Finance calculators

Arbitrage Calculator

Updated Jul 18, 2026 By Jehan Wadia
Rate Formulas

Odds Format

Number of Outcomes

Bet Legs

Total Stake

Your full bankroll — it is distributed optimally across every leg for you.

Results

Enter your odds and total stake to see results.

Introduction

An arbitrage bet happens when you place wagers on every possible outcome of a game or event using odds from different sportsbooks. If the odds are right, you lock in a profit no matter who wins. This is called an arbitrage opportunity, and it exists when the combined implied probability of all outcomes adds up to less than 100%.

Our free Arbitrage Calculator helps you find these opportunities fast. Enter the odds from each sportsbook, set your total stake, and the tool does the rest. It tells you exactly how much to bet on each outcome, shows your guaranteed profit, and breaks down the math step by step. You can use American, decimal, or fractional odds, and the calculator supports up to 16 outcomes at once. It even accounts for exchange commission if you bet on a platform that charges one.

Whether you are new to sports betting or already familiar with arbitrage strategies, this calculator makes it easy to spot profitable bets and divide your money the right way across every leg.

How to Use Our Arbitrage Calculator

Enter your odds from different sportsbooks and your total budget. The calculator will tell you if an arbitrage opportunity exists, how much to bet on each outcome, and your guaranteed profit.

Odds Format: Pick the odds format you want to use. Choose American (e.g., +150 or -110), Decimal (e.g., 2.50), or Fractional (e.g., 5/2). The calculator will convert your odds if you switch formats. If you need help converting between decimal and fractional formats, you can use our Decimal to Fraction Calculator. For a deeper look at how different odds formats relate to each other, try our Betting Odds Calculator.

Number of Outcomes: Set how many possible outcomes the event has. Most bets have 2 outcomes, but some markets like soccer or racing can have 3 or more. Use the dropdown, or click "Add Outcome" and "Remove Last" to adjust.

Outcome Label: Give each leg a name so you can keep track of your bets. This is optional. For example, you might type "DraftKings – Team A" or "FanDuel – Team B."

Odds: Type in the odds for each outcome. Each leg should come from the sportsbook that offers the best price for that outcome. The format must match the odds format you picked above.

Commission %: If you are using a betting exchange that charges a fee on winnings, enter the commission rate here. For regular sportsbooks, leave this at 0.

Total Stake: Enter the full amount of money you want to spread across all outcomes. The calculator splits this amount for you so that every outcome returns the same payout.

Click Calculate to see your results. You will get a breakdown of how much to stake on each leg, your guaranteed payout, profit, ROI, and a step-by-step explanation of the math. Click Reset to clear all inputs and start over.

What Is Arbitrage Betting?

Arbitrage betting is a strategy where you place bets on every possible outcome of a game or event, using different sportsbooks, so you are guaranteed a profit no matter who wins. This works when the odds across different bookmakers are different enough that the combined implied probability drops below 100%.

Think of it this way: one sportsbook might give better odds on Team A, while another gives better odds on Team B. If the gap between them is large enough, you can bet on both sides and lock in a sure profit. This gap is the arbitrage opportunity. To evaluate the size of individual bets and their payouts, our Bet Calculator is a handy companion tool.

How Does This Arbitrage Calculator Work?

This calculator takes the odds from each sportsbook you are comparing and checks if an arbitrage opportunity exists. If it does, it tells you exactly how much money to place on each outcome so your payout is the same no matter which side wins. It splits your total stake across each bet in the perfect ratio.

You can enter odds in American, decimal, or fractional format. The calculator also lets you add an exchange commission percentage for each leg, which is useful if you are using a betting exchange that takes a cut of your winnings. To understand how odds translate into fair probabilities without a bookmaker's margin, check out our No Vig Calculator.

Key Terms to Know

Implied probability is the chance of an outcome happening based on the odds. You find it by dividing 1 by the decimal odds. When you add up the implied probabilities of all outcomes, a total below 100% means an arbitrage opportunity exists. A total at or above 100% means the bookmaker has a built-in edge, often called the vig or hold. For general probability calculations, our Probability Calculator can help you work through the math.

ROI (Return on Investment) shows how much profit you earn as a percentage of the total amount you bet. In arbitrage betting, the ROI is usually small — often between 1% and 5% — but the profit is guaranteed, which is what makes it valuable. You can explore ROI in other contexts using our ROI Calculator.

Tips for Arbitrage Betting

  • Act fast. Odds change quickly. An arbitrage window can close in minutes or even seconds. Use our Odds Calculator to quickly compare and convert odds across formats.
  • Use multiple sportsbooks. You need accounts at several bookmakers to find and place arbitrage bets.
  • Watch for limits. Some sportsbooks may limit or ban accounts that consistently win through arbitrage.
  • Account for commissions. Betting exchanges charge a fee on winnings. Always include this in your calculations, or your guaranteed profit may disappear.
  • Double-check your entries. A single wrong number can turn a sure profit into a loss. Use our Percentage Calculator to verify implied probabilities if you want an extra layer of confidence.
  • Explore related strategies. If you are interested in multi-leg wagers beyond arbitrage, our Parlay Calculator and Round Robin Calculator can help you analyze combined bets across multiple games.
  • Understand expected value. Arbitrage guarantees a positive expected value by design. To evaluate expected value in other betting or investment scenarios, try our EV Calculator.

