below the break-even chance 1/d. The Kelly stake is then zero. Don't bet the other side because of it; that side has its own odds and its own Kelly number.
- Does the Kelly criterion work for casino games?
- Only if you have an edge, and casino games are built so you don't. Red on a single-zero roulette wheel wins 18 times in 37 at even money, which gives a Kelly fraction of -2.70%. Negative means bet nothing. The same is true for every bet with a house edge.
- What happens if you bet more than Kelly?
- Growth falls, and risk rises fast. At double Kelly the typical growth is about zero or below (-0.004% per bet in our example) while the chance of halving within 100 bets is 66%. Bet much more than about double Kelly and your bankroll shrinks in the long run, even with a real edge.