Arbitrage calculator: stakes, return and margin across two or three outcomes
The arbitrage calculator checks whether the prices on each outcome of one market add up to less than 100% implied probability. Enter the odds for each outcome and a total stake. It prints the implied probabilities, their sum, the stake per outcome for an equal return, and the profit in dollars and percent, or the margin if there is none.
| Outcome | Odds | Implied probability | Stake | Returns if it comes in |
|---|---|---|---|---|
| Outcome 1 | 110 | 47.62% | $500.00 | $1,050.00 |
| Outcome 2 | 110 | 47.62% | $500.00 | $1,050.00 |
- Implied probabilities, total
- 95.24%
- Return, whichever outcome
- $1,050.00
- Profit
- +$50.00
- Profit, % of total stake
- 5.00%
An arbitrage exists on paper: the implied probabilities add up to 95.24%, which is under 100%.
Why an arbitrage on paper can still lose money
- Limits. Each book caps what it accepts on a market. The stake you need on one outcome may be larger than that book allows, and a smaller stake breaks the equal return.
- Voids and palpable errors. A book can void a bet it considers a pricing mistake, or settle a push or a void differently from the other. If one bet is voided and the other stands, you hold an ordinary single bet.
- Price movement. The second bet is placed after the first. If the price on the second outcome moves before it is accepted, the equal return is gone and the first bet stands alone.
- The outcomes must cover the market. A two-way entry assumes no draw or third result. Enter all three outcomes where one is possible.
Arithmetic on the prices you type in, taken from two books or more. Prices quoted on a screen may not be available at the stake shown.
The arbitrage formulas
Implied probability = 1 ÷ decimal odds. Sum S = 1/d1 + 1/d2 (+ 1/d3). Arbitrage exists when S < 1.
Stake on outcome i = total × (1/di) ÷ S. Return, whichever outcome = total ÷ S. Profit = total ÷ S − total, and profit % = 1 ÷ S − 1.
Worked example
Two books price the same match. One offers +110 on player A and the other offers +110 on player B, which are both 2.10 in decimal. Each implied probability is 1 ÷ 2.10 = 47.62%, and the sum is 95.24%, under 100%. With $1,000, stake $500.00 on each. Either outcome returns $500 × 2.10 = $1,050.00, a profit of $50.00 or 5.00%. In an ordinary -110 / -110 market the sum is 104.76%, a margin of 4.76%, and the same split returns $954.55 on $1,000, a loss of $45.45.
Questions
What is an arbitrage bet?
An arbitrage is a set of prices on every outcome of one market where the implied probabilities add up to less than 100%. Staking each outcome in proportion to its implied probability returns the same amount whichever outcome comes in, and that amount is above the total staked.
How do you calculate arbitrage stakes?
Convert each price to decimal odds d, find S as the sum of 1/d, and stake total × (1/d) ÷ S on each outcome. Every outcome then returns total ÷ S. If S is 1 or more there is no arbitrage and the same split returns less than the total.
Why is an arbitrage on paper not a sure return?
The equal return holds only if both bets are accepted at the stake and price shown and settle the same way. Limits can cap one stake, a book can void a bet it calls a pricing error, and the price on the second outcome can move before you place it.
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