Formulas used

Implied Probability from Decimal Odds
p_i = \frac{1}{d_i}
Effective Decimal Odds (with Exchange Commission)
d_{\text{eff}} = (d - 1)\left(1 - \frac{c}{100}\right) + 1
Combined Implied Probability (Arbitrage Test)
\sum p = p_1 + p_2 + \cdots + p_n < 1 \Rightarrow \text{Arbitrage exists}
Optimal Stake per Leg
s_i = \frac{S \times p_i}{\sum p}
Guaranteed Payout
\text{Payout} = \frac{S}{\sum p}
Guaranteed Profit
\text{Profit} = \frac{S}{\sum p} - S
Return on Investment (ROI)
\text{ROI} = \frac{\text{Profit}}{S} \times 100

Frequently asked questions

What is an arbitrage opportunity in sports betting?

An arbitrage opportunity happens when different sportsbooks offer odds on the same event that are far enough apart that you can bet on every outcome and still make a profit. If the combined implied probability of all outcomes is below 100%, you have an arbitrage opportunity. This calculator checks that for you automatically.

What does it mean when the combined implied probability is above 100%?

When the combined implied probability is at or above 100%, there is no arbitrage opportunity. The extra amount above 100% is the bookmaker's built-in edge, called the vig or hold. You would lose money over time betting both sides at those odds.

How does the calculator split my total stake across each leg?

The calculator divides your total stake so that every outcome pays out the same amount if it wins. It does this by weighting each leg based on its implied probability. Legs with lower odds (higher probability) get a bigger share of the stake, and legs with higher odds (lower probability) get a smaller share.

Can I use odds from the same sportsbook for every leg?

You can, but it almost never works. A single sportsbook sets its odds so the combined implied probability is above 100%. That is how they make money. To find arbitrage, you usually need to compare odds across two or more different sportsbooks and pick the best price for each outcome.

What is the Commission % field for?

Some betting exchanges like Betfair charge a commission on your winnings. If you enter that percentage in the Commission field, the calculator adjusts the effective odds for that leg so your profit estimate stays accurate. If you are using a regular sportsbook that does not charge commission, leave it at 0.

What odds formats does this calculator support?

The calculator supports three formats: American (e.g., +150 or -110), Decimal (e.g., 2.50), and Fractional (e.g., 5/2). You can switch between them at any time, and the calculator will convert your existing odds to the new format automatically.

How many outcomes can I add?

You can add between 2 and 16 outcomes. Most sports bets have 2 outcomes, but events like soccer (win, draw, lose) have 3, and horse racing or futures markets can have many more.

Why is my guaranteed profit so small?

Arbitrage profits are usually small, often between 1% and 5% of your total stake. The odds gap between sportsbooks is rarely large. To earn a bigger dollar profit, you need to bet a larger total stake. This is normal for arbitrage betting.

What happens if I enter the wrong odds?

Entering wrong odds can make the calculator show a profit that does not actually exist. If you place real bets based on wrong numbers, you could lose money. Always double-check every odds value against the sportsbook before placing your bets.

Does this calculator place bets for me?

No. This calculator only does the math. It tells you how much to bet on each outcome and what your profit would be. You still need to go to each sportsbook and place the bets yourself.

Can the arbitrage opportunity disappear after I calculate it?

Yes. Odds change constantly. An arbitrage window can close in minutes or even seconds. Once you find an opportunity, you need to place all your bets as quickly as possible before any of the odds shift.

What does the ROI number mean in the results?

ROI stands for Return on Investment. It shows your guaranteed profit as a percentage of your total stake. For example, a 3% ROI on a $1,000 stake means you earn $30 in guaranteed profit no matter which outcome wins.

What is the Theoretical Hold or Vig shown in the results?

The theoretical hold (also called vig) is the percentage above 100% when you add up all the implied probabilities. A positive hold means the bookmakers have an edge. A negative hold means an arbitrage opportunity exists and you have the edge.

Do I need to bet the exact stake amounts the calculator shows?

Yes, you should bet as close to the exact amounts as possible. The calculator sets each stake so that every outcome pays the same amount. If you round the numbers too much or change the amounts, one outcome might pay less than your total stake, and you could lose money on that result.

Can I use this calculator for betting exchanges like Betfair?

Yes. Enter the back odds from the exchange and put the exchange's commission rate in the Commission % field for that leg. The calculator will lower the effective odds to account for the fee and give you an accurate profit estimate.

Is arbitrage betting legal?

Arbitrage betting is legal in most places because you are simply placing bets at different sportsbooks. However, sportsbooks do not like it. They may limit your account, reduce your maximum bet size, or close your account if they notice a pattern of arbitrage betting. Always check the terms of service for each sportsbook you use.