On this page (7 sections)
Expected value (EV) is the average result of a bet if it were repeated an unlimited number of times, calculated from the probability of each outcome and its payout. The Kelly criterion is a formula for the bankroll fraction that maximises long-run growth on a bet with a known, positive edge.
What expected value means for a bet
Every bet has three ingredients: how often you win, what you are paid when you win, and what you stake. Multiply the win probability by the profit if you win, subtract the loss probability times the stake, and the result is the bet's expected value — the average outcome across a very large number of repetitions, not a forecast of the next one.
This EV calculator for gambling takes those same three ingredients and returns the expected value per bet, the edge as a clean percentage, and the expected result if you repeated the bet a chosen number of times. It works for any bet you can express as a probability and a payout — a casino game, a sports line, or anything in between.
The EV calculator
Decimal odds = total return per unit staked including the stake back. Even money is 2.00.
The formula is short: EV per bet = stake × (probability × decimal odds − 1). The pre-filled example is close to a European roulette even-money bet — 18 winning numbers out of 37, paid at 2.00 — which returns a small, consistent negative edge. Change the odds to see how quickly a small shift in either number flips the sign.
The Kelly criterion calculator
Both figures are a percentage of total bankroll, for this one bet.
The formula: Kelly fraction f* = (bp − q) ÷ b, where p is win probability, q is 1 − p, and b is the net odds — decimal odds minus one, i.e. profit per unit staked, not the total return. A classic textbook case makes this concrete: a 60% probability of winning at even money (decimal odds 2.00) gives b = 1, and f* = 0.60 − 0.40 ÷ 1 = 0.20, or 20% of bankroll on that single bet.
Why casino games get a Kelly stake of zero
Kelly only has a meaning on a bet with a genuine positive edge. The formula assumes you know p and b accurately and asks what fraction of bankroll grows your balance fastest over repeated bets at that exact edge. When the edge is negative — which describes essentially every standard casino game by construction — the formula returns a negative fraction.
Said plainly, because it should be
A negative Kelly fraction is not a small recommended stake. It is the formula telling you the correct stake is zero. Casino games carry a built-in house edge, so on those games Kelly's answer is always the same: do not place the bet. Anything marketed as a 'Kelly strategy for slots' or 'Kelly system for roulette' is applying a positive-edge formula to a negative-edge game, and the maths does not survive that substitution.
This is also why the calculator clamps a negative full-Kelly result to 0% rather than showing a negative percentage of bankroll — a negative stake has no practical meaning, and rounding it up to a small positive number to make the tool feel more useful would be dishonest.
Worked examples
| Scenario | Win probability | Payout odds | Edge | Full Kelly |
|---|---|---|---|---|
| Even-money coin flip with a real edge | 60% | 2.00 | +20% | 20% of bankroll |
| European roulette, red or black | 48.65% | 2.00 | −2.70% | 0% — do not bet |
| European roulette, single number | 2.70% | 36.00 | −2.70% | 0% — do not bet |
| Sports bet with a modelled 3% edge | 34% | 3.00 | +2% | roughly 1% of bankroll |
Notice the two roulette rows: completely different bet types, completely different probabilities and odds, identical −2.70% edge, identical 0% Kelly verdict. The house edge is baked into the payout table before you ever choose which number to bet on.
What EV and Kelly cannot tell you
- Neither formula accounts for variance — a positive-edge bet can still lose money over a short run, and a negative-edge bet can still win a single session. See our bankroll management guide for how to size play around that variance.
- Both formulas are only as good as the probability you enter. An overestimated edge is the single most common way a Kelly-based staking plan goes wrong in practice.
- Neither tool prices a wagering requirement — for a bonus with turnover attached, use the wagering requirement calculator instead.
- Rakeback and cashback can shift the effective edge on a specific game for a limited time — model that with the brand-specific VIP calculators, not by guessing.
Licence, geo-restrictions and playing safely
Licensing. Understanding EV and Kelly does not turn a negative-edge game into a positive-edge one. Treat these tools as a way to see the true cost of play, not a system for beating it.
Your side of it. Crypto casinos settle fast, which is exactly what makes them easy to overplay. Before your first deposit at these operators, set a deposit cap and a session timer in the account settings — not in your head.
- Deposit limits and self-exclusion tools live in account settings, not support chat
- A losing session is not a signal to raise the stake — it is a signal to stop
- Bonus turnover targets are not a reason to keep playing past your limit
- Free, confidential help: BeGambleAware and Gambling Therapy
Frequently asked questions
What does expected value mean for a single bet?
It is the average result you would get if you repeated the exact same bet an enormous number of times: probability of winning times the profit if you win, minus the probability of losing times the stake you lose. It is an average, not a prediction of any one outcome.
What is the Kelly criterion calculator actually for?
It answers a narrower question than most people think: given a true edge and true win probability, what fraction of a bankroll maximises long-run growth rate. It was built for situations with a genuine positive edge, such as card counting or sports arbitrage — not for casino games with a built-in house edge.
Why does the Kelly calculator say 0% for casino games?
Because the formula (bp − q) ÷ b returns a negative number whenever the house has the edge, and a negative stake has no meaning. The mathematically correct position on a negative-edge bet is not to place it, and the tool reports that plainly rather than rounding it up to something reassuring.
Is a house-edge game ever a positive-edge bet for the player?
Occasionally, through a promotion that overcompensates for the edge — a large cashback or rakeback rate can theoretically flip the sign on a specific game for the duration of the offer. That is the exception, not the rule, and it needs the exact numbers checked, not assumed.
What is 'fractional Kelly' and why would anyone use less than full Kelly?
Fractional Kelly means staking a set percentage of the full Kelly figure — half-Kelly stakes 50% of what full Kelly recommends. It sacrifices some long-run growth rate for a large cut in volatility, which is why it is the more commonly used version even among people betting with a genuine edge.
How is 'payout odds' defined in this tool?
As decimal odds: the total return per unit staked if you win, stake included. Even money is 2.00. A bet that returns three units total for every one staked is 3.00. Convert fractional or American odds to decimal before entering them.
Does the EV calculator account for variance?
No, deliberately. Expected value is a long-run average and says nothing about how bumpy the ride to that average will be. Our bankroll management guide covers variance and the staking discipline that survives it.
Can I use this on a bonus or rakeback offer instead of a single bet?
For a bonus with a wagering requirement, use the wagering calculator instead — it prices the cost of clearing turnover rather than a single wager's odds.