Arbitrage Rate: The One Number That Tells You It's a Lock
- The arbitrage rate comes from adding the implied probabilities (1 ÷ odds) of every outcome, using the best price for each outcome across bookmakers.
- If that sum is below 100%, the prices lock, and the return on total stake is (1 ÷ sum) − 1.
- The same formula works for a two-way sports market and a whole racing field, as long as every outcome is covered.
- Near even money, each one-cent drop in a price removes roughly a quarter of a percentage point from the lock.
- Short-priced legs are far more sensitive to price moves than long-priced ones, so check those first before you stake.
The arbitrage rate is the single percentage that tells you whether a set of prices across different bookmakers locks in a return at the prices shown. You get it by adding up implied probabilities, then turning that total into a return on your total stake. This guide covers how to calculate arbitrage by hand, the full arbitrage betting formula, a worked tennis lock and a whole racing field. It also covers what most calculator pages skip: how many cents a price can move before the lock disappears. AUOdds alerts members to locks with exact stakes, but understanding the number yourself means you can check every alert, catch mistakes and judge how fragile a lock really is.
- What is the arbitrage rate and why is it the one number to check?
- How to calculate arbitrage: what is the arbitrage betting formula?
- What does a 1.5% lock look like in a worked example?
- Can a racing field lock, and how do you check every runner?
- How many cents can a price move before the lock disappears?
- What else can break a lock even when the numbers look right?
What is the arbitrage rate and why is it the one number to check?
The arbitrage rate tells you whether you can cover every outcome of an event across different bookmakers for less than you get back. If it shows a positive return, the prices lock. If it doesn't, they don't, no matter how attractive one price looks on its own.
It starts with implied probability. Divide 1 by any decimal price to get a percentage. A price of 2.00 implies 50%. A price of 4.00 implies 25%. A single bookmaker builds its market so these percentages add up to more than 100%. That extra is its margin, often called the overround.
When you take the best price for each outcome from different licensed bookmakers, the total can occasionally dip below 100%. That gap is the lock.
People quote the number in two ways: - Margin under 100%: 100% minus the implied-probability sum. A sum of 98.5% gives 1.5%. - Return on total stake: (1 ÷ sum) − 1. A sum of 98.5% gives about 1.52%.
The two figures are close at small sizes. The second one is what actually comes back to you, so it's the one this guide uses.
For scale, AUOdds data shows 3,051 locks in the last 30 days across 9 bookmakers, with a typical lock around 1.5%. That's the realistic range. You're working with small percentages that need careful execution, not large windfalls.
How to calculate arbitrage: what is the arbitrage betting formula?
If you've searched 'arbitrage betting how to calculate', you only need three formulas.
1. Implied-probability sum Sum = 1/odds A + 1/odds B (+ 1/odds C and so on for every outcome)
2. Arbitrage rate (return on total stake) Arb % = (1 ÷ Sum − 1) × 100
If Sum is below 1, the result is positive and the prices lock. If Sum equals 1, you break even. If it's above 1, you lose money whichever outcome wins.
3. Stake for each outcome Stake = Total outlay × (1/odds of that outcome) ÷ Sum
This spreads your money so every outcome returns the same amount. That return equals Total outlay ÷ Sum.
A fourth formula is worth knowing because most calculators leave it out:
4. Break-even price for one leg Minimum odds = 1 ÷ (1 − implied probability of all the other legs)
This gives you the lowest price a leg can drift to before the lock vanishes. It's the quickest way to judge how fragile a lock is, and the price-move section below uses it.
Use this checklist when you calculate by hand: - Use the price on the bet slip, not the one in an alert or comparison table. - Keep at least four or five decimal places on implied probabilities. Rounding to two hides small locks and creates fake ones. - Round stakes only at the end, then recheck each payout. - Confirm every outcome is covered, including the draw in three-way markets.
Calculators do the arithmetic for you. Knowing the formula yourself means you can spot an error before you place a stake.
What does a 1.5% lock look like in a worked example?
Here's a two-way tennis match, priced before play starts: - Player A: 2.06 at Bookmaker 1 - Player B: 2.00 at Bookmaker 2
Step 1: implied probabilities 1 ÷ 2.06 = 0.48544 1 ÷ 2.00 = 0.50000 Sum = 0.98544, or 98.54%
Step 2: arbitrage rate 1 ÷ 0.98544 = 1.01478, so the return on total stake is about 1.48%. That's close to the typical 1.5% lock mentioned above.
Step 3: stakes on a $1,000 outlay - Player A: $1,000 × 0.48544 ÷ 0.98544 = $492.61 - Player B: $1,000 × 0.50000 ÷ 0.98544 = $507.39
Step 4: check the payouts - If Player A wins: $492.61 × 2.06 = $1,014.78 - If Player B wins: $507.39 × 2.00 = $1,014.78
Either way you get back $1,014.78, a return of $14.78 at the prices shown. The arbitrage rate becomes a dollar figure that doesn't depend on who wins.
Two things stand out. First, $14.78 on $1,000 shows how thin the edge is. One typo in a stake, such as $529.39 instead of $507.39, changes the result. Second, rules for a player retiring mid-match can differ between bookmakers. Read each bookmaker's rules before you treat a tennis market as a clean two-way lock.
Can a racing field lock, and how do you check every runner?
Yes. The same formula works across a whole field, as long as you cover every runner. This is the case most formula pages leave out.
