Arbitrage Calculator

Check whether two opposing prices form an arbitrage and split your stake for a guaranteed profit, using decimal odds.

An arbitrage (or “arb”) calculator checks whether two opposing prices form a guaranteed profit by comparing them across different bookmakers, and shows you exactly how to split your stake for equal returns.

What Is an Arbitrage?

An arbitrage, often called an “arb” or “surebet”, is a set of bets on every outcome of a market placed at different bookmakers whose prices are generous enough that the total staked returns a profit whatever the result. The mechanism is elegant: if the implied probabilities of the outcomes add up to less than 100%, there is more than enough margin in the market for a savvy bettor to squeeze out a guaranteed win. An arb exists when the math of odds pricing creates an imbalance between bookmakers, and exploiting that imbalance is pure profit.

The key insight is that bookmakers each carry their own margin baked into the prices they quote, and that margin varies between firms. One bookmaker might price an Over 2.5 goals market at 2.10, while another prices the Under at 2.05. Individually, neither is a bad price; together, they form an opening. By backing both outcomes with a stake split between the two bookmakers, you collect both sets of odds while investing only the smaller of the two potential returns, guaranteeing profit. The arbitrage exists because the two bookmakers do not know about one another’s prices, and by the time the market moves, a sharp bettor has already locked in the edge.

How Arbitrage Odds Are Calculated

Arbitrage opportunities are discovered by converting the decimal odds of each outcome into their implied probabilities, then adding those probabilities together. The formula is simple: total implied percentage = (1/Odds A + 1/Odds B) × 100. If that total is below 100%, an arbitrage exists. If it is 100% or higher, there is no edge — the bookmakers have covered the market fully or have built in so much margin that no profit opportunity remains.

Once an arbitrage is confirmed, the stake is split between outcomes in proportion to each outcome’s 1/odds, ensuring that every possible result returns the same amount of money. This is where the guaranteed profit emerges: you invest less than you stand to return, and that difference is your profit regardless of which outcome occurs. The arbitrage profit percentage is calculated as (100 / total implied %) − 100. A 3.73% arbitrage means that for every €100 staked, you keep €100 and gain €3.73 profit. The math always holds if both bets are placed at the quoted prices and neither is rejected or adjusted.

What the Calculator Shows You

Enter the decimal odds for each opposing outcome and your total stake in euros, and the calculator returns five key numbers. Total implied percentage is the sum of the probabilities implied by both odds; if below 100%, an arbitrage exists and the calculator will process it. Stake on each outcome is the calculated split, derived so that both outcomes return the exact same amount of money when multiplied by their respective odds. Guaranteed return is that amount, shown for each outcome after applying the odds to the calculated stake. Arbitrage profit percentage expresses the edge as a percentage return on the total investment. Guaranteed profit is the total amount left after recovering your initial stake — the net win regardless of which outcome actually occurs. The calculator only displays a profit opportunity if the total implied percentage is below 100%.

Worked Example

Take a two-way Over/Under 2.5 goals market with a €200 total stake, split across two bookmakers. The Over is priced at 2.10 with Bookmaker A. The Under is priced at 2.05 with Bookmaker B.

First, check whether an arbitrage exists: (1/2.10 + 1/2.05) × 100 = 96.4%. Since 96.4% is below 100%, an arbitrage is present. Now split the stake proportionally. The stake on Over 2.5 is €98.80, which at 2.10 returns €98.80 × 2.10 = €207.47. The stake on Under 2.5 is €101.20, which at 2.05 returns €101.20 × 2.05 = €207.47. Both outcomes return the same amount. The arbitrage profit percentage is (100 / 96.4) − 100 = 3.73%. The guaranteed profit is €207.47 − €200 = €7.47. No matter which outcome occurs, you net €7.47 from your €200 stake. That is the power of arbitrage: the math guarantees it.

Guaranteed Profit by Total Stake

The beauty of an arbitrage is that your profit is directly proportional to your stake. As long as you maintain the correct stake ratio between the two outcomes, every euro you invest guarantees a return. The table below shows how your guaranteed profit scales with total stake size for this 3.73% arbitrage opportunity. Whether you stake €100 or €1,000, the percentage return remains locked in at 3.73%, making arbitrage a pure scaling game: bigger stakes mean bigger profits, with zero additional risk.

