Arbitrage Betting Calculator

Understanding Arbitrage Betting: The Mathematics of Guaranteed Profits

Arbitrage betting, also known as "arbing" or "sure betting," is a strategy that exploits pricing discrepancies between different bookmakers to lock in a guaranteed profit regardless of the outcome. This calculator helps you identify these opportunities and calculate the precise stakes needed.

The concept relies on a fundamental principle: when the combined implied probabilities of all possible outcomes sum to less than 100%, an arbitrage opportunity exists. The difference between 100% and the combined probability represents your guaranteed profit margin. This mathematical relationship is documented in academic resources on sports betting markets from institutions like the UNLV International Gaming Institute.

How Arbitrage Opportunities Arise

Bookmakers set odds based on their assessment of event probabilities, plus their built-in margin (called "vig" or "juice"). Different bookmakers may have different opinions, different customer bases, or different risk exposures—leading to price variations. Research from the Journal of the American Statistical Association has documented these market inefficiencies in betting markets.

According to analysis from sports betting research platforms, arbitrage opportunities typically appear in:

• Live betting markets: Odds change rapidly as events unfold, creating temporary discrepancies
• Minor leagues and obscure events: Less liquidity means more pricing variation
• Cross-market opportunities: Different markets (moneyline vs. totals) occasionally misprice relative to each other
• Promotional odds: Boosted odds from sportsbook promotions can create arb opportunities

The Arbitrage Calculation Formula

To check for arbitrage, convert each odds to implied probability and sum them:

Example: Two-Way Market Arbitrage

Consider a tennis match where Bookmaker A offers Player 1 at 2.15, and Bookmaker B offers Player 2 at 2.05:

• Player 1: 1/2.15 = 46.51%
• Player 2: 1/2.05 = 48.78%
• Total: 95.29%

Since 95.29% is less than 100%, this is an arbitrage opportunity with a 4.71% profit margin. With a $1,000 total stake, you'd profit approximately $49.43 regardless of who wins.

Risks and Limitations of Arbitrage Betting

While arbitrage offers mathematically guaranteed profits, real-world implementation carries risks that the UK Gambling Commission notes bettors should understand:

Why Bookmakers Discourage Arbitrage

Bookmakers discourage arbitrage betting not because it's illegal, but because arbers take guaranteed profit from the bookmaker's margin. Unlike recreational bettors who accept risk, arbers extract value without providing it. Most sportsbooks have terms allowing them to limit or close accounts at their discretion—a practice that's standard across the industry. Learn more about sports betting arbitrage in our detailed guide, or understand bookmaker margins using our vig calculator.

Practical Tips for Using This Calculator

• Compare multiple bookmakers: Use odds comparison sites to find the best odds for each outcome across different sportsbooks
• Act quickly: Arbitrage opportunities are short-lived as bookmakers adjust prices
• Account for fees: Some payment methods or exchanges charge fees that eat into margins
• Start small: Test with smaller stakes to learn the process before scaling up
• Track your bets: Use our session tracker to monitor your arbitrage betting results

For more on betting mathematics, explore our expected value calculator, learn about hedge betting, or understand closing line value—another key metric for evaluating betting skill. If you're exploring related strategies, our dutching calculator helps with multi-selection betting on single markets.