Key Takeaways
- Implied probability converts betting odds into a percentage — what the bookmaker thinks the chance of winning is.
- Decimal odds: Implied Probability = 1 / Decimal Odds. American odds: 100 / (Odds + 100) for positives, |Odds| / (|Odds| + 100) for negatives.
- Implied probabilities always sum to more than 100% (the overround). The excess is the bookmaker's margin, called vig or juice.
- Removing the vig gives you the true probability — your estimate of the actual chance without the bookmaker's markup.
- When your estimated true probability is higher than the implied probability, you have found a value bet.
Every bet you place is a prediction. The bookmaker offers 2.50 on a team to win — what does that actually mean in terms of probability? Converting odds into implied probability is the first step every sharp bettor takes before deciding whether a bet has value. This guide explains how to calculate implied probability from any odds format, how to remove the bookmaker's margin (vig) to find true probability, and how to use an implied probability calculator to automate the entire process.
What is Implied Probability?
Implied probability is the probability of an outcome implied by the odds offered by a bookmaker. It answers the question: "If these odds are fair, what are the chances of this outcome occurring?"
Here is the key insight: implied probability is not the true probability. It includes the bookmaker's profit margin (vig, juice, or overround). Two outcomes in a match might have implied probabilities of 55% and 52%, which sum to 107%. That extra 7% is the bookmaker's cut. To find the real chance, you must remove the vig.
Understanding this distinction separates recreational bettors from sharp ones. Recreational bettors see odds and think about who will win. Sharp bettors see odds, convert them to implied probability, remove the vig, compare to their own estimate, and only bet when there is a gap.
How to Calculate Implied Probability
The formula depends on the odds format. Below are the exact formulas for decimal, American, and fractional odds.
From Decimal Odds
The simplest and most common format:
Implied Probability = 1 / Decimal Odds
Examples:
- Decimal 2.00 → 1 / 2.00 = 50.00%
- Decimal 2.50 → 1 / 2.50 = 40.00%
- Decimal 1.50 → 1 / 1.50 = 66.67%
- Decimal 4.00 → 1 / 4.00 = 25.00%
From American Odds
American odds have two cases — positive (underdogs) and negative (favourites).
Positive American Odds (+150, +200, etc.)
Implied Probability = 100 / (American Odds + 100)
Examples:
- +150 → 100 / (150 + 100) = 100 / 250 = 40.00%
- +200 → 100 / (200 + 100) = 100 / 300 = 33.33%
- +300 → 100 / (300 + 100) = 100 / 400 = 25.00%
- +500 → 100 / (500 + 100) = 100 / 600 = 16.67%
Negative American Odds (−150, −200, etc.)
Implied Probability = |American Odds| / (|American Odds| + 100)
Examples:
- −150 → 150 / (150 + 100) = 150 / 250 = 60.00%
- −200 → 200 / (200 + 100) = 200 / 300 = 66.67%
- −300 → 300 / (300 + 100) = 300 / 400 = 75.00%
- −500 → 500 / (500 + 100) = 500 / 600 = 83.33%
From Fractional Odds
Implied Probability = Denominator / (Numerator + Denominator)
Examples:
- 3/1 → 1 / (3 + 1) = 1 / 4 = 25.00%
- 5/2 → 2 / (5 + 2) = 2 / 7 = 28.57%
- 1/2 → 2 / (1 + 2) = 2 / 3 = 66.67%
- 4/5 → 5 / (4 + 5) = 5 / 9 = 55.56%
Vig, Overround & True Probability
When you convert both sides of a two-way market to implied probability and add them, the total is always more than 100%. That excess is called the overround or vig (vigorish) — the bookmaker's built-in profit margin.
Example: A Two-Way Market
Team A: 1.90 decimal → 1 / 1.90 = 52.63%
Team B: 1.90 decimal → 1 / 1.90 = 52.63%
Total: 52.63% + 52.63% = 105.26%
Overround: 105.26% − 100% = 5.26%
This means the bookmaker has a 5.26% theoretical margin. If equal money is bet on both sides, the book profits 5.26% of total turnover regardless of the result.
Three-Way Markets
Soccer match odds (home / draw / away) are three-way markets. Add all three implied probabilities:
Home 2.40 → 41.67% | Draw 3.20 → 31.25% | Away 3.00 → 33.33%
Total: 41.67% + 31.25% + 33.33% = 106.25%
Overround: 6.25%
How to Remove the Vig
To find the true probability (the actual chance without the bookmaker's margin), you need to remove the vig. There are several methods, ranging from simple to sophisticated.
Method 1: Normalisation (Simplest)
Divide each implied probability by the total overround:
True Probability = Implied Probability / Total Implied Probability Sum
Example: Team A 52.63%, Team B 52.63%. Total = 105.26%.
Team A true probability = 52.63% / 105.26% = 50.00%
Team B true probability = 52.63% / 105.26% = 50.00%
This assumes the vig is distributed equally — a reasonable first approximation, but not always accurate.
Method 2: Proportional De-Vig (Recommended for Beginners)
Same as normalisation, but applied to all outcomes proportionally. If the overround is 5%, each implied probability is scaled down by roughly 5%. This is the default method in most de-vig calculators.
