To calculate fair odds, estimate the chance of the outcome and divide 1 by it: fair odds = 1 / probability, so an outcome with a 47.6% chance is fair at 1 / 0.476 = $2.10. The estimate is the hard part, and it comes from one of three places: your own model or ratings, a bookmaker market with its margin taken out, or the back and lay prices on a betting exchange.
With a fair price in hand you can measure any offer against it. Using illustrative prices, an offered $2.30 against a fair $2.10 has an edge of 2.30 / 2.10 - 1 = 9.5%. How betting odds work sets out implied probability and margin, the two ideas every fair price rests on. The fair odds calculator de-vigs a market by any of four methods and shows the edge on a price you enter.
What fair odds are, and why true odds are an estimate
Fair odds are the price an outcome would carry if nobody took a margin: the price at which a bet breaks even on average. Probability and price are two views of the same number:
fair odds = 1 / probability
probability = 1 / fair odds
A 50% chance is fair at $2.00, a 25% chance at $4.00 and a 10% chance at $10.00. A bookmaker prices below fair because of its margin: with a 6% margin spread evenly, that 25% chance would be offered at about 4.00 / 1.06 = $3.77.
True odds are the same idea framed as the real chance of the event. The trouble is that the real chance of a game or a race is never observed, because the event happens once. So every fair price, true odds included, is an estimate, worth as much as the source behind it. Fair odds betting means comparing offered prices with that estimate and betting only where the offer is longer.
Three places a fair price comes from
| Source | How you get the fair price | Its weakness |
|---|---|---|
| Your own model or ratings | Rate each outcome's chance, frame the chances to 100%, then take 1 / chance | An untested model can be confidently wrong, and its errors only show over hundreds of bets |
| A bookmaker market, de-vigged | 1 / price for every outcome, then a method to take the margin out | One bookmaker's opinion, and the method chosen moves long shots |
| An exchange market | The midpoint of the back and lay chances | Thin markets, wide spreads and commission on winnings |
With illustrative prices for a basketball game, where overtime means there is no draw, here is each source pricing the away side, Team B.
Your own model or ratings
Say your ratings give Team B a 45.5% chance. Its fair price is 1 / 0.455 = $2.20. A model can use information the market has not priced, which is its strength, but nothing says it is right until its prices have been tested against results and against closing prices. The rated price entry covers how punters build their own prices.
A bookmaker market with the margin removed
Bookmaker A has Team A at $1.83 and Team B at $2.01: 1 / 1.83 + 1 / 2.01 = 0.54645 + 0.49751 = 1.04396, a 104.4% market. The multiplicative method gives Team B 0.49751 / 1.04396 = 47.66%, a fair price of 2.01 x 1.04396 = $2.10. On a close two-way market like this the other methods land within a cent of it, as how to remove the bookmaker margin shows; on a long shot they do not.
The weakness is that this is still one bookmaker's view, its errors and any lag included, with only the margin taken off. De-vigging several bookmakers' markets and averaging their fair chances spreads that risk.
An exchange market
On an exchange, Team B shows $2.08 to back and $2.12 to lay. The fair chance sits between the two implied chances, 1 / 2.08 = 0.480769 and 1 / 2.12 = 0.471698, and the midpoint is (0.480769 + 0.471698) / 2 = 0.476234, a fair price of 1 / 0.476234 = $2.10. A 4-cent back lay spread like this pins the price down well. A spread of 40 or 50 cents, or a market with little money waiting at each price, which is low exchange liquidity, does not.
De-vigged bookmaker markets vs the exchange as a reference
The two market sources fail in different ways, so the choice depends on the market in front of you:
| Situation | Lean on | Why |
|---|---|---|
| A race close to the jump | The exchange | It carries the latest money and news, and no margin is built into its prices |
| A race early in the day | Neither alone | An early exchange market can be thin and an early bookmaker market can carry a big margin, so ask for a bigger edge |
| A big sports market with a busy exchange | Either, and check they agree | Two sources that agree are worth more than one |
| A sports market with little exchange money | Several de-vigged bookmaker markets, averaged | A thin exchange midpoint can sit anywhere inside a wide spread |
| A long shot | The exchange, if money is matched there | De-vig methods disagree most on long shots |
When one source is clearly stronger, use it; when two disagree, the size of the gap is a measure of how uncertain the fair price is. The exchange price as fair odds guide covers when an exchange price is a sound reference and when thin money makes it misleading.
Commission-adjusting an exchange price
An exchange charges commission on net winnings in each market, at a rate of its own choosing, so the rate is an input you supply. With an illustrative 5%:
net back price = 1 + (back price - 1) x (1 - commission rate) = 1 + (2.08 - 1) x 0.95 = 2.026
effective lay price = 1 + (lay price - 1) / (1 - commission rate) = 1 + (2.12 - 1) / 0.95 = 2.179
The net back price is what backing Team B on the exchange really pays: $2.026, not $2.08. It answers a where-to-bet question, and here the bookmaker's $2.30 pays 2.30 / 2.026 - 1 = 13.5% more than backing the same team on the exchange. It does not change the chance. Commission is a charge on winnings, not information about the game, so the fair price stays at the $2.10 midpoint and the edge at 9.5%.
