AUOdds

Arbitrage Betting Calculator: How to Work Out Each Stake

By the AUOdds team · Updated 1 Oct 2026 · 7 min read

Key takeaways
  • An arbitrage betting calculator splits your outlay so each outcome returns roughly the same amount at the prices shown.
  • Prices form a lock when the implied probabilities (1 ÷ odds) of every outcome add up to less than 1.00.
  • Each stake equals your total outlay multiplied by that outcome's share of the total implied probability.
  • After rounding or hitting a stake limit, recheck every outcome and judge the result by its lowest return.
  • Prices move, stakes get limited and bets can be voided, so check every leg before you confirm.

An arbitrage betting calculator works out how much to stake on each outcome so you get roughly the same return whichever way a result goes. It's a useful tool, but it's only as good as the prices you feed it and your understanding of what the numbers mean. This guide walks through the maths step by step. It shows how to convert odds into implied probabilities, check whether a set of prices forms a lock, and split your outlay between outcomes. It covers two-way and three-way markets and what to do when you round stakes or hit a limit. It also explains the real risks that sit outside any formula. By the end, you should be able to check a calculator's output by hand in under a minute.

In this guide
  1. What does an arbitrage betting calculator actually do?
  2. How do you check whether prices form a lock?
  3. How do you work out each stake in a two-way market?
  4. How does the maths change for three-way markets?
  5. What happens when you round stakes or hit a stake limit?
  6. What can still go wrong after the numbers add up?

What does an arbitrage betting calculator actually do?

An arbitrage betting calculator takes the decimal odds for every outcome in a market and tells you how much to stake on each one. The goal is a return that is roughly the same whichever outcome wins. That is the whole job. It doesn't find opportunities, and it doesn't know whether a price is still available.

Most calculators ask for three inputs:

From those inputs it returns the stake for each outcome, the expected return and the percentage margin on your total outlay.

Understanding the maths behind it matters for two reasons.

First, you can sanity-check the output before you place anything. A typo in one price, such as 2.80 instead of 2.08, can make an ordinary market look like a lock.

Second, real betting rarely matches the neat numbers. Accounts get stake limits, and prices move between the first and second bet. If you know how the calculator reaches its figures, you can adjust quickly without guessing.

The good news is that the maths is simple. It rests on one idea, implied probability, and one formula for stakes. Once you have done it by hand a few times, a calculator becomes a time-saver rather than a black box you have to trust.

How do you check whether prices form a lock?

Every decimal price converts into an implied probability: divide 1 by the odds. A price of 2.00 implies 50%, and a price of 4.00 implies 25%.

In a normal market, the implied probabilities of all outcomes add up to more than 100%. The extra is the bookmaker's margin. For example, a head-to-head market at 1.90 and 1.90 adds up to about 105.3%.

A lock exists when you take the best price for each outcome and the total comes in under 100%. Those prices often come from different bookmakers. The size of the gap tells you the size of the return.

The quick test:

Say one bookmaker offers 2.08 on Team A and another offers 2.02 on Team B. The implied probabilities are 0.4808 and 0.4950, a total of 0.9758. Divide 1 by 0.9758 and you get 1.0248, so the prices lock in a return of about 2.48% at the prices shown.

That size is realistic. AUOdds data shows a typical lock of 2.4% over the last 30 days, across 241 locks found in that period.

Anything far bigger deserves a second look. Large gaps often mean a stale price or a keying error. They can also mean a mismatched market, such as one bookmaker including overtime and the other not. Always confirm every side is the same market with the same rules before you trust the number.

How do you work out each stake in a two-way market?

The stake formula spreads your outlay in proportion to each outcome's implied probability:

Stake on an outcome = total outlay × (implied probability of that outcome ÷ total implied probability)

Here is a worked example using the same prices, a total outlay of $1,000 and unrounded probabilities:

Now check the returns:

Either way, the return is about $1,024.78 on $1,000 outlaid. That leaves you roughly $24.78 ahead at the prices shown. The two figures differ by a couple of cents only because of rounding.

A shortcut gives the same answer. Decide the return you want, then divide it by each price. For a return of $1,024.78, the Team A stake is 1,024.78 ÷ 2.08 and the Team B stake is 1,024.78 ÷ 2.02. This version is handy when you are working backwards from a target.

