Arbitrage betting calculator

Enter the two prices you have been offered on opposite sides of the same market and a total stake. The calculator returns whether the pair leaves a locked profit, how to split the stake so both outcomes pay the same, and what that profit is as a share of the money at risk. Nothing to sign up for, and nothing is stored.

Arbitrage is a strategy independent of sports and of prediction. It does not use a forecast, a model or a simulation, and it does not care which team is better or which side is more likely. It is arithmetic on two prices. If the two implied chances add up to less than 100%, the gap is a profit that exists whatever happens on the field, and if they add up to more than 100% there is nothing there. That is the whole method, and it works identically on baseball, tennis, an election or the weather.

Everything else on this site is the opposite kind of question. Outside arbitrage, the first step on any bet is to check the price against what the simulations say the outcome actually is, because a single price on a single side is only good or bad relative to a probability. Check a bet before you place it.

How is an arbitrage calculated?

Convert both prices to their implied chances and add them together.

  1. Convert each American price to a decimal price.
  2. Take 1 divided by each decimal price. That is the chance each price implies.
  3. Add the two implied chances. Call the total the book sum.
  4. If the book sum is below 1, the pair is an arbitrage and the profit is 1 minus the book sum, as a share of the total stake.

A worked example. One book has the home side at +115, another has the away side at -105:

How do you split the stake?

Each side gets the share of the total stake that matches its implied chance, divided by the book sum. On the example above, a $1,000 total stake splits to about $476 on the +115 side and about $524 on the -105 side. Either result returns about $1,023, so the profit is about $23 whichever way the game goes.

Splitting it any other way is not an arbitrage. It is two bets that happen to be on opposite sides, and one outcome pays more than the other.

Why is the book sum usually above 100%?

Because the rake is in every price. A book prices each side to balance its own action and bank a margin, so both implied chances are shaded up and the pair adds to more than 100%. The overage is what the book keeps. That is the normal state of a market, and it is why arbitrage opportunities are rare rather than routine: the sum has to come out below 100% before there is anything to take.

What makes an arbitrage stop being one?

The arithmetic assumes both bets get placed, in full, at the prices you saw. In practice:

The calculator prices the pair you enter. It cannot tell you whether both bets will still exist a minute later, and that risk is the reason the arithmetic is the easy part.

Is an arbitrage the same as a good bet?

They are unrelated questions, and this is the one to be clear about. An arbitrage does not need the price to be wrong about the world. It needs two prices to disagree with each other by more than their combined rake.

A bet that is not part of an arbitrage is a forecast whether you call it one or not, and its price is only good or bad relative to how often the outcome actually happens. That number has to come from somewhere other than the price on the slip. On this site it comes from thousands of simulated runs of the game itself, which is what the bet checker grades against.

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