Betting Arbitrage Calculator
Find arbitrage opportunities by comparing odds across bookmakers for guaranteed profit. Calculate optimal stake distribution and expected returns.
Betting Arbitrage Calculator
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Formula: Arbitrage % = (1/Odds1 + 1/Odds2) x 100
Worked example — Arbitrage exists | Guaranteed profit: $37.26 (3.73%) on $1,000 stake
Formula
Arbitrage % = (1/Odds1 + 1/Odds2) x 100
If the sum of the inverse of each decimal odd (the implied probabilities) is less than 1 (or 100%), an arbitrage opportunity exists. Stakes are distributed proportionally to the implied probabilities to equalize payouts.
Worked Examples
Example 1: Two-Outcome Arbitrage on Tennis Match
Problem:Bookmaker A offers 2.10 on Player X. Bookmaker B offers 2.05 on Player Y. Your total stake is $1,000. Is this an arbitrage opportunity?
Solution:Implied prob (Player X) = 1/2.10 = 47.62% Implied prob (Player Y) = 1/2.05 = 48.78% Total implied = 96.40% (< 100%, so YES, it is an arb) Stake on Player X = $1,000 x (47.62/96.40) = $494.02 Stake on Player Y = $1,000 x (48.78/96.40) = $505.98 If Player X wins: $494.02 x 2.10 = $1,037.44 If Player Y wins: $505.98 x 2.05 = $1,037.26 Guaranteed profit: ~$37.26 (3.73%)
Result:Arbitrage exists | Guaranteed profit: $37.26 (3.73%) on $1,000 stake
Example 2: No Arbitrage Scenario
Problem:Bookmaker A offers 1.90 on Team X. Bookmaker B offers 1.95 on Team Y. Total stake is $500.
Solution:Implied prob (Team X) = 1/1.90 = 52.63% Implied prob (Team Y) = 1/1.95 = 51.28% Total implied = 103.91% (> 100%, so NO arbitrage) Bookmaker margin = 3.91% No guaranteed profit possible — the bookmakers' margins eliminate the opportunity.
Result:No arbitrage | Combined implied probability: 103.91% | Loss guaranteed
Frequently Asked Questions
What is betting arbitrage and how does it guarantee profit?
Betting arbitrage, also known as sure betting or arbing, is a strategy where you place bets on all possible outcomes of an event across different bookmakers whose combined odds create a mathematical guarantee of profit regardless of the outcome. This occurs when the sum of the implied probabilities from the odds across different bookmakers totals less than 100 percent. For example, if Bookmaker A offers 2.10 on Team X winning and Bookmaker B offers 2.05 on Team X losing, the combined implied probability is 47.62% + 48.78% = 96.40%, which is below 100%. By distributing your stake proportionally, you can lock in a profit no matter which outcome occurs.
How do you calculate the optimal stake distribution for arbitrage betting?
The optimal stake distribution ensures equal profit regardless of the outcome. First, calculate the implied probability for each outcome: divide 1 by each decimal odd. Then divide each implied probability by the sum of all implied probabilities to get the percentage of your total stake allocated to each bet. For two outcomes with decimal odds of 2.10 and 2.05: Implied probability 1 = 1/2.10 = 0.4762, Implied probability 2 = 1/2.05 = 0.4878. Total = 0.9640. Stake 1 = total stake x (0.4762/0.9640) = 49.40%. Stake 2 = total stake x (0.4878/0.9640) = 50.60%. This proportional distribution equalizes the payout from each bookmaker.
What are the risks and limitations of arbitrage betting?
While arbitrage betting is mathematically risk-free in theory, several practical risks exist. Bookmakers actively detect and limit or ban arbitrage bettors, often restricting accounts or reducing maximum stakes after a few successful arbs. Odds can change rapidly between the time you spot an opportunity and place all required bets, turning a profitable arb into a loss if one leg is placed at worse odds. Minimum and maximum bet limits may prevent you from placing the exact stake amounts needed. Currency conversion fees, deposit or withdrawal charges, and transfer times can eat into slim margins. Most arbitrage profits are in the range of 1 to 5 percent, making these additional costs potentially significant.
