Arbitrage Calculator

Three sums give every stake, and the arbitrage calculator above runs them as you type. Here they are for India at 2.10 and Australia at 2.00, with ₹1,000 to bet.

1. Add up 1/odds for each result. 1/2.10 = 0.47619 and 1/2.00 = 0.5, so the sum is 0.97619, or 97.62%. Under 1 means a sure bet.
2. Split the stake. Each stake is the total × 1/odds ÷ 0.97619. That puts ₹487.80 on India and ₹512.20 on Australia.
3. Work out the return. The total ÷ 0.97619 = ₹1,024.39, whichever side wins. The profit is ₹24.39.

Your profit as a share of the stake is 1 ÷ the sum, minus 1. Here that is 2.44%. With 2.10 on both sides, the prices add up to 95.24%, and ₹500 on each side returns ₹1,050: a 5.00% profit.

Say two bookmakers price the same India v Australia match. On its own, each book's prices add up to more than 100%, so neither is a sure bet.

Take the best price for each result and the sum falls to 97.62%. Bet ₹487.80 on India with Book A and ₹512.20 on Australia with Book B. Either result then returns ₹1,024.39 for your ₹1,000.

In whole rupees, that is ₹488 and ₹512. If India win, Book A pays 488 × 2.10 = ₹1,024.80. If Australia win, Book B pays 512 × 2.00 = ₹1,024.00. So the profit is ₹24.00 to ₹24.80, if both bets stand. Type 2.10 and 2.00 into the arbitrage calculator to see both versions.

A bookmaker builds a margin into its odds by paying out a little less than the fair price. That is why one book's prices for all results normally add up to more than 100%. The extra is the overround, or margin. Our implied probability calculator shows it for any market.

So a sure bet needs two books to disagree by more than their margins. Above, Book A has the bigger price on India and Book B the bigger price on Australia. To look for a gap, start from one price, such as the match odds on our cricket odds page, and compare it with other books.

When there is no sure bet, the arbitrage calculator shows the price each result would need. Enter Book B's prices alone, India 1.90 and Australia 2.00, and it asks for 2.01 or more on India. Book A's 2.10 clears that.

No. The sums are exact, but they lock in a return only if every bet stands at the odds you took. These are the ways it breaks.

• The price moves. Odds change all the time. If the second price drops before you bet, the sure bet can vanish and you hold one open bet.
• Stake limits. A bookmaker can cap how much it takes. If one bet is accepted for less than you asked, the stakes no longer balance.
• A voided bet. A bookmaker can cancel a bet after it is placed. If one side is void and the other stands, you hold an ordinary bet with nothing locked in.
• Settlement rules. Each bookmaker sets its own rules for a tie, a super over, a rain-reduced match and a no-result. If two books settle the same match in different ways, the return is no longer the same. Read both sets of rules first.
• Account limits. Bookmakers look out for arbitrage. Accounts that do it often get lower stake limits, and some are closed.
• Commission. If a site takes commission on winnings, set it in the calculator. At 5% on both bets, the 2.10 and 2.00 example turns into a loss of ₹1.81.

A Test can end in a draw, so its match odds have three results: either team or the draw. A sure bet has to cover all three, so use the 3-way tab of the arbitrage calculator.

Say England are 2.50 at Book A, India 3.10 at Book B and the draw 4.00 at Book C. 1/2.50 + 1/3.10 + 1/4.00 = 0.9726, or 97.26%. On ₹1,000, the calculator puts ₹411.28 on England, ₹331.67 on India and ₹257.05 on the draw. Each result returns ₹1,028.19, a 2.82% profit, if all three bets stand.

Leave out the draw and the sum drops to 72.26%. That looks like a big sure bet, but a draw would lose both bets. T20 and ODI match-winner markets usually list just the two teams. There, a tie may go to a super over, and each bookmaker's rules say how a tie is settled.

Back-lay, or khai-lagai, is another way to cover a match. You back a team (lagai) and lay the same team (khai), which means betting that it will not win, usually on an exchange. When the back price is higher than the lay price, the pair can show a profit whichever side wins. Our khai-lagai calculator works out the lay stake, and back and lay betting explained covers the terms.

Dutching splits a stake over several selections so each one returns the same if it wins, as this calculator does. The difference is cover. Dutching often backs only some of the results, so it can lose. An arbitrage covers every result. Our dutching calculator handles two to six selections.