Arbitrage Calculator

What is an arbitrage in sports betting?

Bookmakers offer odds based on the probability of any one outcome. Bettors earn money by wagering on options where the bookmaker's estimate of the probability of an outcome is lower than the bettor's own estimate. An arbitrage, or a "sure bet", opportunity can appear when two bookmakers have different enough views on event outcomes.

As an example, in a match between two players, you could be offered the following odds for a 2-way bet:

Bookmaker	Option 1	Option 2	Margin
A	1.8	2.1	3.17 %
B	2.2	1.7	4.28 %
Highest	2.2	2.1	-6.93 %

From the profit margin we can see that there exists an arbitrage opportunity by

betting on option 2 on Bookmaker A, and
betting on option 1 on Bookmaker B.

3-way bets work the same way. For example, in a match between two teams, you could be offered the following odds for a 1x2 bet:

Bookmaker	Option 1	Option 2	Option 3	Margin
A	2.0	3.0	3.5	11.9 %
B	1.8	4.5	3.0	11.11 %
C	2.8	3.0	3.0	2.38 %
Highest	2.8	4.5	3.5	-13.49 %

In this scenario, there is an arbitrage opportunity by

betting on option 3 on Bookmaker A,
betting on option 2 on Bookmaker B, and
betting on option 1 on Bookmaker C.

But how much should you wager? To take advantage of the arbitrage, the stakes must be computed for each bookmaker -- and that is exactly what this calculator was made for!

How does MeasuredBets surebet calculator work?

In practice, the calculator computes the stake ratio $\vec{r} = (r_1, \dots, r_n)$ between bets such that their payouts are equal when multiplied by odds $\vec{o} = (o_1, \dots, o_n)$ :

\vec{r} = diag (\vec{o}) * \vec{1}

The stakes $\vec{s} = (s_1, \dots, s_n)$ are then scaled to match the total stake $s$ :

\vec{s} = s * \vec{r}

When determining the total stake from an individual stake, we can use its ratio:

s = \frac{s_n}{r_n}

To satisfy the equations, you'll see the following behaviour when using the calculator:

If an option's odds are changed, new stakes are calculated based on the total stake
If an option's stake is changed, new total stake is calculated
If the total stake is changed, all individual stakes are re-scaled

Finally, because the equations work with continuous values, but most bookmakers with cents as the minimum divisable value, the exact results may have a couple cents of error.