What odds formats are commonly used in sports betting?
Three main odds formats are used worldwide. Decimal odds, popular in Europe and Australia, represent the total payout per unit staked including the original stake; odds of 2.50 mean a $1 bet returns $2.50 total. Fractional odds, traditional in the UK, show profit relative to stake; 3/2 means $3 profit on a $2 bet. American (moneyline) odds are standard in the United States and show either how much you need to bet to win $100 on a favorite (negative numbers like -150) or how much you win on a $100 bet on an underdog (positive numbers like +200). Converting between formats is essential for comparing odds across international bookmakers to identify arbitrage opportunities.
How do you find arbitrage opportunities in practice?
Finding arbitrage opportunities requires monitoring odds across multiple bookmakers simultaneously, which is practically impossible to do manually for a large number of events. Most serious arbitrage bettors use specialized odds comparison websites and software that scan dozens of bookmakers in real time and alert users when the combined implied probability drops below 100 percent. Popular tools include OddsPortal, RebelBetting, and BetBurger. Arbitrage opportunities tend to appear during live or in-play betting when odds fluctuate rapidly, on lesser-known sports or leagues where bookmakers are less precise, and shortly after significant news breaks that affects event outcomes. Most opportunities only last for seconds or minutes before the market corrects.
What is the overround and how does it relate to an arbitrage?
The overround, also called the vigorish or margin, is the amount by which a single bookmaker's implied probabilities exceed 100 percent. If a two-way market is priced at 1.90 and 1.90, the implied probabilities are 52.63 percent each, summing to 105.26 percent, so the book holds a 5.26 percent margin. Arbitrage is simply the mirror image: by combining the best price for each outcome across competing bookmakers, the summed implied probability falls below 100 percent and the negative margin becomes the bettor's guaranteed return.
How do you convert the combined implied probability into a profit percentage?
Once you have the sum of the inverse decimal odds, call it S, the guaranteed return on total stake is 1/S minus 1. With S equal to 0.9640 the return is 1/0.9640 - 1 = 0.0373, or 3.73 percent of the amount staked. A stake of 1,000 currency units therefore returns about 1,037 whichever outcome wins. Because the profit is a percentage of total turnover rather than of one bet, arbitrage requires large stakes across many events to produce meaningful absolute returns.
How does arbitrage work on three-way markets such as football 1X2?
A three-way market adds the draw, so you must cover home win, draw and away win and the same test applies to all three legs: sum the inverse of each decimal odd and check whether the total is below 1. Stakes are again split in proportion to each leg's implied probability divided by that sum, which equalises the payout across the three possible results. Three-way arbs are harder to execute because a price on any of the three legs can move while you are still placing the others, and the draw is often the leg that shortens first.
What is the difference between an arbitrage and a middle?
An arbitrage locks in the same profit for every possible outcome, so the result of the event is irrelevant. A middle covers two overlapping lines on a handicap or totals market so that most results give roughly break-even but a narrow band of scores wins both bets at once. For example, backing over 2.5 goals at one book and under 3.5 at another wins both legs when exactly three goals are scored. A middle carries a small expected cost outside that band in exchange for a large payoff inside it, which makes it a variance play rather than a sure bet.
How does betting-exchange commission change an arbitrage calculation?
On an exchange you can lay an outcome instead of backing its alternative, but the exchange charges commission on net winnings, typically a few percent of the winning side. That commission must be subtracted before you judge the arb, which is done by using effective lay odds: subtract the commission rate from the profit side of the price rather than treating the quoted odds as final. Because most arbitrage margins are only a few percent, a commission of two to five percent can wipe out the entire edge, so exchange legs must always be evaluated net of fees and of the required lay liability.
References
Reviewed for accuracy by Daniel Agrici, Founder & Lead Developer · Editorial policy
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