Arbitrage Betting Calculator: Split One Stake So Every Result Pays

How to use the arbitrage calculator

1. Pick the odds format you will type in.
2. Set the number of outcomes. A market with a draw needs three; a tennis match or a two-way handicap needs two.
3. Enter the best available price for each outcome. Each price will usually come from a different site.
4. Type the total stake you want to spread across the market.
5. Read the sum of implied probabilities first. If it is under 100%, the table gives the stake for each outcome and the return each would pay.
6. Place the bets in the order explained under the risks below, starting with the price most likely to move.

The formula behind the split

Every decimal price converts to an implied probability of one divided by the odds. Add those for all outcomes and call the total Σ.

Σ = 1/odds₁ + 1/odds₂ + … + 1/oddsₙ

If Σ is below 1, each outcome gets:

stake_i = total / (odds_i × Σ)

Every outcome then returns total / Σ, and the profit is total / Σ − total. The profit percentage is 1/Σ − 1. The stake on each outcome is its share of Σ: a short price carries a large slice of the probability, so it takes a large slice of the money.

Worked example: a two-way market at 2.10 and 2.05

Two players, two sites. One sportsbook prices the first player at 2.10, another prices the second at 2.05. The total stake is 100.

Σ is 0.4762 + 0.4878 = 0.9640, or 96.40%. The exact return is 100 / 0.9640 = 103.73, a profit of 3.73 on 100, or 3.73%. Once the stakes are rounded to the cent, 49.40 × 2.10 pays 103.74 and 50.60 × 2.05 pays 103.73, so the result is 3.73 or 3.74 depending on which player wins. Either way the 100 comes back with the margin on top.

A gap of 3.7% is large. It is a clean teaching number, but prices this far apart tend to be the ones a site corrects within minutes.

Worked example: a three-way football market

Football adds the draw, so all three outcomes need covering. Suppose the best prices across three sites are 2.50 on the home side, 3.50 on the draw and 3.25 on the away side, with a total stake of 200.

Σ comes to 99.34%. The exact return is 200 / 0.99341 = 201.33, a profit of 1.33, which is 0.66% of the stake. Rounding moves each return by a cent either side of that figure. This is what a typical football arbitrage looks like: real, and thin. It takes three accounts, three bets placed quickly and a fair amount of money to earn little more than one unit.

Why margins make arbitrage rare

Each sportsbook prices a market so that its own implied probabilities add up to more than 100%. The excess is the margin. Two players at 1.91 each add up to 104.71%; back both for 50 and you get 95.50 back on 100 whichever wins. A football match at 2.40, 3.30 and 3.00 adds up to 105.30%. Inside one site, every split of the stake loses.

Arbitrage needs the opposite: the best price on each outcome must come from a site that disagrees with the others by more than both their margins combined. That happens when one sportsbook is slow to react to team news, when sites set prices from different models, or when one shades a price to attract money on a side. Low-margin books make the gap easier to reach, which is why bettors who look for arbitrage start with the sites with the best odds. To measure the margin of a single site's market, use the odds calculator.

Main markets on major events are priced tightly and move together, so gaps there are small and close fast. Lower leagues, player markets and early prices drift further apart, and that is where most arbitrage betting opportunities appear.

The practical risks

The arithmetic is exact. What happens between the calculator and the settled bets is not.

The price moves before the second bet. You place one side, and by the time you reach the other site, its price has dropped. The arbitrage is gone and you hold a single bet you did not want. Place the bet on the price most likely to move first, usually the one that stands out from the rest of the market, and keep enough balance on every site to act at once.

Palpable-error voids. Sportsbook terms allow a bet struck at an obvious pricing mistake to be voided or resettled at the correct price. If one leg is voided and the other stands, your position is a straight bet. Prices far out of line with the market are exactly the ones at risk.

Stake limits. A site may accept only part of the stake you asked for. A smaller stake on one side breaks the balance; enter the accepted amount back into the arb calculator and rework the other legs before placing them.

Account restrictions. Sites watch for accounts that only bet when their price is out of line. Restrictions to small maximum stakes are common, and some accounts are closed. Mixing in ordinary bets does not change the pattern for long.

Different settlement rules. Two sites can settle the same event differently. Tennis is the usual example: if a player retires injured, one sportsbook may void match bets, another may settle them once a set is complete, another may pay whoever goes through. If your two legs follow different rules, you can lose one side while the other is refunded. Overtime, abandoned matches and dead heats raise the same question in other sports, so read the rules for the market before staking. Retirement rules are covered in more depth on the tennis betting hub.

What the calculator does not include

• Rule differences between sites. The arbitrage calculator assumes every leg is settled on the same result.
• Exchange commission or deposit and withdrawal fees. Subtract them from the profit yourself.
• Currency conversion. If your accounts hold different currencies, exchange rates can erase a thin gap.
• Rounding by the sportsbook. Some sites round stakes or returns; recheck with the amount actually accepted.
• Whether the price is still there. The figures are only as current as the odds you typed.

For full bet slips, from doubles to each-way and full-cover bets, use the bet calculator.

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