A stake of €100 yields €3.73 guaranteed. Double that to €200, and your profit doubles to €7.47. Scale up to €500, and you lock in €18.67 regardless of which outcome occurs. At €1,000 total stake, your guaranteed profit reaches €37.35. The proportional relationship never changes: the 3.73% edge multiplies with your investment. The calculator makes this scaling instant, allowing you to determine your ideal stake based on your available bankroll and profit targets.

Implied Probabilities of Each Price

An arbitrage is only possible when the implied probabilities of both outcomes sum to less than 100%. The table below shows how each price converts to its probability, and why the total of 96.4% signals a profitable opportunity.

When the Arbitrage Breaks

An arbitrage exists purely on paper until both bets are actually placed and confirmed at the quoted prices. This is the critical gap between theory and practice in arbitrage betting. Odds move fast — sometimes in seconds — and by the time you place the second leg, prices may have shifted enough to close the arbitrage or even reverse it entirely. A 3.73% margin can evaporate into nothing, turning a guaranteed profit into a gamble.

Bookmakers also retain explicit rights that threaten arbitrage execution. They can reject bets outright without explanation, limit the maximum stake you can place on a particular market, or void a market entirely if a material event occurs before the result settles. If one leg of your arbitrage is rejected or voided while the other stands, you are left exposed on one side — no longer facing a guaranteed return, but a real bet with genuine risk of loss. You have backed one outcome only, and that outcome is not guaranteed to win.

This is why execution discipline matters more than mathematical knowledge in arbitrage betting. Always place the shorter-priced leg first, because it is more likely to be accepted by the bookmaker; if the second leg is subsequently rejected, you can still hedge or close out the first leg before the market settles. Modern bookmakers have become increasingly sophisticated at detecting arbitrage activity. They employ betting pattern algorithms and oddsmovement analysts who flag accounts placing correlated bets on opposite outcomes across time zones and sportsbooks. When an account is flagged, bookmakers may silently limit stake sizes, restrict access to high-value markets, or close the account entirely. Winning arbitrage bettors are bad business for bookmakers, so expect eventual limitations even if you operate responsibly.

The mathematical edge is genuinely risk-free only if both bets are placed, accepted, and confirmed at the exact prices you locked in before you placed the first bet. Once that confirmation happens, the profit is yours regardless of what the market does next. But until that moment, execution risk is real.

When an Arbitrage Makes Sense

Arbitrage opportunities represent genuine mathematical edges — a rare commodity in betting. They occur when two bookmakers price the same market significantly differently, leaving a small but real window of profit. The challenge is not understanding whether an arb is a good bet; the maths always says yes. The challenge is finding arbitrages in the first place, moving fast enough to exploit them before odds adjust, and placing both legs before one is rejected. Most arbitrage opportunities offer profit margins between 1% and 5%, which seems modest until you realise it is a guaranteed return in a market where most punters expect nothing but zero or losses.

The best approach is to treat arbitrage as occasional profit when you spot an opportunity, not as a reliable income stream. Monitor the odds across your bookmakers regularly; look for large price differences on the same market, especially at off-peak times when liquidity is lower and prices can diverge; and act immediately when you find an arb. Keep your stakes proportional to the quality of the opportunity and to how much movement in prices you can tolerate before the edge evaporates. Use the calculator to confirm the maths before placing bets. Arbitrage betting is legitimate, but bookmakers disapprove of it, so be prepared for the possibility that your accounts may be limited.

Common Mistakes

Treating a total implied percentage of 100% or more as an arbitrage is the most costly error — it is not, and you will lose money. Staking equal amounts instead of in proportion to each price means different outcomes return different amounts, destroying the guaranteed profit and creating real risk on one side. Ignoring that odds can move before the second bet is placed leaves you exposed if the window closes between placing your two legs. Forgetting exchange commission or bookmaker limits that erode the margin is another silent killer — a 3% arb can evaporate if a bookmaker applies a 2% limit on your stake or if a betting exchange takes commission on your winnings.

Arbitrage vs Bookmaker Margin

The difference between an arbitrage and a bookmaker’s margin hinges on the total implied percentage.