What commission does change is how tightly the exchange pins the fair price down. Before commission, the back and lay prices are consistent with a chance between 1 / 2.12 = 47.2% and 1 / 2.08 = 48.1%. After it, backing pays only if the chance is above 1 / 2.026 = 49.4%, and laying only if it is below 1 / 2.179 = 45.9%, so any fair price from $2.03 to $2.18 leaves neither side a profit. The midpoint is still a sound single estimate, but the band around it is wider than the 4-cent spread suggests.
Risk: Betting involves risk. Paying more than the exchange does not make a bet a winner, the commission rate is the exchange's to set and can change, and there is no guarantee of profit. See responsible gambling for limits and support.
A fair $2.10 against an offered $2.30
Bookmaker B offers Team B at $2.30. Against a fair price of $2.10, the figure both sources round to (unrounded, the de-vigged market's $2.098 gives 2.30 / 2.098 - 1 = 9.6%, the edge the fair odds calculator shows):
edge = offered price / fair price - 1 = 2.30 / 2.10 - 1 = 0.0952, about 9.5%
expected value per $1 = fair chance x offered price - 1 = 0.47619 x 2.30 - 1 = 0.0952
On a $40 bet that is worth about 40 x 0.0952 = $3.81 on average. No single bet pays $3.81: each one either returns $40 x 2.30 = $92, a $52 profit, about 47.6% of the time, or loses $40 the other 52.4%.
That 9.5% depends entirely on the fair price. Here is the same $2.30 against the fair prices each source might give:
| If the fair price is really | Chance | Edge at $2.30 | Expected value on $40 |
|---|---|---|---|
| $2.00 | 50.0% | 15.0% | +$6.00 |
| $2.10 | 47.6% | 9.5% | +$3.81 |
| $2.20 | 45.5% | 4.5% | +$1.82 |
| $2.30 | 43.5% | 0.0% | $0.00 |
| $2.40 | 41.7% | -4.2% | -$1.67 |
Working for the $2.20 row: 2.30 / 2.20 - 1 = 0.0455, and 40 x 0.0455 = $1.82.
Your own model's $2.20 cuts the edge to 4.5%. The price stops being worth taking only if the fair price is $2.30 or longer, a chance of 43.5% or less, which is 4.1 points below the 47.6% estimate. How far your estimate can be wrong before the edge disappears is the real test of a value bet, and positive EV betting covers what edges like this do over many bets.
Risk: Betting involves risk. A 9.5% edge is an average over many bets, the fair price behind it is an estimate, and this bet still loses more often than it wins. See responsible gambling for limits and support.
Mistakes that inflate an edge
| Mistake | What it does to the $2.30 | The fix |
|---|---|---|
| Using the exchange back price as fair | Against $2.08 the edge reads 2.30 / 2.08 - 1 = 10.6% | Use the midpoint of the back and lay chances |
| Using the net back price as fair | Against $2.026 it reads 13.5% | Use the net price only to decide where to back |
| Trusting a thin exchange market | With $1.95 to back and $2.40 to lay, the edge could be anything from 2.30 / 2.40 - 1 = -4.2% to 2.30 / 1.95 - 1 = +17.9% | Check the spread and the money matched before you use a midpoint |
| Trusting an untested model | A model that says 50% shows a 15.0% edge | Test it against closing prices first |
| Using a fair price from earlier in the day | Prices move, and a fair price describes only the moment it was read | Rebuild it from current prices |
| De-vigging one outlying bookmaker | Its errors survive the de-vig | Average several bookmakers, or use the exchange |
Fair prices on B337's screeners
B337 takes its fair prices from the two market sources, not from a model of its own. For racing, the reference is Betfair's own market, and EV overlays on the Terminal show how each bookmaker's price compares with it. For sports, the fair price comes from a global market reference with the bookmaker margin removed: the +EV screener takes the margin out of prices across the market, exchanges included, and combines them into one figure per selection. Both are estimates, and a price above either can still lose.
Sports prices above that fair price appear on the +EV screener, ordered by edge. Its rows come with Terminal Pro, Full Automation or a Screeners plan set up with the team, and Terminal View does not include them. A free account shows how many prices sit above fair, and the biggest edge among them, without the rows. Any bet you take from it, you place yourself, in your own bookmaker account. Bookmaker names are trade marks of their owners. B337 is not affiliated with them.
For free and confidential support call 1800 858 858 or visit gamblinghelponline.org.au.
Risk: Betting involves risk. A screener's edge is measured against an estimate, prices can shift before a bet is struck, and there is no guarantee of profit. See responsible gambling for limits and support.