Every price a bookmaker publishes contains margin. The advertised number is never the operator's honest probability estimate — it is that estimate distorted by the cushion they need to be profitable across the population of bets they take. De-vigging is the process of stripping that cushion out so you are working with fair probabilities you can actually compare against your own model, against sharper books, or against a market consensus. Without de-vigging, every EV calculation, every Kelly stake, and every closing line value measurement is contaminated by an unknown distortion that varies bookmaker to bookmaker, market to market, and minute to minute. This guide walks through the maths, the common methods, three worked examples, and the operational workflow Australian punters need to apply de-vigging consistently. Start with the foundation in our positive EV guide, then layer the techniques below on top.
What de-vigging is and why it matters
De-vigging is the conversion of bookmaker prices into the probabilities those prices would carry if the operator took no margin at all. The word "vig" — short for vigorish — refers to the built-in commission the bookmaker collects regardless of which side wins. Devigging is sometimes written as "no-vig odds", "fair odds", or "true probability", but the goal is the same: produce a calibrated probability estimate for each outcome that sums to exactly 100% and reflects what the bookmaker — or a sharper consensus — actually believes about the event.
The reason this matters is simple. A published price of $1.91 does not mean the bookmaker believes there is a 52.4% chance the outcome occurs. It means they have priced the outcome such that, after their margin is applied, $1.91 is what you are offered. The bookmaker's actual belief might be 50% — they have shaded both sides to capture roughly five percent margin on the market. If you confuse the published implied probability with the bookmaker's honest probability, every comparison you make against your model or against another book is wrong by a non-trivial amount. De-vigging fixes that.
For Australian punters, this skill has three practical applications. First, it gives you a defensible baseline for expected value calculations — see the methodology in our devigging article. Second, it lets you measure closing line value honestly by comparing your taken price against the de-vigged close from a sharp book. Third, it sanity-checks your own model: if you are consistently disagreeing with the de-vigged consensus by more than two or three percent on liquid markets, your model probably has a bias rather than an edge.
How bookmaker margin works
Margin — also called overround, juice, or the book percentage — is the amount by which the sum of implied probabilities exceeds one hundred percent. The mechanics are easiest to see in a coin-flip market. If a bookmaker priced a fair fifty-fifty event at $2.00 on each side, each price would imply a 50% probability and the implied probabilities would sum to exactly 100%. The operator would break even long term and absorb all variance — a non-viable business. So instead they price both sides at $1.91, each implying 52.36%, summing to 104.72%. That extra 4.72 percentage points is their margin. If they balance the book perfectly (equal volume on both sides) the margin is locked in as profit regardless of the result.
Margin is not uniform across operators or markets. A typical Australian recreational book runs 5-8% on head-to-head NRL and AFL lines, 4-6% on NFL and NBA, 6-10% on player props, and 15-25%-plus on first-scorer and exotic novelty markets. Sharp operators like Pinnacle and Circa run 1-3% on top markets, which is why those books are referenced as the global anchor for true pricing. The lower the margin, the less the published price has been distorted away from honest probability, and the more reliable de-vigging is as an approximation of the operator's true belief.
Margin also moves asymmetrically. Bookmakers do not always split the vig evenly between the two sides of a market. When sharp money has come in on one outcome, the operator will often shade the price of that outcome harder — pushing the implied probability above the bookmaker's actual estimate — while leaving the other side close to fair. Proportional de-vigging assumes margin is split evenly, which is a workable approximation on liquid markets but introduces error on markets where the bookmaker has clearly shaded one side. We will return to this when we discuss the power method.
Proportional de-vigging method
The proportional method is the workhorse de-vigging technique. It is fast, it is easy to explain, and on low-margin markets it produces fair probabilities accurate to within a fraction of a percent. The recipe has three steps. First, convert every published price to an implied probability by taking one divided by the decimal price. Second, sum those implied probabilities across every possible outcome in the market — the total will exceed one hundred percent by the margin. Third, divide each implied probability by that total to rescale every outcome back to a fair probability that sums to exactly 100%.
