AUOdds

Arbitrage Betting Formula: Every Calculation on One Page

By the AUOdds team · Updated 29 Oct 2026 · 7 min read

Key takeaways
  • A lock exists when the sum of 1 ÷ odds across every outcome, at the best available prices, is below 1.00.
  • Each stake equals total outlay × (1 ÷ that outcome's odds) ÷ the arb sum, or target payout ÷ odds.
  • Profit on outlay is (1 ÷ arb sum − 1) × 100, which differs from the margin figure some calculators show.
  • Racing dutches use the same formula across every runner, and a partial dutch is not a lock.
  • Rounding stakes can shrink or erase a thin lock, so always recheck the worst-case return before placing.

The arbitrage betting formula is short enough to fit on a sticky note, but most formula pages explain it with American odds and NFL teams. This guide puts every calculation an Australian punter needs on one page, using decimal odds and A$ stakes. It covers how to spot a lock, how to calculate arbitrage stakes for two, three or more outcomes, how to work out the profit percentage, how to dutch a whole racing field, and what rounding does to your numbers. Each formula comes with a worked example you can check on a phone calculator. The maths is the easy part. Prices move and stakes get limited, so we also cover the checks that stop a good calculation becoming a bad bet. AUOdds runs these sums automatically, but knowing them yourself means you can verify any alert.

In this guide
  1. What is the arbitrage betting formula for spotting a lock?
  2. How do you calculate arbitrage stakes for each outcome?
  3. How do you work out the profit percentage of a lock?
  4. How does the formula work for an n-runner racing dutch?
  5. What does rounding do to your locked return?
  6. What else can break the maths, and how do you check it?

What is the arbitrage betting formula for spotting a lock?

The core arbitrage betting formula is one line. Add up 1 ÷ odds for every possible outcome, using the best decimal price you can find for each one. Call the total the arb sum.

Each 1 ÷ odds figure is the implied probability of that outcome. A single bookmaker's market almost always sums above 1.00 because the margin is built in. A lock only appears when you take different outcomes from different bookmakers and their best prices disagree enough.

Worked check, NRL head-to-head. Team A is 2.10 at one bookmaker and Team B is 2.02 at another.

The sum is below 1.00, so those prices lock in a return.

Keep five decimal places at this stage. Rounding the reciprocals early can push a 0.995 sum up to 1.00 and hide a real lock. It can also invent a lock that isn't there.

Two habits make detection reliable. First, compare like with like. The market rules must match on both sides, including how a draw or extra time is settled. A two-way market and a three-way market can't be mixed. Second, use current prices. A sum calculated from prices that are a minute old describes a market that may no longer exist.

How do you calculate arbitrage stakes for each outcome?

If you've searched for how to calculate arbitrage stakes, there are two formulas. Both give every outcome the same return.

Method 1, fixed total outlay: Stake for an outcome = Total outlay × (1 ÷ that outcome's odds) ÷ arb sum

Here it is with $1,000 on the NRL example:

To check, multiply each stake by its odds. $490.29 × 2.10 = $1,029.61, and $509.71 × 2.02 = $1,029.61. Either result returns the same amount, $29.61 more than you staked.

Method 2, fixed payout: Stake for an outcome = Target payout ÷ that outcome's odds

For a $1,000 payout, the stakes are $476.19 and $495.05. That's a total of $971.24, for $28.76 profit. This method is handy when one bookmaker's maximum stake sets the ceiling. Multiply the limited stake by its odds to get the payout, then divide that payout by every other price.

Three-way soccer. The same formula works for any number of outcomes. Say the best prices are Home 2.45, Draw 3.55 and Away 3.30.

Each outcome returns about $604.30. Always do the multiply-back check before placing anything. It catches typos in the odds, which are the most common error.

How do you work out the profit percentage of a lock?

Once you have the arb sum, the profit is one more step.

Profit % on outlay = (1 ÷ arb sum − 1) × 100

For the NRL example, 1 ÷ 0.97124 = 1.02961, so the lock returns 2.96% on the money staked.

Dollar profit = Total outlay × (1 ÷ arb sum − 1)

On $1,000 that gives $29.61, which matches the multiply-back check.

Some calculators show a different figure: margin = (1 − arb sum) × 100. For the same prices that's 2.88%. It measures profit as a share of the payout, not of your stake. Both numbers describe the same lock. Just know which one a tool displays before comparing it with another.

The soccer example is thinner. 1 ÷ 0.99288 = 1.00717, a 0.72% return, or about $4.30 on $600.

To put real-world sizes in context: AUOdds data shows 3,463 locks in the last 30 days, with a typical lock of about 1.5%. At 1.5%, a $1,000 outlay returns roughly $15.

You can also run the formula backwards to set a filter. The arb sum needed for a target return is:

Required arb sum = 1 ÷ (1 + target return)

A 1.5% target needs a sum of 0.98522 or lower. A 1% target needs 0.99010.

