arbitrage betting: guaranteed-profit stakes when books disagree

what arbitrage betting is

Arbitrage betting, or arbing, is the closest thing betting has to a guaranteed return. You back every possible outcome of the same event, but not at the same bookmaker. Instead you take the best price on each outcome from whichever book offers it, and you size the stakes so that the winning ticket returns more than all the stakes put together. Whichever outcome lands, you collect: a sure bet, a locked-in profit, an arb.

The remarkable part is that you need no opinion at all. A value bettor has to be right more often than the market thinks; an arber only needs two books whose prices disagree enough. The profit does not come from predicting the match. It comes from the disagreement itself, converted into a small guaranteed gain. That is why arbs are sometimes called riskless: the risk is in the mechanics, not the prediction, and the mechanics get their own section below.

how to spot an arb: the under-round

Every decimal price is an implied probability: 1 divided by the odds. A price of 2.00 implies a 50% chance, 3.00 implies 33.3%, and a single book's prices on a market always sum to more than 100%. That excess is the overround, the margin the book charges for taking your bet, explained properly in the implied probability guide.

Now take the best price on each outcome across every book you can reach. Usually the best prices still sum above 100%, because each book is charging its own margin. But occasionally two books disagree sharply: one is heavy on the favourite, the other heavy on the outsider, and each offers a price better than the other's. When the best prices on all outcomes sum to less than 100%, the market has an under-round, and that gap is pure guaranteed profit waiting to be split. The margin is usually small, a percent or two, but it is certain.

So the spotting rule fits in one line: sum the implied probabilities of the best available price on every outcome, and if the total is under 100% an arb exists, with 100% minus the total as your profit margin. The odds converter turns any price into its implied probability and shows the sum for you.

worked example: one tennis match, two books

A men's singles match, Alcaraz against Sinner, has only two outcomes, which makes it the cleanest arb shape. Book A prices Alcaraz 1.95 and Sinner 2.00, implied probabilities of 51.3% and 50.0%, summing to 101.3%, a normal margin. Book B prices Alcaraz 2.10 and Sinner 1.85, implied probabilities of 47.6% and 54.1%, summing to 101.7%, also a normal margin. No single book offers a sure bet; both are charging their standard overround.

But take the best price on each outcome: Alcaraz at 2.10 from Book B, Sinner at 2.00 from Book A. The implied probabilities are 1 ÷ 2.10 = 47.6% and 1 ÷ 2.00 = 50.0%, summing to 97.6%. Under 100%: the two books disagree enough that between them they have created an arb, and the 2.4% gap is your guaranteed margin.

The stake split uses the same rule as dutching: stakes proportional to 1 divided by the odds, normalised so they add up to your total. With £200 to deploy, S = 0.476 + 0.500 = 0.976. Alcaraz takes £200 × 0.476 ÷ 0.976 = £97.56. Sinner takes £200 × 0.500 ÷ 0.976 = £102.44.

Now run both outcomes. If Alcaraz wins, £97.56 × 2.10 returns £204.88, a profit of £4.88 over the £200 staked. If Sinner wins, £102.44 × 2.00 returns £204.88, the same return and the same £4.88 profit. Rounding to the penny wobbles the return by a few pence either way. £200 in, £204.88 out, whichever player wins: a 2.4% return on a tennis match whose result is completely irrelevant to you.

the stake-split maths in one formula

Generalise the example. For outcomes with best decimal odds o1, o2 and so on, compute S = (1 ÷ o1) + (1 ÷ o2) + …. If S is under 1, the arb is on, and the stake on outcome i is total × (1 ÷ oi) ÷ S. The guaranteed return is total ÷ S, so the guaranteed profit is total × (1 ÷ S − 1). In the tennis example, 1 ÷ 0.976 − 1 = 2.4% of the total, the £4.88 on £200.