Algebraically, if the bookmaker offers prices d-one through d-n on n outcomes, the implied probability for outcome i is one over d-i, the overround is the sum of those implied probabilities, and the fair probability for outcome i is the implied probability divided by the overround. The fair price for outcome i is therefore one divided by the fair probability, which is the overround divided by the implied probability, which can be written more directly as d-i times the overround.
The implicit assumption is that the bookmaker has spread the margin proportionally across all outcomes — that is, each outcome has been shaded by the same factor. This assumption is approximately true on balanced, liquid head-to-head markets where neither side has been heavily steamed. It breaks down on lopsided favourite-versus-underdog markets, on markets with very high margin (10%-plus), and on markets where one side has been clearly shaded by recent action. For those cases the power method (below) is more defensible.
Power and Shin methods
The power method de-vigs by raising each implied probability to a common exponent rather than dividing by a common factor. It accommodates the empirical observation that bookmakers shade favourites less aggressively than underdogs — long-shot prices carry proportionally more of the margin than short-priced favourites. Mathematically, the method finds the exponent k such that the sum of each implied probability raised to k equals one, then reports each implied probability raised to k as the fair probability. The exponent is solved numerically — there is no closed form for markets with three or more outcomes — but a few iterations of Newton's method converges in milliseconds.
The Shin method, named for Hyun Song Shin's 1992 paper on insider trading in betting markets, models the bookmaker as facing a population of bettors composed of mostly recreational players plus a small fraction of insiders. The bookmaker shades prices to protect against the insiders, and the Shin solution backs out both the true probabilities and the implied insider proportion (z). On most public markets z is small (1-5%) and the Shin-de-vigged probabilities sit between the proportional and power outputs. Shin is more accurate on horse racing and on markets with thin liquidity where insider information is a bigger factor. For mainstream Australian punter use, proportional de-vigging on a sharp anchor book is sufficient ninety percent of the time, with power method as a sanity check when the favourite is short-priced (under $1.50) or the market is lopsided.
A practical compromise many bettors use is proportional de-vigging on the Pinnacle line, then comparing the result against the power-method output. If the two methods agree within a percentage point, take the proportional number. If they diverge meaningfully, the market is lopsided enough that the assumption of evenly-spread margin is suspect — flag the line for manual review rather than trusting a single algorithmic output.
Worked two-way example
Take an NRL head-to-head where a recreational Australian book is pricing the Storm at $1.65 to beat the Roosters at $2.35. The implied probability of the Storm winning is one over 1.65, which equals 0.6061 or 60.61%. The implied probability of the Roosters winning is one over 2.35, which equals 0.4255 or 42.55%. The sum of implied probabilities is 1.0316 or 103.16%, so the book has an overround of 3.16% — a typical NRL head-to-head margin from a competitive operator.
Apply proportional de-vigging. The fair probability of the Storm winning is 0.6061 divided by 1.0316, which equals 0.5876 or 58.76%. The fair probability of the Roosters winning is 0.4255 divided by 1.0316, which equals 0.4124 or 41.24%. These two numbers now sum to exactly 100%. The fair price for the Storm is one over 0.5876, which equals $1.70. The fair price for the Roosters is one over 0.4124, which equals $2.425. Notice that the Storm's fair price moved from $1.65 to $1.70 (the bookmaker had shaded their price by five cents) and the Roosters' fair price moved from $2.35 to $2.43.
With fair probabilities in hand you can now do the EV maths. If a competing book is offering the Storm at $1.78, the expected value of a one-unit bet at that price is 0.5876 times 0.78 minus 0.4124 times 1, which equals 0.0455 — a 4.55% edge. If your own model says the Storm should win 62% of the time, your EV against the $1.78 line is even bigger. If your model says 56%, then the line is actually against your view despite the market consensus suggesting value. The point is that every comparison flows from honest fair probabilities, not raw implied numbers.
