This expected value calculator works out what one bet is worth on average. Type the stake, the decimal price on offer and your own estimate of the chance (or the price you think is fair), and it shows the EV in dollars, the EV per $1 staked, the edge and the break-even chance.
Expected value is an average over many identical bets, never a forecast of this one. A bet worth +$6.00 on average still returns 75 x 5.40 = $405 or nothing, and value betting covers why positive bets can still finish behind.
How to use the expected value calculator
Four inputs, only the last optional:
- Stake. What goes on the bet, in dollars.
- Odds on offer. The decimal price you can bet at, before commission. Fractional and American prices need the odds converter first.
- Chance it wins, or Fair odds on the other setting. A chance reads as a percentage: 50 and 50% are the same, and 0.8 means 0.8%.
- Commission on winnings. Blank for a bookmaker bet. On an exchange, type your own rate: none is assumed, because rates differ by exchange and account.
Under the four tiles, a table splits the bet into its two outcomes: chance, profit or loss, and contribution. Those rows add to the total before rounding, so the cents shown can differ by one. Money rounds to the nearest cent, percentages to two decimal places.
Refused rather than answered: a stake under $0.01 or over $10,000,000, a price outside $1.01 to $10,001, a chance outside about 0.01% to 99% (that price band read as a chance), a rate below 0% or at 100% or more, and a decimal comma such as 2,50. A half-typed entry shows three dots and names the field to fix.
The expected value formula
Two outcomes, each weighted by its chance:
EV = chance x stake x (odds - 1) - (1 - chance) x stake
Divide by the stake and it shortens to EV per $1 = chance x odds - 1, which is also the betting edge while nothing is charged on the winnings:
edge = offered odds / fair odds - 1
They agree because the fair price is 1 / chance: $5.00 fair and a 20% chance are one input written two ways. The chance that makes the EV nothing is the break-even chance, 1 / the price after any commission, so a chance above it means positive EV.
A worked example on $75 at $5.40
Illustrative prices, not a real market. You can bet $75 at $5.40 and put the chance at 20%, a fair price of 1 / 0.20 = $5.00:
| Outcome | Chance | Profit or loss | Chance x profit |
|---|---|---|---|
| It wins | 20.00% | +$330.00 | +$66.00 |
| It loses | 80.00% | -$75.00 | -$60.00 |
| Expected value | +$6.00 |
A win makes a profit of 75 x (5.40 - 1) = $330, so the sum is 0.20 x 330 - 0.80 x 75 = +$6.00, or 8.00% of the stake. The edge is the same figure, 5.40 / 5.00 - 1 = 8.00%, and break-even is 1 / 5.40 = 18.52%.
Risk: Betting involves risk. An expected value is an average built on your own estimate of the chance, so a bet worth +$6.00 can still lose, and often does. See responsible gambling for limits and support.
What commission does to the answer
On an exchange, commission comes off net winnings in a market, not the stake, and a losing bet is not charged. The tool prices this bet alone, not your whole position there, so the real price is
net price = 1 + (odds - 1) x (1 - commission rate)
With illustrative numbers: $100 at $3.00 against a fair price of $2.80, at a 5% rate. The chance is 1 / 2.80 = 35.71%, the net price is 1 + 2.00 x 0.95 = $2.90, a win makes a profit of 100 x (2.90 - 1) = $190, and the sum is 0.357143 x 190 - 0.642857 x 100 = +$3.57.
The edge tile still reads 3.00 / 2.80 - 1 = 7.14%, because it measures the offered price before commission; the EV per $1 tile reads 3.57%, half of it. At 10% the $5.40 bet above turns negative: its net price is 1 + 4.40 x 0.90 = $4.96, and 0.20 x 4.96 - 1 = -0.80%.
Where the win chance should come from
A hunch gives you an answer about your hunch. A chance worth typing usually comes from taking the margin out of a market, which how to calculate fair odds works through and the fair odds calculator does.
With illustrative prices of $1.75 and $2.25, the chances are 1 / 1.75 = 57.143% and 1 / 2.25 = 44.444%, which add to 101.587%. Dividing the $2.25 side by that total leaves 44.444 / 101.587 = 43.75%, a fair price of 1 / 0.4375 = $2.29, by the proportional method that calculator calls Multiplicative. Typed unrounded, against a second bookmaker's $2.40, that chance makes a $50 bet worth 0.4375 x 50 x 1.40 - 0.5625 x 50 = +$2.50 on average, an EV of 5.00% per $1.
Risk: Betting involves risk. A fair price taken out of one market is an estimate, so +$2.50 is an average, and at 43.75% this bet loses more often than it wins. See responsible gambling for limits and support.
Bonus bets and place bets
The calculator prices a cash bet, where losing costs the stake. Two common bets need care.
- A bonus bet. On most Australian bonus bets the stake is not returned and losing one costs nothing out of pocket, so the expected value is chance x bonus x (odds - 1). An illustrative $25 bonus bet at $6.50 on an 18% chance is worth 0.18 x 25 x 5.50 = $24.75 on average, and a bonus bet that loses pays nothing. The bonus bet converter sizes the lay to hedge one at an exchange instead, and each bookmaker's terms decide how its bonus bets work.
- A place bet. Type the place price and your chance of placing. How many places are paid, and how a dead heat for one is settled, comes from the rules that apply: the tote rules, your state's on-course betting rules, or the bookmaker's own terms. Where they halve a two-way dead heat, type your chance of placing plus half your chance of that dead heat: exact while no commission is charged.
Risk: Betting involves risk. A bonus bet that loses pays nothing, and the $24.75 is an average on your own estimate of the chance. See responsible gambling for limits and support.
Mistakes that change the answer
Illustrative numbers on a $75 stake:
| Mistake | What it does to the answer | The fix |
|---|---|---|
| Inverting a rounded chance | $1.91 implies 52.36%, shown as 52.4%; typing 52.4% back reads +$0.06, an edge made of the rounding | Type the $1.91 itself, on the Fair odds setting |
| Leaving commission out of an exchange bet | At a 10% rate the $5.40 bet's +8.00% is really -0.80%, so +$6.00 becomes -$0.60 | Type your own rate |
Where the screeners fit
B337's +EV screener does this job over sports markets in two steps: strip the margin out of a market for a fair price, then list the bookmaker prices above it, largest edge first, filtered by sport, market and bookmaker. Its rows unlock with Terminal Pro, Full Automation or a Screeners plan set up with the team; on a free account the live count and the best edge show, and the rows stay locked. The screener places nothing itself: on Terminal Pro you click a price to bet it in your own account, and bets placed through B337 use credits. Positive expected value betting works through why a +EV bet still loses often, and betting strategy covers staking and testing.
Risk: Betting involves risk. An edge is measured against an estimated fair price, and a +EV bet can still lose, and often does. Many bookmakers restrict or prohibit automated betting, third-party access and multiple accounts in their terms, and a bookmaker can cut a price, limit your stakes, void bets or close your account; that risk is yours. See responsible gambling for limits and support.
For free and confidential support call 1800 858 858 or visit gamblinghelponline.org.au.