The percentage applies per lock, not per year, and it holds only at the prices shown. With margins this small, one mistyped stake or a price that moves before your second bet can cost more than several locks return. That's why the checks later in this guide matter as much as the formulas.

How does the formula work for an n-runner racing dutch?

A whole-field racing dutch is the same formula with more legs. List every runner, take the best fixed-odds price for each across licensed bookmakers, and add the reciprocals.

Worked example, five-runner field:

The fixed-payout method is easiest here. For a $500 payout, each stake is $500 ÷ the runner's odds:

The big rule is that every runner must be covered. If you leave one out, the sum of the runners you backed may well be under 1.00. That's a partial dutch, not a lock, and you lose the lot if the uncovered runner wins.

Racing adds risks the maths doesn't show:

Work out the minimum price for each remaining leg before you start, so you know when to stop.

What does rounding do to your locked return?

Calculated stakes come out in odd cents, and many punters round them to whole dollars or fives. Rounding changes the result, so use this formula to see the real outcome:

Worst-case return = lowest of (stake × odds) across all outcomes − total stakes

NRL example, rounded to whole dollars. $490.29 becomes $490 and $509.71 becomes $510, still $1,000 in total.

That cost is minor because the lock was reasonably wide.

Racing example, rounded to the nearest $5. The stakes become $210, $110, $85, $55 and $35, for a $495 outlay.

The 1.69% lock has disappeared. Two runners now only return your outlay, and nothing ahead.

The lessons are simple:

Rounding to whole dollars is a personal choice, not a requirement. Whatever you choose, the worst-case figure is the number that counts, not the headline percentage.

What else can break the maths, and how do you check it?

One formula protects you when prices move between bets. It gives the minimum price for the last leg:

Minimum price = 1 ÷ (1 − sum of reciprocals already placed)

In the NRL example, once Team A is on at 2.10, Team B needs at least 1 ÷ (1 − 0.47619) = 1.91 to break even. Above that, restake using: stake = payout of placed leg ÷ new price. Below it, you're holding an open bet and must decide how to handle it. Knowing that number before you start stops panicked decisions.

Prices shift quickly. AUOdds tracks prices that are about 10 seconds old, and even that is enough time for a market to change. Other real risks include stakes being limited, bets being voided under a bookmaker's rules, and simple keying errors.

Run this checklist before every lock:

Stick to fixed-odds bets placed through licensed Australian bookmakers. In-play online sports betting isn't offered to Australians, so plan locks around the markets that are.

A quick reminder: betting is for adults 18+ only, and even careful arbitrage involves real money at risk. If betting stops feeling like a controlled hobby, BetStop, the National Self-Exclusion Register, lets you exclude yourself from licensed online bookmakers. Gambling Help Online offers free, confidential support at any hour.

Frequently asked questions

What is the simplest arbitrage betting formula?

Add up 1 ÷ odds for every outcome using the best decimal price for each. If the total is below 1.00, the prices lock in a return. Each stake is then total outlay × (1 ÷ that outcome's odds) ÷ the total. Profit on outlay is (1 ÷ total − 1) × 100. Check by multiplying each stake by its odds. Every result should be the same.

Can I use these formulas with American or fractional odds?

Convert to decimal first. Australian bookmakers display decimal odds, so most local punters never need to. For fractional odds, divide the top number by the bottom and add 1, so 5/2 becomes 3.50. For American odds, +150 becomes 2.50 and −200 becomes 1.50. Once everything is decimal, the detection, stake and profit formulas work exactly as shown in this guide.

Does the arbitrage formula change for horse racing?

No, the maths is identical. You just add the reciprocal of every runner's best fixed price, not two or three outcomes. The practical differences are covering every runner, checking each bookmaker's rules on scratchings and deductions, and allowing for more rounding error across more legs. Leaving out one runner turns the bet into a partial dutch, which is not a lock.

Do I pay tax on arbitrage betting returns in Australia?

The ATO's Taxation Ruling IT 2655 covers how gambling and betting winnings are treated. The ATO also has guidance on gambling winnings more generally. How it applies depends on your own circumstances, including whether your activity could be treated as a business. Read the ATO material and talk to a registered tax agent rather than relying on general rules of thumb.

Sources

  1. Check if a gambling operator is legal, Australian Communications and Media Authority
  2. BetStop: the National Self-Exclusion Register, Australian Communications and Media Authority
  3. BetStop, Australian Government
  4. Taxation Ruling IT 2655: gambling and betting winnings, Australian Taxation Office
  5. Crypto asset prizes and gambling winnings, Australian Taxation Office

More guides

18+ only. Betting involves risk, and prices and limits can change before you place a bet. If gambling isn't fun any more, Gambling Help Online (1800 858 858) is free and confidential, and BetStop lets you exclude yourself from every licensed Australian bookmaker.