Worked three-way example
Soccer head-to-head markets are three-way (home, draw, away) and the maths is identical but adds a third term. Consider an A-League match where Sydney FC is $2.10 to win, the draw is $3.40, and Melbourne Victory is $3.60 away. Implied probabilities are 0.4762 for Sydney, 0.2941 for the draw, and 0.2778 for Victory, summing to 1.0481 — a 4.81% margin. Fair probabilities are 0.4543 for Sydney, 0.2806 for the draw, and 0.2651 for Victory, which sum to exactly 100%. The corresponding fair prices are $2.20, $3.56, and $3.77.
Three-way markets are where the proportional method's evenly-spread-margin assumption starts to show stress, particularly when the home favourite is short-priced. Run the power method on the same market for a sanity check. Numerically solving for the exponent that forces the sum of probabilities to one returns roughly k equals 1.0455. The Sydney implied of 0.4762 raised to 1.0455 is 0.4567. The draw implied of 0.2941 raised to 1.0455 is 0.2803. The Victory implied of 0.2778 raised to 1.0455 is 0.2630. The numbers sit within a quarter of a percent of the proportional output on this particular market — small enough that the proportional shortcut is fine — but on a more lopsided three-way (a favourite at $1.30 against a draw at $5.50 and an underdog at $11) the divergence between methods can reach a full percentage point and the power method is meaningfully better.
Market-consensus de-vigging
Single-book de-vigging is only as good as the book you use as your anchor. A weak, high-margin recreational book carries the operator's own bias and tilt into the de-vigged number. The professional solution is to de-vig multiple sharp books independently and then aggregate. The recipe is to pull current prices from the sharpest books you can access (Pinnacle is the global gold standard, BetCRIS, Circa, Bookmaker.eu, and a few European exchanges fill out the consensus), de-vig each book's prices to fair probability, then take the median of the fair probabilities across books.
Median is preferred over mean because it is robust to outliers. If one book is mid-update and showing a stale line, the mean will be dragged toward the stale number; the median will ignore it. A common refinement is to use a weighted median where books are weighted by their margin (lower margin = higher weight) or by their liquidity (higher limits = higher weight). For most Australian punters, a simple median across three or four sharp anchor books is more than enough.
Consensus de-vigging also produces an implicit no-vig market price that can be compared directly against the Australian recreational books you actually bet through. If the consensus fair price on a Storm-Roosters head-to-head is $1.70, and Sportsbet is offering $1.78, that is a defensible +EV bet. If TAB is offering $1.62, that is a clear -EV bet, regardless of how confident you feel about the Storm. The consensus is your tribunal — not infallible, but the best available estimate of true probability you can build without a proprietary model.
Using de-vigging in an EV workflow
Once you have a fair probability for an outcome, the EV calculation is mechanical. Expected value per unit staked equals fair probability times (decimal price minus one) minus (one minus fair probability) times one. Positive EV means the bet is mathematically favourable in the long run; negative EV means the bet is mathematically unfavourable regardless of how the next single bet resolves. Sample size and variance will be covered in our variance and bankroll guide — the relevant point here is that you need fair probabilities before you can compute EV honestly.
A clean workflow looks like this. Pull live prices from your shop list — say five Australian books plus Pinnacle as the anchor. De-vig Pinnacle's line using the proportional method to produce a fair probability for each outcome. Compute the consensus-implied fair price (one divided by fair probability). Compare every Australian book's offered price against that fair price. Any price meaningfully above the fair price is +EV; size the stake using fractional Kelly (covered in our Kelly criterion guide). Record the bet, the taken price, the fair price, and the implied edge. Track closing line value over time as the truest single proxy for whether your process is profitable — covered in our CLV guide.
This workflow scales. Once it is automated — a simple spreadsheet refreshed every minute is enough for most punters, with API-fed odds for those operating at higher volume — you can scan hundreds of markets a day and surface only the prices that beat consensus by a defensible margin. The de-vigging step is the foundation that makes the entire scanner meaningful.