Notice the pattern: the outcome with the shorter price (2.02) gets the larger stake. That is always true. A shorter price needs more money behind it to return the same amount.

A practical habit is to place the bet on the side most likely to move or be limited first. If that bet is accepted at the expected price and stake, place the second straight away. If it isn't, recalculate before doing anything else.

How does the maths change for three-way markets?

The formula doesn't change. You just have one more outcome to include. Three-way markets are common in soccer (home, draw, away). The same logic works for any market with more outcomes, provided they cover every possible result.

Example prices across three bookmakers:

The total is 0.9720. That's under 1.00, and 1 ÷ 0.9720 gives a return of about 2.88%.

With a total outlay of $600, and working from unrounded figures:

Each outcome returns close to $617.30, so you are about $17.30 ahead on $600 at the prices shown.

Three-way markets add a few extra things to check:

Markets with many outcomes, like racing or futures, follow the same maths. With many runners, though, the chance of at least one price moving climbs quickly. Most people find two-way and three-way markets easier to manage cleanly.

What happens when you round stakes or hit a stake limit?

Calculators give stakes to the cent, but many people prefer round figures to exact amounts like $507.32. Rounding is fine, as long as you check what it does to each outcome.

Here is the two-way example rounded to whole dollars:

The total outlay is still $1,000, and the worst case is now $1,024.14, about $24.14 ahead. The margin shrinks slightly and becomes uneven, but it stays positive. Always judge a rounded set of stakes by its lowest return, not its highest.

Stake limits are the other common problem. Say the bookmaker offering 2.08 on Team A will only accept $300. You can't use the total-outlay method any more. Instead, fix the limited stake and build around it:

The percentage stays about the same; only the size shrinks. Many calculators have a 'fix this stake' option for exactly this situation.

Avoid placing a big first bet before checking the limit on the second side. If that side turns out to be limited, you are left with an uneven position. That's why many people place the side more likely to be limited first. If it gets cut back, you haven't committed anything on the other side yet, and you can recalculate from the accepted amount.

What can still go wrong after the numbers add up?

A calculator can only work with the prices you give it. Real-world risks sit outside the maths, and they are worth taking seriously:

Before every lock, run through this quick checklist:

Only use bookmakers licensed in Australia. The Australian Communications and Media Authority lets you check whether a gambling operator is legal. On tax, the Australian Taxation Office's ruling on gambling and betting winnings is the place to start. A registered tax agent can advise on your own circumstances.

Keep your betting within limits you can afford. You must be 18+ to bet. If gambling stops feeling in control, BetStop, the National Self-Exclusion Register, lets you exclude yourself from licensed online and phone bookmakers. Gambling Help Online also offers free, confidential support.

Frequently asked questions

Do I need a calculator, or can I work out stakes by hand?

You can do it by hand with a phone calculator. Divide 1 by each price, add the results and check the total is under 1.00. Then multiply your total outlay by each outcome's share of that total. A dedicated calculator is faster and reduces keying errors. Knowing the manual method lets you spot a wrong price or an odd result straight away.

Why does the shorter price get the bigger stake?

A shorter price pays less per dollar, so it needs more money behind it to produce the same return as the longer price. In the two-way example, Team B at 2.02 needed $507.32, while Team A at 2.08 needed $492.68. Both return about $1,024.78, which is the whole point of balancing the stakes.

What is a realistic lock percentage?

Most genuine locks are small. AUOdds data puts the typical lock at 2.4% over the last 30 days. A result well above that is worth checking carefully. It often points to a stale price, a keying error or two markets with different settlement rules, rather than a real opportunity at the prices shown.

Should I round my stakes?

Rounding to whole dollars is common and usually costs only a small amount of margin. Recheck every outcome after rounding and judge the result by its lowest return. If rounding pushes any outcome below your total outlay, adjust the stakes until every outcome still returns more than you have put in.

Sources

  1. Check if a gambling operator is legal, Australian Communications and Media Authority
  2. Taxation Ruling IT 2655: gambling and betting winnings, Australian Taxation Office
  3. 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.