# How arbitrage works

# How arbitrage works

To understand how arbitrage works, we will try to convert a £25 sign-up bonus into real cash, using a live offer from a high-street bookie. In this example we will use decimal odds throughout, since this will make the necessary calculations very easy.

## A) An idealised example: No commission at exchange

We use this example simply to understand the principle of arbitraging and the simple maths behind atbitraging bets; the inclusion of commission only leads to slighlty more complicated calculations, but does not change the principles involved.

**Step 1: The qualifying bet**

In this step we simply want to keep the loss as small as possible; on a £25 bet, the loss should ideally be around £1. In case you find anything better or a proper arbitrage producing a small profit, all the better. Since it does not really matter on what we bet, we can use something unsuspicious, e.g., a bet in a normal win/draw/win market; sometimes, this first bet has to meet minimum odds requirements, e.g. odds of 2.0 or higher. After comparing some back and lay odds, I decide for the following back bet: Portugal v Sweden – The Draw @ 3.9, giving a virtual payout of *£25 * 3.9 = £97.50* and possible winnings of *£25 * (3.9-1) = £72.50*.

I chose this bet since I can lay it at an exchange for odds of 3.95. The optimal lay stake can be easily calculated by dividing the virtual payout by the odds of the lay bet, i.e., as *£97.50 / 3.95 = £24.68*; the liability of this bet is* £24.68 * (3.95-1) = £72.81*. Thus we have the following two bets:

- Back bet: £25.00 @ 3.9, possible winnings of £72.50
- Lay bet: £24.68 @ 3.95, liability of £72.81

If the back bets comes in, our total profit/loss is the winnings of the back bet minus the liability of the lay bet, i.e.,* £72.50 – £72.81 = -£0.31*. If the lay bet comes in, we win the lay stake but lose the back stake, so our total profit/loss is * £24.68 – £25.00 = -£0.32*. We see that we make the same small loss in both cases.

**Step 2: The free bonus bet**

In most cases the free bet will be of the type “stake not returned”, which means that your payout will only consist of the winnings portion of the bet. This means for our calculations that the virtual payout of our back bet is identical to the possible winnings from this bet, not to the possible winnings plus its stake. For this reason it is also preferable to **use bets with higher odds** (ideally from ~7 and up, if one can afford the liability) in the conversion of the free bet; often, horse racing is ideal for this. In this example, I stay with football and choose the following bet: Ukraine v France – 1:0 Correct Score @ 9.5, giving possible winnings and virtual payout of *£25 * (9.5-1) = £212.50*.

I chose this bet since I can lay it at an exchange for odds of 9.6. The optimal lay stake can again be easily calculated by dividing the virtual payout by the odds of the lay bet, i.e., as *£212.50 / 9.6 = £22.14*; the liability of this bet is* £22.14 * (9.6-1) = £190.40*. Thus we have the following two bets:

- Back bet: £25.00 @ 9.5, possible winnings of £212.50
- Lay bet: £22.14 @ 9.6, liability of £190.40

If the back bets comes in, our total profit/loss is the winnings of the back bet minus the liability of the lay bet, i.e.,* £212.50 – £190.40 = £22.10*. If the lay bet comes in, we win the lay stake, but this time we don’t lose any back stake, since we used a free bet; therefore, our total profit is * £22.14 – £0.00 = £22.14*. Independent of the result of this match, we make a profit of over £22.

In the ideal world, this two step process thus would result in a total profit of £21.80.

## B) The real world: Exchange charging 5% commission

The principle remains unchanged, and so do the back bets. Nevertheless, the optimised lay stakes change, and with that our liabilities as well as the overall profits and losses of each arbitrage. Fortunately, Blarber, our back/lay arbitrage calculator, will do all the maths now, and we end up with:

**Step 1: The qualifying bet**

- Back bet: £25.00 @ 3.9, possible winnings of £72.50
- Lay bet: £25.00 @ 3.95, liability of £73.75

Total loss: £1.25

**Step 2: The free bonus bet**

- Back bet: £25.00 @ 9.5, possible winnings of £212.50
- Lay bet: £22.25 @ 9.6, liability of £191.35

Total profit: £21.15

Even in the real world this simple two-step process leads to a total profit of £19.90. We just converted a **£25 sign-up bonus** into **real £19.90**! Hooray, free cash!