When implied probabilities sum below 100%, you have an arb

A normal vigged market has implied probabilities summing to 104-110% — the overround is the book's margin. Two different books can disagree on the underlying probability enough that the cheapest cross-book combination sums to less than 100%. When that happens, the differential — 100% minus the implied sum — is the guaranteed return percentage. A combined implied sum of 96% means a roughly 4% ROI on the total wager regardless of which side wins.

Stake split: solve for equal payout

The arbitrage stake split is proportional to implied probability: stake_i = total × (implied_i / implied_sum). This guarantees that whichever leg wins, the total payout matches the others. Equal-dollar splits do not achieve this — the favored side pays out less and turns the arbitrage back into a regular bet with risk.

Worked example: +110 / +110 cross-book

Book A: +110 implied 47.62%. Book B opposite side: +110 implied 47.62%. Sum = 95.24%. With $100 total stake, split is $50.00 on each side. Each leg returns 50 × 2.10 = $105.00 on win, $0 on loss — exactly $105 returned regardless of outcome. Guaranteed profit: $5.00 (5.00% ROI). Real-world arbs are rarely this clean and usually 1-3% ROI, but the math scales identically.

FAQ

What is arbitrage betting (a "surebet")? +

Arbitrage betting means staking on every outcome of a market across two or more sportsbooks at prices that guarantee a profit regardless of result. When the cross-book implied probabilities sum to less than 100%, the differential between the sum and 100% becomes your guaranteed return. Real arbs are rare, small (usually 1-4% return), and short-lived — books move lines or limit accounts as soon as one side gets hit. The math is risk-free; the execution rarely is.

How do I know if a two-book line spread creates an arbitrage opportunity? +

Sum the implied probabilities of both sides across the books you have access to. If the sum is less than 100% (1.00 in decimal terms), an arb exists. For example: Book A offers Team Home +105 (implied 48.78%) and Book B offers Team Away +110 (implied 47.62%). Sum = 96.40%. Stake split proportional to implieds across $100 total: $50.60 on home, $49.40 on away. Either side wins; total payout is $103.74 — a guaranteed $3.74 profit (3.74% ROI).

How are stakes split between books? +

The split solves for equal payout regardless of which side wins. The formula is stake_i = total_stake × (implied_prob_i / implied_sum). Each leg's stake share is proportional to its implied probability, which guarantees both legs return the same total amount. If you stake equally instead, one outcome pays out more than the other and you stop being arbitraged on one side. The calculator handles the split automatically — paste the prices, set the total stake, get the per-book amounts.

What are the real risks of arbitrage betting? +

Several. (1) Limits — books limit consistently arbed accounts within weeks. (2) Line moves — by the time you place the second leg, the price might have moved and the arb is gone. (3) Voids and pushes — if one book voids or pushes a leg, the other side becomes a single open bet (often -EV). (4) Account closures — sportsbooks identify arbers via betting patterns and close accounts. (5) Bonus restrictions — promo terms often exclude arb-eligible markets. Real arbing requires multiple funded accounts, fast execution, and tolerance for declining account quality.

How is arbitrage different from a middle or a hedge? +

Arbitrage: bet ALL outcomes simultaneously across books for guaranteed return regardless of result. Middle: bet OPPOSING sides at different lines, hoping the result lands between them so both win — both bets can lose if the result lands outside the corridor. Hedge: take a SECOND bet AFTER placing the first to reduce variance on an already-open position; rarely zero-risk, usually trades EV for variance reduction. Arbing is the only one of the three that is genuinely zero-risk on paper; the others involve real downside.

Arbitrage Calculator