Take a six-runner race with the best fixed-odds price for each runner taken from different bookmakers: - Runner 1: 2.70 → 0.37037 - Runner 2: 4.40 → 0.22727 - Runner 3: 6.50 → 0.15385 - Runner 4: 9.00 → 0.11111 - Runner 5: 13.00 → 0.07692 - Runner 6: 21.00 → 0.04762
Sum = 0.98714, or 98.71%. The arbitrage rate is 1 ÷ 0.98714 − 1 = 1.30%.
On a $500 outlay, the stakes are Total × implied probability ÷ 0.98714: - Runner 1: $187.60 - Runner 2: $115.12 - Runner 3: $77.93 - Runner 4: $56.28 - Runner 5: $38.96 - Runner 6: $24.12
Each winning bet returns about $506.52. For example, $187.60 × 2.70 and $24.12 × 21.00 both come to $506.52. That's roughly $6.50 back on $500 at the prices shown. Rounding adds a cent to the total outlay.
Racing adds risks that a two-way sports market doesn't have: - More legs. Six bets means six chances for a price to move or a stake to be cut. - Scratchings. If a runner is scratched after you've staked, each bookmaker's rules on refunds and deductions apply. That can break the lock, so read those rules first. - Missing a runner. If you leave out even one runner, you no longer have a lock. You have a bet against that runner.
A racing field can lock. It just needs more care than a head-to-head.
How many cents can a price move before the lock disappears?
This is the sensitivity check most guides skip. It tells you how much room you have between seeing a price and getting it accepted.
Go back to the tennis lock. Player B stays at 2.00, and Player A's price starts to drop: - 2.06: 1.48% - 2.05: 1.24% - 2.04: 0.99% - 2.03: 0.74% - 2.02: 0.50% - 2.01: 0.25% - 2.00: 0.00%
The break-even formula agrees: 1 ÷ (1 − 0.5) = 2.00. Near even money, each cent is worth roughly a quarter of a percentage point. A typical 1.5% lock survives about six cents of movement on one leg.
If Player B's price moves instead, the break-even is 1 ÷ (1 − 0.48544) = 1.943. At 1.95 you'd keep about 0.17%. At 1.94 you'd lose money.
The racing field shows why short prices matter most: - Favourite (2.70): break-even is 1 ÷ (1 − 0.61677) = 2.61. A drop of just nine cents wipes out the lock. - Longshot (21.00): break-even is 1 ÷ (1 − 0.93952) = 16.53. It could shorten by more than four full points before the lock disappears.
The practical lesson is to place the leg most likely to move first. That's usually the shortest price, or the one sitting well above every other bookmaker's. Once it's accepted at your price, the remaining legs have more room. If the first leg is rejected or re-priced, recalculate before you go any further.
What else can break a lock even when the numbers look right?
A correct arbitrage rate only describes the prices at one moment. Real-world problems can still get in the way.
AUOdds tracks about 15,000 prices at any moment, each typically about 10 seconds old. That's fast, but prices can still change before your bet goes through. Here are the main risks: - Price moves. Covered above. Always confirm the slip price. - Stake limits. A bookmaker may accept only part of your stake, which leaves the other legs out of balance. - Voided bets. Obvious pricing errors can be voided under a bookmaker's terms, leaving one side exposed. - Rule differences. Retirements, scratchings and extra time can settle differently between bookmakers. - Your own mistakes. Wrong market, wrong runner, a misplaced decimal point.
Use only bookmakers licensed in Australia. ACMA lets you check whether an operator is legal (ACMA-LEGAL). Online in-play sports betting isn't offered to Australians, so every example here is priced before the event starts.
Keep a simple record of every lock: prices, stakes, payouts and anything that went wrong. Over time, that record shows whether your execution matches the theory.
A quick reminder: betting is for adults 18+ only. Even with locks, set a budget and stick to it. If betting stops feeling under control, BetStop, the National Self-Exclusion Register, lets you exclude yourself from all licensed Australian online bookmakers (BETSTOP, ACMA-BETSTOP). Free, confidential support is also available through Gambling Help Online.
Frequently asked questions
What is a good arbitrage rate?
Any positive return on total stake is technically a lock, but very small ones leave little room for price moves or rounding. Most real locks sit in the low single digits, often around 1% to 2%. A much higher figure usually points to a stale price, a pricing error that could be voided, or mismatched markets. Check those before you stake anything.
Is the arbitrage rate the same as the margin under 100%?
Not quite. The margin is 100% minus the implied-probability sum, while the return on total stake is (1 ÷ sum) − 1. For a sum of 98.5%, the margin is 1.5% and the return is about 1.52%. The difference is small at typical sizes, but the return figure matches what actually comes back to you.
How do I calculate arbitrage for a three-way soccer market?
Use the same formula with three legs. Add 1 ÷ odds for the home win, draw and away win, each taken from whichever licensed bookmaker offers the best price. If the sum is below 1, divide your total outlay by the sum to get the return. Then stake each outcome as total × (1 ÷ odds) ÷ sum.
Why did my lock disappear before I placed the second bet?
Prices move constantly, and near even money a one-cent drop removes roughly a quarter of a percentage point. A 1.5% lock can disappear after about six cents of movement on one leg. Place the shortest or most out-of-line price first, confirm the slip price, and recalculate before placing the remaining legs if anything changes.
Sources
- Check if a gambling operator is legal, Australian Communications and Media Authority
- BetStop, Australian Government
- BetStop: the National Self-Exclusion Register, Australian Communications and Media Authority
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.