What Is Arbitrage Betting?
Arbitrage betting is placing bets on every possible outcome of the same event at different sportsbooks when the odds create a mathematical opportunity for profit. By sizing each bet correctly, you can lock in a profit no matter which bet wins. These opportunities occur when sportsbooks have different odds on the same market. The profit is typically 1-3% of the total amount wagered. Learn more in our What Is Arbitrage Betting guide.
What Is An Arbitrage Calculator?
Arbitrage calculators determine how much you need to bet on each side of an event to secure a profit based on the available odds. You enter the primary bet amount and odds, as well as the hedge(s) odds and the calculator tells you how much to bet on each side.
Finding Arbitrage Opportunities
Arbitrage opportunities are most common among smaller markets such as player props and alternate lines. Although this is where you will find the largest arbitrage opportunities, small markets come with the largest risk; learn more about avoiding small markets. The DarkHorse Odds Arbitrage Bet Finder is another way to find sportsbook arbitrage. You can explore the demo site, or start a free trial.
How To Check If An Arbitrage Exists
Before sizing any bets, confirm the opportunity is real. Convert both prices to implied probability and add them together. If it is less than 100% it is an arbitrage opportunity.
Example: The home team is +120 at Sportsbook A and the away team is -110 at Sportsbook B.
Step 1. Convert odds to probability
\[
\begin{aligned}
\text{Probability (positive odds)} &= \dfrac{\strut 100}{\strut \text{Odds} + 100} \\
\text{Probability (negative odds)} &= \dfrac{\strut |\text{Odds}|}{\strut |\text{Odds}| + 100} \\
\\
\text{Team A } (+120) &= \dfrac{\strut 100}{\strut 120 + 100} = \dfrac{\strut 100}{\strut 220} = 45.45\% \\
\text{Team B } (-110) &= \dfrac{\strut 110}{\strut 110 + 100} = \dfrac{\strut 110}{\strut 210} = 52.38\%
\end{aligned}
\]
Step 2. Add the probabilities together
\[
\begin{aligned}
\\
\text{Sum of Implied Probs} &= 45.45\% + 52.38\% = 97.84\%
\end{aligned}
\]
The implied probabilities sum to less than 100%, therefore this is an arbitrage opportunity.
Step 3. Determine the arbitrage percent
\[
\begin{aligned}
\text{Arbitrage \%} &= 100\% - \text{Sum of Implied Probabilities} \\
&= 100\% - 97.84\% \\
&= 2.16\%
\end{aligned}
\]
How The Math Works
Note: The calculations below use decimal odds. If you are starting with a different odds format, first convert them to decimal odds using the Odds Converter.
You place $100 on the home team at +120 (decimal 2.20) at Sportsbook A. The away team is -110 (decimal 1.9091) at Sportsbook B.
Step 1. Determine the payout on a winning bet
\[
\begin{aligned}
\text{Payout} &= \text{Primary Bet Stake} \times \text{Primary Bet Decimal Odds} \\
&= 100 \times 2.20 = \$220.00
\end{aligned}
\]
Step 2. Determine hedge amount
\[
\begin{aligned}
\text{Hedge Bet Stake} &= \dfrac{\strut \text{Payout}}{\strut \text{Hedge Bet Decimal Odds}} \\
&= \dfrac{\strut 220.00}{\strut 1.9091} = \$115.24
\end{aligned}
\]
Step 3. Verify the profit on both sides
If the primary bet wins...
- Profit $120.00 from the primary bet
- Lose $115.24 from the hedge bet
- Net profit of $4.76
If the hedge bet wins...
- Profit $104.76 from the hedge bet
- Lose $100.00 from the primary bet
- Net profit of $4.76
\[
\begin{aligned}
\text{Arbitrage \%} &= \dfrac{\strut \text{Profit}}{\strut \text{Total Staked}} \\
&= \dfrac{\strut 4.76}{\strut 215.24} \\
&= 2.21\%
\end{aligned}
\]
No matter which bet wins profit $4.76.
Three-way And Multi-outcome Markets
Arbitrage does not have a theoretical limit to the number of possible outcomes in a market. There is a practical limit, since sportsbooks often have a higher vig on markets with more possible outcomes. A three-way money line in soccer, or any market with more than two outcomes, works the same way as outlined above. Using the DarkHorse Odds arbitrage calculator you can add a leg for each outcome and the math is done for you.
Editing Bet Amounts
The arbitrage calculator solves bet amounts to the penny, which results in uneven bet amounts like $115.24. In order to avoid limits it is best to round your bets. There are two ways to do this in the arbitrage calculator.
- In settings you can select rounding in $1, $5, $10, or $25 increments.
- You can also turn on edit bet amounts which allows you to override the calculated hedge amount(s).
