The one-line test
Turn each price into an implied probability by dividing 1 by the price, and add up every possible outcome. If the total is under 1, there is a surebet. With 2.10 and 2.10 the sum is 0.952: there is margin. With 1.90 and 1.90 the sum is 1.053, and there the bookmaker is the one winning.
How to split the stake
The share going to each side is its implied probability divided by the total sum. In the 2.10 and 2.10 example that is half and half. When the prices differ, so does the split: the shorter price takes more money, because it pays less per unit.
A full worked example
Prices of 2.30 and 1.95 at different bookmakers. The implied probabilities are 0.435 and 0.513, adding up to 0.948. On 10,000 units, 4,588 go on the first side and 5,412 on the second. Whichever one lands, you collect around 10,552: the margin is the difference against the 10,000 you put in.
The realistic margin
Large surebets barely exist: when they appear it is usually because of an error that gets corrected within minutes. What you actually find are small margins, and with small margins any detail eats them: a commission, a stake limit, an exchange rate or a delay on the second click.
The risks the calculator does not show
That the second bet does not go through and you end up exposed on one side. That the bookmaker voids it for a palpable pricing error. That your account gets limited, which is what usually happens once the pattern becomes obvious. And rules risk: not every bookmaker settles an abandoned match the same way.
Why the maths is worth knowing anyway
Even if you never arbitrage for a living, the same calculation tells you how much margin a bookmaker is charging you and which one pays best on the market you want. It is the simplest tool there is for stopping betting blind against the price.