Arbitrage calculator
Key facts
- An arb exists when the best prices for every outcome, from different bookmakers, imply chances that add up to less than 100%.
- Stake on each outcome = total stake x (1 / its odds) / market total. The return is the same whichever outcome wins.
- $2.12 and $2.05 add up to 95.95%. $100 split $49.16 and $50.84 returns $104.22 either way, a $4.22 profit.
- Bonus bets work differently: the stake is not returned. A $50 bonus bet at $4.00 hedged with $115.38 at $1.30 locks in $34.62.
How to use the arbitrage calculator
Enter your total stake, then the best decimal price you can find for each outcome of one market. A head to head needs two prices; a soccer result needs three. The calculator adds up the market, tells you whether it is under 100%, and if it is, shows the stake for each outcome and the profit you lock in.
Every price must be for exactly the same market. A head to head that includes extra time and a three-way result that settles at full time are different bets, even on the same match.
How the arbitrage maths works
An arb is a market where the best prices on offer cover every outcome for less than they pay out. The test is the same sum used for a bookmaker's margin:
- Add up 1 / odds for the best price on each outcome. Call it the market total.
- If the total is 100% or more, there is no arb.
- If it is under 100%, stake on each outcome = total stake x (1 / odds) / market total.
- Every outcome returns total stake / market total. Profit = that return minus your total stake.
Worked example: a two-way arb
One bookmaker offers $2.12 on Team A and another offers $2.05 on Team B. 1 / 2.12 = 47.17% and 1 / 2.05 = 48.78%, so the market total is 95.95%.
| Outcome | Best price | Stake from $100 | Returns | Profit |
|---|---|---|---|---|
| Team A wins | $2.12 | $49.16 | $104.22 | $4.22 |
| Team B wins | $2.05 | $50.84 | $104.22 | $4.22 |
The profit is 1 / 0.9595 - 1 = 4.22% of the total, whatever the stake. Scale up to $500 and the stakes become $245.80 and $254.20, returning $521.10 and $521.11 after rounding to the cent.
Three-way arbs and near misses
Soccer and other sports with a draw need all three prices. Here are two examples at $200.
| Prices (home, draw, away) | Market total | Stakes | Profit |
|---|---|---|---|
| $2.30, $3.60, $3.75 | 97.92% | $88.80, $56.73, $54.47 | about $4.24 (2.12%) |
| $2.40, $3.50, $3.40 | 99.65% | $83.63, $57.34, $59.03 | about $0.70 (0.35%) |
The second line is technically an arb, but a 70 cent profit on $200 disappears with one price change or one rounding of a stake. The smaller the gap under 100%, the less room you have for any of the problems below.
Arbitrage calculator for bonus bets
A bonus bet is not a cash stake. On the TAB, when a bonus bet wins, the stake goes back to TAB and only the winnings are credited to your account. That changes the maths, so the calculator above (built for cash stakes) does not apply directly. Use this instead:
- Bonus bet of B at odds A. If it wins, you get B x (A - 1).
- Cash hedge on the other outcome at odds H, stake = B x (A - 1) / H.
- Locked-in amount = B x (A - 1) - hedge stake, the same either way.
| Bonus bet at | Hedge price | Hedge stake | Locked in from a $50 bonus | Share of bonus kept |
|---|---|---|---|---|
| $1.50 | $2.60 | $9.62 | $15.38 | 30.77% |
| $2.00 | $1.90 | $26.32 | $23.68 | 47.37% |
| $3.00 | $1.45 | $68.97 | $31.03 | 62.07% |
| $4.00 | $1.30 | $115.38 | $34.62 | 69.23% |
| $6.00 | $1.17 | $213.68 | $36.32 | 72.65% |
Longer prices keep more of the bonus, because the stake you never get back matters less when the price is long. The cost is cash: the hedge stake climbs fast, and at $6.00 you need $213.68 in the other account. Check the conditions on any bonus too: the TAB says most of its bonus bets are valid for 7 days and that bets placed with a bonus bet cannot be cashed out. To lock in a profit on a cash bet you already hold, use the hedge bet calculator instead.
Pundit tip: write down both prices before you place the first bet. If the second price has moved by the time you get there, run the numbers again before you chase it.
What can break an arb
The maths is fixed once both bets are on. Getting both bets on is the hard part.
- Prices move. A price can change between your first and second bet, and the arb can be gone before you finish.
- Bets get refused or cut. The TAB's Conditions of Use say it may refuse a proposed bet "without giving notice or reasons" (clause 34.1) and may place limits on the bets you can buy over a period (clause 16.1).
- Settlement rules differ. The TAB's Victorian sports rules include extra time in results unless it says otherwise when you bet (rule 10.8), but where a draw price is offered, the result excludes extra time (rule 10.9). If a game is drawn and no draw price was offered, a dead heat rule divides the payout (rule 12.5). Make sure both of your bets settle the same way.
- In-play is out. Online in-play betting on sport is prohibited in Australia, so arbs during a game are not available online from licensed bookmakers.
The full guide to arbitrage betting in Australia covers where arbs come from and the bookmaker terms in more detail, and matched betting explains how exchanges are used to lock in bonus value, with the lay bet calculator for the exchange side. Check any one-bookmaker market with the implied probability calculator, split a stake across runners with the dutching calculator, or see every tool on the bet calculators page.
Frequently asked questions
How does an arbitrage calculator work?
It adds up 1 / odds for the best price on each outcome. If the total is under 100%, it splits your stake in proportion to each 1 / odds so every outcome returns the same amount, and shows the profit.
How much profit does an arb make?
The profit as a share of your total stake is 1 / market total - 1. A market at 95.95% returns 4.22% on the total staked; one at 99.65% returns only 0.35%, or 70 cents on $200.
How do you hedge a bonus bet?
Place the bonus bet at odds A and a cash bet on the other outcome at odds H with a stake of bonus x (A - 1) / H. For a $50 bonus at $4.00 and a hedge at $1.30, that is $115.38, and you keep $34.62 whichever side wins.
Is an arb really risk free?
No. The maths is fixed once both bets are on, but a price can move before your second bet, a bet can be refused or limited, and two bookmakers can settle the same event under different rules. Any of those can turn a small profit into a loss.
Why does this calculator say there is no arbitrage?
Because your prices add up to 100% or more. At one bookmaker that is normal, since every market carries a margin. You need the best price for each outcome, usually from different bookmakers.
Related reading
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Calculator Hedge bet calculator Got a futures bet or a multi that is one result from paying? Work out how much to put on the other side to guarantee a profit, what that guarantee costs you, and when a hedge cannot lock anything in. Read more 
Calculator First four calculator The first four needs the first four runners in exact order. See what a box or standout really costs and your flexi share of the dividend. Read more 
Calculator Quinella calculator A quinella pays if you pick the first two in any order. See what any quinella box costs, your flexi percentage and what you collect. Read more 
Calculator Multi bet calculator Add as many legs as you like and see the combined odds, what your multi returns and the real chance that every leg gets up. Read more 
Calculator Wagering calculator Work out how much you must bet to clear a casino bonus, what that costs on average, and whether the bonus is worth taking at all. Read more Sources
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