De-Vig Methods Explained
For more accurate vig removal, professionals use advanced methods:
Proportional Method
Removes vig proportionally from all outcomes. Simple, fast, and works well for balanced markets. This is the most commonly used method in betting tools.
Power Method
Finds a single exponent that, when applied to all implied probabilities, makes them sum to 100%. Better for markets where the favourite and underdog have very different true probabilities. The BetBank.ai De-Vig Calculator includes this method.
Shin Method
Assumes the bookmaker overestimates the probability of low-probability outcomes. Complex but theoretically sound. Used by advanced bettors and academic researchers.
Wooster Method
A simplified approximation of Shin's method. Offers a middle ground between proportional and Shin.
For most practical betting, the proportional or power method is sufficient. The differences between methods are typically 1–2% on individual outcomes — not enough to change a betting decision in most cases.
Worked Examples
Example 1: AFL head-to-head
Richmond: 1.75 → Implied probability = 1 / 1.75 = 57.14%
Collingwood: 2.20 → Implied probability = 1 / 2.20 = 45.45%
Total: 57.14% + 45.45% = 102.59%
Overround: 2.59%
True probability (proportional):
- Richmond: 57.14% / 102.59% = 55.70%
- Collingwood: 45.45% / 102.59% = 44.30%
Example 2: NBA spread (American odds)
Lakers −3.5: −110 → Implied probability = 110 / (110 + 100) = 110 / 210 = 52.38%
Celtics +3.5: −110 → Implied probability = 110 / (110 + 100) = 52.38%
Total: 52.38% + 52.38% = 104.76%
Overround: 4.76% (standard for US spreads at −110 each side)
True probability: 52.38% / 104.76% = 50.00% each side
Example 3: Soccer three-way
Man City: 1.60 → 62.50% | Draw: 4.00 → 25.00% | Liverpool: 5.50 → 18.18%
Total: 62.50% + 25.00% + 18.18% = 105.68%
Overround: 5.68%
True probability (proportional):
- Man City: 62.50% / 105.68% = 59.14%
- Draw: 25.00% / 105.68% = 23.66%
- Liverpool: 18.18% / 105.68% = 17.20%
Using an Implied Probability Calculator
An implied probability calculator automates all of the above:
- Enter odds in any format (decimal, American, fractional).
- Instant implied probability for all outcomes.
- Overround calculation (vig identification).
- True probability using your choice of de-vig method.
- Side-by-side comparison for value identification.
Use the BetBank.ai De-Vig EV Calculator to convert odds to implied probability, remove the vig using proportional, power, or Shin methods, and see the true probability instantly.
Using Implied Probability to Find Value Bets
Once you have true probability, finding value is simple:
Value exists when: Your Estimated True Probability > Implied Probability
Example
A book offers 2.40 on the Sydney Swans to win. Implied probability = 1 / 2.40 = 41.67%.
You have analysed the match and believe the Swans' true chance is 50%.
50% > 41.67% → This is a value bet.
EV% = (2.40 × 0.50) − 1 = 1.20 − 1 = +20%. A strong +EV opportunity.
The challenge, of course, is accurately estimating true probability. Methods include:
- Sharp consensus: Average the true probabilities from Pinnacle, Betfair, and Circa.
- Power ratings: Build a team strength model and convert to win probabilities.
- Historical data: Use large samples of similar matchups to estimate base rates.
- Market timing: Bet early before the market fully adjusts to news.
Conclusion
Implied probability is the bridge between odds and value. Every bet you place should start with converting the bookmaker's price into a percentage, removing their margin, and comparing the result to your own estimate of the true chance. When your estimate is higher, you have found an edge.
Mastering implied probability transforms betting from guesswork into a mathematical discipline. Use the BetBank.ai De-Vig Calculator to handle the conversions automatically, remove vig with multiple methods, and focus on what matters: finding value and placing +EV bets.
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Frequently Asked Questions
What is the difference between implied probability and true probability?
Implied probability includes the bookmaker's margin (vig). True probability is the actual chance of the outcome, estimated by removing the vig.
Can implied probability ever be wrong?
Implied probability is always mathematically correct — it is exactly what the odds say. But it reflects the bookmaker's estimate + their margin, not the real world. Sharp bettors find situations where the bookmaker's estimate is inaccurate.
How much vig is normal?
2–5% for main markets on sharp books. 5–10% for soft books and prop markets. 10–20% for novelty or exotic bets. Lower is better for bettors.
Why do implied probabilities sum to more than 100%?
That excess is the bookmaker's profit margin. If a fair coin flip were offered at 1.90 each side, the implied probabilities would be 52.63% + 52.63% = 105.26%. The 5.26% is the vig.
Is there a quick way to estimate vig mentally?
For decimal odds, a rough rule: if both sides of a two-way market are near 2.00, the vig is approximately (2.00 − your odds) × 100. So 1.90 vs 1.90 → (2.00 − 1.90) × 100 = roughly 5% vig.
Which de-vig method should I use?
Start with proportional — it is simple and accurate enough for most markets. Use power for markets with very heavy favourites (odds below 1.20). Use Shin only if you are doing academic-level analysis.
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