Arbitrage calculator.

Type the odds for each outcome. It tells you whether they make an arb, how much to put on each bet, and what comes back whichever way the game ends.

Arb+3.73%Stakes
Market
Odds format
Outcome 147.6% implied
Outcome 248.8% implied

Fee: the commission a betting exchange takes from your winnings on that bet. Leave it empty for a bookmaker.

Round each stake to
Where the profit lands

"Only" puts the whole profit on one outcome. Any other result gives your stake back and nothing more.

Result

Arb +3.73%

The prices add up to 96.40%. The missing 3.60% is what pays you, whichever way it ends.

Stake, return and profit for each bet
BetStakeReturnsProfit
1Outcome 1493.981,037.36+37.36
2Outcome 2506.021,037.34+37.34
Total staked1,000.00

How it works

Every price a bookmaker offers hides a probability: 1 divided by the decimal odds. Odds of 2.10 say "47.6%". Take the best price for each outcome of one event, each from a different bookmaker, and add those percentages up.

A single bookmaker always lands above 100%, and the part above is its margin. When the best prices from different bookmakers land below 100%, the shortfall is an arbitrage: split your money in proportion to those percentages and every outcome returns the same amount, more than you put in.

S = 1 ÷ 2.10 + 1 ÷ 2.05 = 0.9640 (under 1, so it is an arb) profit = 1 ÷ S − 1 = 3.73% of the total staked stake on each bet = total × (1 ÷ its odds) ÷ S

The step-by-step version, with a three-way example and the awkward cases, is in How to calculate an arb.

Questions

What goes in the fee field?

The commission a betting exchange charges on the net winnings of that bet, in percent: 2, 5, whatever your exchange takes. The calculator lowers the price accordingly (2.08 at 2% is really 2.058) before it does anything else. A bookmaker charges no commission, so leave the field empty. Every bet here is a back bet; laying on an exchange is different arithmetic and is not covered.

Why round the stakes?

A stake of 493.98 is a signature. Rounded stakes look like everyone else's, and bookmakers limit accounts that look like arbers. Rounding moves the returns apart a little, so the slip shows the real profit on each outcome after rounding, and warns you when a step is so coarse that one outcome no longer covers the total.

What is "only 1" or "only 2" for?

It puts the whole profit on one outcome. The other bets are sized to return exactly your total stake, and everything left goes on the outcome you chose. You cannot lose on paper, you win more if you are right, and you win nothing if you are not. People use it when they have an opinion on the game, or when one bookmaker's limit is too low for an even split.

Does a positive number mean guaranteed profit?

No. It means the sum works for the prices you typed. Prices move between your first bet and your second, bookmakers void bets on obvious pricing errors, stake limits cut a bet short, and two bookmakers can settle the same event differently. The calculator knows none of that. Check both prices on the bookmakers' own pages before you bet.