Sure bets and arbitrage betting explained (with the maths)

Each bookmaker builds a margin into its own prices, so a single bookmaker's market always adds up to more than 100% (see implied probability). But bookmakers don't always agree. If one is generous on "over" and another is generous on "under", the best price on each side can add up to less than 100%. That gap is the arbitrage.

The check:

• Two outcomes: 1 ÷ a + 1 ÷ b < 1
• Three outcomes (1X2): 1 ÷ home + 1 ÷ draw + 1 ÷ away < 1

The profit margin of the arb = 1 ÷ (that total) − 1.

The stake on each outcome = total stake × (1 ÷ odds of that outcome) ÷ total.

Note the return is the same whichever side wins. That's the point of the stake split. In real life you'd round stakes (for example £48.80 and £51.20, returning £102.48 or £102.40), which moves the profit a few pence either way.

A 3% three-way arb on a major league is unusual. When you see one, the first question should be "what's wrong with this price?" rather than "how much can I stake?". Run your own numbers with the calculator:

Bookmakers watch each other and the betting exchanges. A price that's out of line is usually corrected within minutes, sometimes seconds. That's why the arbs that do exist are often:

• Small: 1–2% is typical; anything above 5% is usually a mistake or a stale price.
• Short-lived: by the time you've placed the first leg, the second price may have moved.
• In thinner markets: lower leagues, player props or in-play markets, where limits are lower and rules differ.

An arb only locks in a profit if every leg is placed at the price you saw and every leg is settled as expected. Each of those can fail.

The price moves before you place the second leg

A bet is voided or the price is corrected

Bookmakers' terms let them void or re-price bets placed at an obvious error ("palpable error"). If one leg is cancelled after the match starts, the other leg is a normal bet with full risk on it.

Different settlement rules

Two bookmakers may settle the same market differently: one counts only 90 minutes plus stoppage time, the other includes extra time; one voids a bet if a player doesn't start, the other doesn't; abandoned matches are handled differently. An arb on mismatched rules can lose on both legs. Check how each bookmaker defines the market; for match-result rules see 1X2 betting.

Account limits

Arbitrage is legal, but bookmakers don't like it. Accounts that regularly take out-of-line prices tend to get stake limits quickly, sometimes after a handful of bets. Many arbers find that their accounts are restricted long before the small profits add up to much.

Capital, fees and mistakes

You need money spread across several accounts, payments can carry fees, and a single typo in a stake (£512 instead of £51.20) can wipe out months of 2% gains. Currency conversion can also eat a thin margin.

Arbs are a good way to understand how prices and margins work. They're rarely a sensible way to make money, and they reward speed, capital and rule-reading more than football knowledge. For the approach that relies on judgement, see value betting.

• Trusting a big margin. A 7% "arb" is almost always a pricing error that will be voided.
• Placing the easy leg first. Place the leg most likely to move or be limited first.
• Not checking market rules (90 minutes vs extra time, void conditions).
• Ignoring maximum stakes. If the second leg is capped at £20, your first leg is now unbalanced.
• Spreading money over unlicensed sites to find more arbs. If a site won't pay, the arb is a loss. Use only licensed bookmakers.

Before you bet on any market, look at the context too: our trends and stats pages show how teams have been scoring, which helps you spot when a price is simply stale.