The formula
Take the best price for each outcome and add up 1 ÷ odds. If the total is below 1, there is an arbitrage. The return on the total stake is 1 ÷ total − 1.
Example. Player A at 2.10 at one bookmaker, player B at 2.05 at another.
1 ÷ 2.10 + 1 ÷ 2.05 = 0.4762 + 0.4878 = 0.9640. Below 1, so this is an arbitrage. Return: 1 ÷ 0.9640 − 1 = 3.7 %.
How to split the stakes
Each stake is the total stake × (1 ÷ odds) ÷ total. For €100 in the example above:
| Bet | Odds | Stake | Payout if it wins |
|---|---|---|---|
| Player A | 2.10 | €49.40 | €103.74 |
| Player B | 2.05 | €50.60 | €103.73 |
You stake €100 and get about €103.73 back, whoever wins.
With a betting exchange
You can also cover a bet by laying the same outcome on an exchange. The commission counts: with 2 % commission, a win at odds of 2.20 is worth only 1 + 1.20 × 0.98 = 2.176.
Example. Back at 2.30 at a bookmaker with €100, lay at 2.26 on an exchange with 2 % commission.
Lay stake = 100 × 2.30 ÷ (2.26 − 0.02) = €102.68, with €129.37 at risk on the exchange. Either way, about €0.63 is left. Prices that look close leave little after commission.
What are middles?
A middle uses two different lines. For example, team A −2.5 at one bookmaker and team B +3.5 at another. If A wins by exactly three goals or points, both bets win. In every other case one bet wins and one loses, and you pay a small cost. A middle is not risk-free. It is a cheap ticket on a rarer outcome, and it only pays if that outcome is priced too low.
Why arbitrage is not risk-free
- The second bet can fail. The price moves or the stake is capped after the first bet is placed. You then hold an open position you never wanted.
- Different rules. Bookmakers settle retirements in tennis, overtime or abandoned matches differently. One bet can be voided while the other stands.
- Obvious errors. A price that looks too good is often a mistake, and a bookmaker may void it in its terms.
- Money is tied up. You need balances at many bookmakers, for a small return per bet.
- Accounts get limited. Bookmakers limit winning accounts, and this is your risk.
Arbitrage or value betting?
Arbitrage locks in a small return per bet, if both sides go through. Value betting takes one side only: results swing far more, and it does not need a second price at the same moment. Many professionals do both.
The Manometer board shows arbitrage and middles across bookmakers and the exchange with stake splits, next to value bets against the Pinnacle fair price.
All guides: overview. Betting is for adults only and can be addictive: responsible betting.