Sports betting arbitrage, or “arbing,” is a strategy that generates profit by exploiting variations in odds across different sportsbooks. It involves placing proportional bets on all possible outcomes of an event, guaranteeing a return regardless of who wins. This approach relies on mathematical certainty rather than luck or prediction.
This article explains what arbitrage is, how it works with clear examples using American odds, and how you can get started. Everything is broken down step-by-step, contrasting a naive equal-betting approach with the proper arbitrage method to show why precise calculations are essential for locking in a guaranteed profit.
What Is Sports Betting Arbitrage?
Arbitrage betting involves wagering on every outcome of an event across multiple sportsbooks. The key is to find discrepancies in the odds that create a “gap” where the total amount staked is less than the guaranteed payout.
This gap exists because sportsbooks set their odds independently, which can be influenced by their own analysis, public betting trends, or simple pricing errors.
In American odds:
- Positive odds (e.g., +120) show the profit from a $100 bet. A successful $100 bet at +120 returns $220 ($120 profit + $100 stake).
- Negative odds (e.g., -110) show the amount you must bet to win $100. A successful $110 bet at -110 returns $210 ($100 profit + $110 stake).
An arbitrage opportunity exists when the combined implied probabilities of all outcomes total less than 100%. That shortfall is your guaranteed profit margin.
How Does It Work? (Step-by-Step Examples)
The following is an example for an NFL game and one for a tennis match, demonstrating two approaches. We first show what happens when you bet an equal amount on each side (e.g., $100 on each outcome). This simple method results in uneven profits because the differing odds create unbalanced payouts. The higher-odds side yields a larger profit, which defeats the purpose of a risk-free guarantee.
In contrast, the proper arbitrage method adjusts the stakes proportionally to the odds. Stakes are calculated to ensure the net profit is identical regardless of the outcome. This is done by allocating more of the total stake to the lower-odds (higher-probability) side and less to the higher-odds side, perfectly balancing the returns and locking in a guaranteed profit.
NFL Example: Kansas City Chiefs vs. Baltimore Ravens
This example uses a moneyline bet (who will win outright) with odds from two different sportsbooks.
- Sportsbook 1: Chiefs to win at +120
- Sportsbook 2: Ravens to win at +110
❌ Incorrect Method: Equal Betting ($100 on Each Side)
Betting equal amounts ignores the odds difference, leading to uneven profits.
| Outcome | Stake on Chiefs (+120) | Stake on Ravens (+110) | Payout | Total Stake | Profit (ROI) |
|---|---|---|---|---|---|
| Chiefs Win | $100.00 | $100.00 | $100 × 2.20 = $220.00 | $200.00 | $20.00 (10%) |
| Ravens Win | $100.00 | $100.00 | $100 × 2.10 = $210.00 | $200.00 | $10.00 (5%) |
✅ Proper Arbitrage Method (Total Stake $100)
First, we calculate the implied probabilities for each outcome:
- Chiefs (+120): 100 / (120 + 100) = 45.45%
- Ravens (+110): 100 / (110 + 100) = 47.62%
- Total Implied Probability: 93.07%
The arbitrage profit margin is 100% – 93.07% = 6.93%.
Next, we calculate the correct stakes to guarantee the same profit. For a $100 total stake, the calculations are:
- Stake on Chiefs = ($100 / 93.07%) × 45.45% = $48.84
- Stake on Ravens = ($100 / 93.07%) × 47.62% = $51.16
| Outcome | Stake on Chiefs | Stake on Ravens | Payout | Total Stake | Profit (ROI) |
|---|---|---|---|---|---|
| Chiefs Win | $48.84 | $51.16 | $48.84 × 2.20 = $107.45 | $100.00 | $7.45 (7.45%) |
| Ravens Win | $48.84 | $51.16 | $51.16 × 2.10 = $107.44 | $100.00 | $7.44 (7.44%) |
Tennis Example: Player A vs. Player B
This example applies the same logic to a tennis match.
- Sportsbook 1: Player A to win at +150
- Sportsbook 2: Player B to win at +140
❌ Incorrect Method: Equal Betting ($500 on Each Side)
Once again, equal stakes create an unbalanced and unpredictable profit.
| Outcome | Stake on Player A (+150) | Stake on Player B (+140) | Payout | Total Stake | Profit (ROI) |
|---|---|---|---|---|---|
| Player A Wins | $500.00 | $500.00 | $500 × 2.50 = $1,250.00 | $1,000.00 | $250.00 (25%) |
| Player B Wins | $500.00 | $500.00 | $500 × 2.40 = $1,200.00 | $1,000.00 | $200.00 (20%) |
✅ Proper Arbitrage Method (Total Stake $500)
First, find the implied probabilities:
- Player A (+150): 100 / (150 + 100) = 40.00%
- Player B (+140): 100 / (140 + 100) = 41.67%
- Total Implied Probability: 81.67%
The arbitrage profit margin is 100% – 81.67% = 18.33%.
For a $500 total stake, the correct wager amounts are:
- Stake on Player A = ($500 / 81.67%) × 40.00% = $244.88
- Stake on Player B = ($500 / 81.67%) × 41.67% = $255.08
| Outcome | Stake on Player A | Stake on Player B | Payout | Total Stake | Profit (ROI) |
|---|---|---|---|---|---|
| Player A Wins | $244.88 | $255.08 | $244.88 × 2.50 = $612.20 | $499.96 | $112.24 (22.45%) |
| Player B Wins | $244.88 | $255.08 | $255.08 × 2.40 = $612.19 | $499.96 | $112.23 (22.45%) |
How to Use Sports Betting Arbitrage
- Find Opportunities: Manually compare odds across multiple sportsbook websites or use arbitrage alert software to find them automatically.
- Set Up Accounts: Open and fund accounts with at least 5-10 different licensed sportsbooks to ensure you have access to a wide range of odds.
- Calculate and Bet Fast: Use a free online arbitrage calculator to determine the exact stakes instantly. Place your bets quickly, as odds can change in seconds.
- Manage Your Bankroll: Dedicate a specific amount to arbitrage (e.g., $500–$5,000). Keep a detailed record of all bets, wins, and losses.
- Avoid Detection: Sportsbooks may limit the accounts of users they identify as arbers. To avoid this, round your bets to whole numbers (e.g., $50 instead of $48.84) and place occasional regular (non-arbitrage) bets.
Benefits
- Risk-Free Profit: When done correctly, profit is guaranteed by math, not left to chance.
- Scalable: The strategy works for any sport or market where odds discrepancies exist.
- Beginner-Friendly: The concept is straightforward and only requires basic math and online tools.
Challenges
- Time-Consuming: Finding opportunities manually requires significant effort. Software helps but often comes with a subscription fee.
- Modest Gains: Profits are typically small percentages (1-5%), so you need to place many bets to see significant returns.
- Account Risks: Your betting accounts may be restricted or closed if a sportsbook detects consistent arbitrage activity.
Disclaimer: This content is for educational purposes only. Odds shown are examples and fluctuate constantly. Always use real-time data from licensed sportsbooks. Please gamble responsibly and adhere to your local regulations.