Limitations and edge cases
De-vigging is not magic. It produces a fair probability conditional on the bookmaker (or consensus) having priced the market honestly net of margin. On novelty markets, props with thin liquidity, and futures with stale lines, the de-vigged output can be wildly off because the underlying prices reflect almost no real market opinion — they are guesses with margin slapped on top. Treat de-vigged probabilities on those markets as rough indications, not as defensible truth.
The proportional method also assumes the margin is independent of the price level. As discussed under the power method, this assumption frays on long-shots. A 50-to-1 outsider in a horse race carries proportionally more margin than the favourite, and proportional de-vigging will overstate the long-shot's true probability. For racing, long-shot-heavy futures, and three-way soccer where one side is heavily favoured, prefer the power or Shin method.
Finally, de-vigging assumes the book in front of you is liquid and current. A line that has not updated in five minutes during in-play, or a book that is intentionally lagging the market to wait for a sharper line, will produce a de-vigged number that is already stale by the time you act on it. Always check the timestamp on the price you are de-vigging and prefer books that move quickly with the consensus.
Common mistakes
The first and most common mistake is comparing raw implied probabilities against a model without de-vigging. The published implied number is inflated by margin, so every comparison shows the book as more confident than it actually is, biasing the punter toward concluding their model has an edge when it does not.
The second mistake is using a single high-margin recreational book as the de-vigging anchor. A 7% margin Australian book de-vigged to fair probability inherits the book's own bias; the resulting "consensus" is just one operator's opinion stripped of obvious markup. Use sharp books for the anchor — Pinnacle is the standard. Australian recreational books are the targets you bet through, not the sources you anchor against.
The third mistake is averaging the offered prices across books without de-vigging each independently. Averaging raw prices conflates the price level with the margin level — a cheap book with high margin will look the same as an expensive book with low margin. De-vig each book first, then aggregate the fair probabilities.
The fourth mistake is failing to refresh. Lines move; de-vigged probabilities computed from a five-minute-old snapshot are stale, particularly in-play. Build your workflow around live data or accept that pre-game-only operation is your ceiling.
The fifth mistake is using proportional de-vigging on a market where the assumption clearly breaks — short-priced favourite, three-way market with one heavy favourite, or long-shot-heavy racing book. Cross-check with the power method and accept the divergence as a flag to review the line manually.
Building a de-vigging operation
The minimum viable de-vigging setup is a spreadsheet with columns for the market, the outcome, the anchor book's price, the implied probability, the overround, the fair probability, and the fair price. Add a column for each Australian book you shop through, with a formula that computes EV against the anchor fair price. Highlight any cell with EV above 1.5% — that is your bet list. Refresh manually or via a scraper depending on volume.
Scaling up requires an odds API. Pull current prices from your anchor source (a sharp book directly, an odds aggregator like Krok Odds, or a feed provider), de-vig algorithmically, compare against your Australian shop list, and surface +EV opportunities with their fair price, taken price, edge, and required stake. Build alerting if your volume is high enough that you cannot watch the dashboard continuously.
Track every bet you place against the fair price at the time you placed it, and against the closing fair price. The difference between your taken price and the close is CLV, and CLV averaged across hundreds of bets is the cleanest evidence you have that your de-vigging operation is profitable. If CLV is positive and your bet selection is disciplined, profit follows over a long enough sample. If CLV is negative despite the de-vigging maths checking out, the problem is upstream — you are anchoring against a weak book, you are using the wrong method on lopsided markets, or your scanner is too slow to catch the +EV prices before they steam back to consensus.
De-vigging is not the entire game. It is the foundation. Stake sizing, line shopping, market selection, and discipline matter at least as much. But every one of those downstream skills is built on top of fair probabilities, and fair probabilities come from de-vigging. Get this layer right and everything above it has a chance of working. Get it wrong and nothing above it can save the operation.