Using an arb calculator for 3-way markets, lay bets, and commission
An arb calculator works the same way for three outcomes as for two: add every leg's implied probability, and if the total is under 100%, split your stake in proportion. For a lay bet, it converts the lay odds into back odds and takes the exchange's commission off your winnings. Arbocado's free arbitrage betting calculator handles 2- to 6-way markets, lay bets, commission, and free bets.
- A 3-way market is an arbitrage when the implied probabilities of home, draw, and away add up to under 100%.
- Home at 2.55, draw at 3.60, and away at 3.30 add up to 97.3%, so $200 split across them returns $205.56 whatever happens.
- Laying an outcome at decimal odds L works like backing it to lose at L ÷ (L − 1), and the money at risk is the liability, not the lay stake.
- On a $100 back at 2.30 and a lay at 2.20, a 2% exchange commission lowers the locked-in profit from $4.54 to $3.40.
- An arb calculator can also put all the profit on one outcome and break even on the rest.
The short answer
An arb calculator runs one rule for any number of outcomes: add every leg's implied probability, check the total is under 100%, and give each leg a share of your stake equal to its implied probability divided by that total. Three outcomes take three stakes instead of two.
Lay bets need one extra step. The calculator converts the lay odds into the equivalent back odds, takes the exchange's commission off the winnings, and then balances the stakes. If you're new to the basic two-way math, start with how to calculate arbitrage bets.
3-way markets
Soccer's 1X2 market has three results: home win, draw, and away win. All three need a bet, and each can sit at a different book.
3-way arbitrage percentage
arb % = (1 ÷ home odds) + (1 ÷ draw odds) + (1 ÷ away odds)
| Outcome | Book and odds | Implied | Stake on $200 | Pays if it wins |
|---|---|---|---|---|
| Arsenal | bet365, 2.55 | 39.2% | $80.61 | $205.56 |
| Draw | BetMGM, 3.60 | 27.8% | $57.10 | $205.56 |
| Chelsea | Caesars, 3.30 | 30.3% | $62.29 | $205.56 |
Check that every book settles the market at 90 minutes plus stoppage time. A book that includes extra time is pricing a different bet.
Try the 3-way example
The calculator below is preloaded with these prices. Change any of the odds and the three stakes update. The full arbitrage betting calculator lives at the arbitrage calculator page and handles up to 6 outcomes.
3-way arb calculator
Arsenal 2.55 (bet365), draw 3.60 (BetMGM), Chelsea 3.30 (Caesars), $200 total.
Guaranteed profit $5.56 (2.78%) whichever outcome wins
Lay bets and commission
On an exchange you can lay an outcome, which means betting that it won't happen. That lets you cover both sides of a game with one sportsbook bet and one exchange bet on the same team.
Lay odds as back odds
equivalent back odds = lay odds ÷ (lay odds − 1)
Liability (what you risk on a lay)
liability = lay stake × (lay odds − 1)
Say you back the Dodgers for $100 at 2.30 on FanDuel and lay them at 2.20 on an exchange. With no commission, an arb bet calculator puts the lay stake at $104.55 (a $125.46 liability), and either result profits about $4.54. Most exchanges charge 2% to 5% on net winnings, which changes the numbers:
| Commission | Lay stake | Liability | Profit if Dodgers win | Profit if they lose |
|---|---|---|---|---|
| 0% | $104.55 | $125.46 | $4.54 | $4.55 |
| 2% | $105.50 | $126.60 | $3.40 | $3.39 |
At 2%, the lay winnings of $105.50 shrink to $103.39 after commission, so the calculator raises the lay stake to keep both outcomes even. The profit drops by about $1.15. Always enter the commission. An arb that ignores it can turn out to be a loss. For more on using exchanges, see the best sportsbooks and exchanges for arbitrage.
Putting the profit on one outcome
An even split gives the same profit on every outcome. You can also break even on all but one and put the whole edge there. With the same $200 and the profit on the draw, the stakes become $78.43 on Arsenal, $60.96 on the draw, and $60.61 on Chelsea.
| Result | Payout | Profit |
|---|---|---|
| Arsenal win | $200.00 | $0.00 |
| Draw | $219.46 | $19.46 |
| Chelsea win | $200.01 | $0.01 |
You still can't lose, but you only profit if the favored outcome hits. Use it when you think one result is underpriced.
Odds formats
A good arbing calculator accepts any format and converts it to decimal before doing the math. The 3-way prices above look like this in each:
| Decimal | American | Fractional | Implied |
|---|---|---|---|
| 2.55 | +155 | 31/20 | 39.2% |
| 3.60 | +260 | 13/5 | 27.8% |
| 3.30 | +230 | 23/10 | 30.3% |
Free bets work too: the stake isn't returned, so the calculator counts only the winnings. The matched betting comparison has a free bet example.
Skip the manual entry
Arbocado's Arbitrage Finder spots sure bets across books and exchanges and sizes every leg, so you don't have to type in odds.
Open the Arbitrage FinderTo put these numbers to work, follow the step-by-step guide to placing an arb.
Frequently asked questions
How do you calculate a 3-way arbitrage bet?
Convert each outcome's odds to implied probability (1 ÷ decimal odds) and add all three. If the total is under 100%, stake each outcome your total times its implied probability divided by that total. At 2.55, 3.60, and 3.30, $200 splits into $80.61, $57.10, and $62.29.
How does an arb calculator handle lay bets?
It treats a lay at odds L as a back bet on the outcome losing at L ÷ (L − 1), sizes the liability, then converts it to the lay stake you enter on the exchange (liability ÷ (L − 1)). Commission comes off the lay winnings before the stakes are balanced.
What's the difference between an arbing calculator and an arbitrage finder?
An arbing calculator sizes stakes for odds you already have. An arbitrage finder scans sportsbooks to find those odds in the first place, then sizes them. Arbocado has both: a free arbitrage calculator and the Arbitrage Finder.