If those same prices sat at one book, this would be exactly the arithmetic of dutching, and the dutching calculator performs the split for two to six selections: type in the best prices, read off the stakes and the book percentage. The only difference is where the losing legs are placed. A dutch keeps them at one book and pays that book's overround. An arb places them at a second book that happens to price them at under 100% combined. Same maths, opposite sign on the margin.

why books limit and gub arbers

A bookmaker's model assumes its customers lose in aggregate: every bet carries the overround and the book keeps the difference. An arber breaks the model, because every arb is a guaranteed loss for the book holding the value price. It pays out to a customer whose position cannot lose, and it does so at the sharpest price on the board.

So books defend themselves. The first defence is limiting: maximum stakes cut to a few pounds, sometimes pence, so that even a successful arb moves trivial amounts. The second is gubbing, barring the account entirely, sometimes with the balance paid out and the door locked behind you. Books share intelligence on known arbers, and odds-compiler teams watch for accounts that only ever take the best price on every outcome. An arber's edge erodes exactly as fast as the accounts that fund it get shut down, which is why arbing is usually a small-stakes hobby spread across many accounts, not a scalable income.

the real risks: movement, palpable errors, limits

Sure bet describes the maths, not the execution, and three risks sit between the maths and the money. Odds movement is the first: an arb exists only while both prices stand. Books move prices continuously, and the window between your first leg and your second is exposure. Place the Sinner leg at 2.00 and, if Book B cuts Alcaraz from 2.10 to 2.00 before you bet, the arb is gone and you hold a naked one-sided position that can lose.

Palpable errors are the second. If a book's price was an obvious mistake, a 50.00 on a player priced 2.00 everywhere else, it can void the bet as a palpable error, sometimes after the event has settled. Your matched position suddenly has a leg removed and the risk-free arb becomes a real bet on the remaining leg.

Account limits are the third and the most certain: even a winning arb accelerates the limit or the gub, and a limited account is a dead account for arbing. The practical controls are the usual ones: stake both legs within seconds, keep the total small relative to your bankroll, spread accounts across books, and never chase a price that looks too good, because too good usually means voided later.

arbing vs value betting vs dutching

Arbing, value betting and dutching are often confused, and each deserves a clear line. Value betting is an opinion bet: you price an outcome yourself, compare it with the market's implied probability and bet when your estimate is better. The edge is your judgement, and the full method is set out in the value betting guide. Arbing has no opinion at all: the edge is the books' disagreement, locked in before the event starts.

Dutching is one book, your shortlist, insurance: you cover several selections at a single book, sized for equal profit, and you pay that book's overround on every leg. Arbing is two books, every outcome, margin reversed: the combined implied probability is under 100% instead of over it, so the position profits instead of paying. A dutch shapes a bet you already believe in; an arb avoids having a belief at all.

Where the tools fit: the odds converter compares fractional, decimal and American quotes across books and shows each implied probability, which is the fastest way to find a sum under 100%. The dutching calculator turns the best prices into the exact stake split. And when you graduate from arbs to genuine edges, the staking calculator sizes the position properly with full, half or quarter Kelly, because a real edge deserves a real stake while an arb's 2.4% needs a stake your accounts can survive.

the arbitrage checklist

A short routine before any arb, in order: collect the best price on every outcome across your books; convert each to an implied probability; sum them, and under 100% means an arb with the gap as your margin; split the stake in proportion to 1 ÷ odds, which the dutching calculator does; place every leg as fast as the accounts allow; keep the total small enough that a voided leg cannot hurt; and expect the limits, banking the profit and never reloading a gubbed account with fresh money. Seven checks, and the last is the one most arbers ignore.

the honest endnote

Arbitrage betting is real: the arithmetic genuinely locks in a profit. But it is small, fragile and heavily policed. The 2.4% in the tennis example is typical, the accounts that make it possible are short-lived, and the execution risks can turn a sure bet into a one-sided one in seconds. Treat arbing as a disciplined side activity with modest stakes, not a money machine. Bet within your means, treat the bankroll as money you can afford to lose, and if betting stops being enjoyable, stop. 18+ | BeGambleAware.