Removing the margin: how to de-vig odds to true probability
Step-by-step guide to removing bookmaker margin for true probabilities and leveraging arbitrage betting for guaranteed profits.
Removing the margin: how to de-vig odds to true probability
Removing the margin means adjusting bookmaker odds to reflect the true underlying probabilities of outcomes without the built-in profit margin or 'vig'.
Bookmakers include a margin in odds to ensure profit regardless of the event outcome, which distorts the true probabilities and can mislead bettors about their chances.
By removing the margin and understanding true probabilities, bettors can identify arbitrage opportunities where placing bets on all outcomes guarantees a profit, eliminating guesswork and risk.
Understanding Bookmaker Margin and Its Impact
Bookmakers build a margin, often called the 'vig' or 'juice', into odds to secure a guaranteed profit. This means the sum of implied probabilities from the odds exceeds 100%. For example, in a two-outcome event, true probabilities might add to 100%, but the bookmaker's odds imply a total over 100%, reflecting their margin. This margin reduces bettors' value and can obscure the true likelihood of outcomes.
- •Margin ensures bookmaker profit regardless of event results
- •Implied probabilities from odds sum to over 100% due to margin
- •Margin varies by bookmaker, sport, and event
- •Higher margin means lower value for bettors
💡Example of Margin in Odds
Consider a tennis match with odds 1.80 and 2.00 on two players. Implied probabilities are 1/1.80 = 55.56% and 1/2.00 = 50%, totaling 105.56%. The 5.56% over 100% is the bookmaker's margin.
Margin = (1/1.80 + 1/2.00) - 1 = 1.0556 - 1 = 0.0556 or 5.56%
How to Remove the Margin and Calculate True Probabilities
To find the true probabilities, you need to 'de-vig' the odds by normalizing the implied probabilities so they sum to 100%. This involves dividing each implied probability by the total sum of all implied probabilities. The resulting values reflect the bookmaker's estimation without the margin.
- •Convert each odd into implied probability: 1/decimal odd
- •Sum all implied probabilities to find total overround
- •Divide each implied probability by total to normalize
- •Normalized probabilities add up to 100%, representing true chance
Why De-Vigging Matters
Understanding true probabilities helps bettors assess value bets and avoid overestimating chances based on inflated odds. It also aids in identifying arbitrage opportunities where odds from different bookmakers can be combined for guaranteed profit.
- →Improves betting decisions by revealing real chances
- →Highlights discrepancies between bookmakers
- →Essential for finding arbitrage bets
💡Calculating True Probabilities
Using the previous tennis match example: implied probabilities are 55.56% and 50% totaling 105.56%. Divide each by 1.0556 to normalize: 55.56%/1.0556 = 52.63%, 50%/1.0556 = 47.37%. These are the true probabilities without margin.
True probability = implied probability / total implied probability sum
Limitations and Challenges in Removing Margins
While de-vigging odds provides clearer insight into true probabilities, it assumes the bookmaker's odds accurately reflect real-world chances, which may not always be true due to market inefficiencies or insider knowledge. Additionally, odds fluctuate, and calculating correct margins can be complex, especially in multi-outcome events.
- •Bookmaker odds might not perfectly reflect true probabilities
- •Market fluctuations can change margins quickly
- •Calculations become more complex with multiple outcomes
- •Manual calculations can be error-prone
💡Complex Margins in Multi-Outcome Events
For a three-way soccer match outcome with odds for home win, draw, and away win, summing implied probabilities may significantly exceed 100%, making de-vigging essential but more complex. Tools like ArbitUp help automate these calculations to reduce errors.
Sum implied probabilities = 1/odd1 + 1/odd2 + 1/odd3; then normalize each by dividing by sum
How Arbitrage Betting Leverages De-Vigged Odds
Arbitrage betting uses de-vigged odds to identify situations where placing bets on all possible outcomes across different bookmakers guarantees a profit regardless of the result. By removing margins, bettors can spot mismatches and exploit them safely. This eliminates the guesswork and risk associated with traditional betting strategies that rely on predicting winners.
- •Arbitrage relies on true probabilities without bookmaker margin
- •Ensures guaranteed profit by covering all outcomes
- •Reduces risk compared to speculative betting
- •Calculations can be complex but tools like ArbitUp automate them
💡Arbitrage Opportunity Example
If one bookmaker offers odds implying a 48% chance and another offers odds implying a 55% chance on opposite outcomes after de-vigging, betting proportionally on each can lock in profit. Manual calculations are complex but automated tools simplify this process.
Arbitrage percentage = 1/oddA + 1/oddB; if < 1, arbitrage exists
Practical Tips for Removing Margin and Using True Probabilities
Bettors should always check the implied probabilities and remove margins to understand the true chances before placing bets. Using spreadsheets or software can reduce errors. Monitoring odds across multiple bookmakers increases chances of finding value or arbitrage. Staying disciplined and using arbitrage betting eliminates guesswork and protects bankrolls.
- •Convert odds to implied probabilities and sum them first
- •Normalize probabilities by dividing by total sum
- •Use software like ArbitUp to automate complex calculations
- •Compare odds across bookmakers for opportunities
- •Consider arbitrage betting for guaranteed returns
💡Using Tools to Simplify De-Vigging
Manually calculating true probabilities can be tedious, especially with multiple outcomes or frequent odds changes. Tools such as ArbitUp automate these steps and identify arbitrage opportunities, making it easier and faster to make informed bets.
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Common Mistakes to Avoid
- ⚠️Ignoring the bookmaker margin and assuming odds directly reflect true probabilities, leading to overestimating chances.
- ⚠️Failing to normalize implied probabilities after summing them, resulting in inaccurate de-vigged probabilities.
- ⚠️Using fractional or American odds incorrectly without converting them to decimal odds first.
- ⚠️Overlooking odds differences across bookmakers, missing arbitrage opportunities.
- ⚠️Attempting complex calculations manually, increasing the risk of arithmetic errors.
- ⚠️Assuming all bookmakers have the same margin, which can vary significantly.
- ⚠️Not accounting for odds movement over time, which affects margin and probabilities.
The Power of Arbitrage Betting
Arbitrage betting removes the uncertainty inherent in traditional betting by using de-vigged odds to guarantee profits regardless of event outcomes.
- ✓Eliminates risk by covering all outcomes
- ✓Maximizes use of true probabilities without bookmaker margin distortion
- ✓Automates complex calculations for efficient betting decisions
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