What a rounded stake, a voided leg or a moved price does to an arbitrage

An arbitrage gain of about 15 on 1,000 can be moved by small things. Rounding stakes to whole numbers shifts it by a pound or two, but one leg accepted at a lower price or voided turns the result from a fixed gain into a bet that can lose about 21. The calculation is exact. The execution is where the margin goes.

The arbitrage calculator shows the margin and stakes for exact prices; this page shows how it behaves when the real world does not match.

The starting position

Prices of 2.04 and 2.02 total 98.52% (the working is in the stake article). On 1,000 the exact stakes are 497.54 and 502.46, and either result returns 1,014.98, a gain of 14.98.

1. Rounding the stakes

Few accounts take stakes to the cent on every market, and many people prefer whole numbers.

The rule is that rounding error is about half the rounding step times the price, so it matters most when the margin is thin and the minimum step is large relative to the stake.

2. One price moves before the bet is accepted

The 2.02 side is accepted at 1.95 instead. The stakes stay 498 and 502. If the 2.04 side wins you still gain 15.92. If the 1.95 side wins you receive 502 × 1.95 = 978.90 against 1,000 outlay, a loss of 21.10. The sum of probabilities is now 0.4902 + 0.5128 = 1.003, over 100%, so no split can make both sides pay. You hold a bet that wins 15.92 or loses 21.10, and the result depends on the match.

Prices can move because the bet slip ticks, because a price is withdrawn on an event the moment you confirm it, or because a stake over a limit is accepted only in part. Whatever the cause, the second bet placed is the one at risk. Some people place the harder-to-get price first for that reason.

3. A leg is voided

A bet can be cancelled for a pricing error, for a stake over a limit, for a match that does not start, or because the market rules differ from the other book's. A void returns the stake.

An abandoned or postponed match can void one place's bet while the other keeps it open for a longer window. Terms on this are in the article on voids, and they differ between places. Read both before assuming the two legs settle together.

4. A line that is not quite the same

On totals and spreads, a half-point difference between two places makes a middle or a hole rather than an arbitrage. Over 220.5 at one place and under 221.5 at the other is a middle: both bets win on a total of 221, and on any other total one wins and one loses, so the result depends on the prices and not on the sum test. Reverse the two lines, over 221.5 and under 220.5, and a total of 221 loses both. Only the same line on opposite sides gives the sum test its meaning.

Check the margin first. The arbitrage calculator gives the exact stakes and the gain for each side, so you can see how much room there is before rounding or a change in price removes it.