Betting Arbitrage Calculator
Find arbitrage opportunities by comparing odds across bookmakers for guaranteed profit. Enter values for instant results with step-by-step formulas.
Reviewed for accuracy by Daniel Agrici, Founder & Lead Developer
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.
How does Kelly Criterion work for betting?
The Kelly Criterion calculates the optimal bet size to maximize long-run bankroll growth: f = (bp − q) / b, where b = net odds, p = probability of winning, q = probability of losing. For a 55% win probability at even money: f = (1 × 0.55 − 0.45) / 1 = 10% of bankroll. Over-betting the Kelly fraction increases ruin risk; under-betting is safer but grows slower.
References
Reviewed for accuracy by Daniel Agrici, Founder & Lead Developer · Editorial policy
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