The art of making a book is to 'balance' it so that a profit is made no matter what the outcome. Bookmakers make money by offering odds that are different to the real probabilities in the underlying event.
Our binary bookmaker decides to accept betting on an event where there are only two outcomes. He decides to choose on whether the Footsie will move up or down
The bookmaker might open his book by offering odds of 2-1 on the Footsie Moving Up and 6-4 on the Footsie Moving Down (i.e. against the Footsie moving up). By a simple calculation (Two divided by three, the sum of the odds) we can see that 2-1 on represents a probability of 66-67 per cent and 6-4 against represents 40 per cent (Four over ten).
The probabilities add up to 106.67. The excess of 6.67 over 100 percent is known as the over-round. In short he has sold odds of 106.67 but the outcome can only ever be 100. There is a 100% chance that the Footsie will move up or down. (We are talking simplistically here). The bookmaker, if he can take bets in the proportion of the probabilities, say £66.67 on the Footsie moving up and £40 on the Footsie moving down, will pay out £100 whichever wins on £106.67 taken, a percentage profit to him of 6.25 per cent.
In practice, of course, the binary bookmaker will need to adjust his odds in accordance with supply and demand. More money bet on the Footsie moving down than the estimated probability indicates will cause him to shorten the odds against the Footsie moving down and lengthen those for the Footsie moving up. The same principle also works on the stock market when market makers buy and sell shares on their books at different bid and offer prices.
His final book might look like this :-| Footsie Moving Up | Footsie Moving Down |
| £50 @ 2-1 on | £40 @ 6-4 |
| £42 @ 4-6 on | £32 @ 5-4 |
| £50 @ 4-5 on | £30 @ Evens |
In this example, he began by seriously under-estimating the demand on the Footsie moving down, and has been forced to reduce his odds from 6-4 to evens, at the same time offering better odds on the Footsie moving up. Before adjusting his odds he stood to pay out £100 on the Footsie moving down, having taken only £90 in stakes. The odds offered on an event with many possible outcomes is calculated and adjusted in the same way. The over-round usually increases with the size of the field.
In short as I once heard in a gambling forum "If you see a binary bookie jump out of a window follow him........ There must be money in it"!
The key to arbitrage is ensuring you back a bet 'under round', lay it 'over round' or lay a bet under the price at which you can back it. When we say back a bet under round, what we are saying is that we want to back all the outcomes of an event for less than a 100% chance. We want to buy 100% probability for less than 100%.
Normally we would expect the back side of a book to be over round, priced above 100% chance. That's because this is the way that bookmakers make money. If we had a two runner market like a tennis match or a FTSE daily up and down market and both sides of the market were priced at 1.96, then the book would have 4% margin in it. This is because if we laid £10 at 1.96 and both orders were filled, we would have a liability of £9.60 with a guaranteed return of £10.
Normally the market operates with an over round in place. However, there are times when it is possible that the book is firmly in the punter's favour. Quite a common arbitrage opportunity occurs on small fields. This typically means sports events such as a tennis, football or even a financial binary betting market. Services such as Betbrain.com have a sports 'sure bet' service which scans all bookmakers it lists to search out arbitrage positions. When writing this article, I visited the site and there were 47 arbitrage opportunities available on future sports events. In some cases the book was under round by up to 9% - in other words you could back all selections with different bookmakers and the payout would exceed your stake by 9%.
However, a lot of the arbitrages were tiny. One football match, Motherwell versus Falkirk, had an opportunity on the over and under 2.5 goal market. You could back over 2.5 goals at 1.92 with 52% of your stake and also back under 2.5 goals at 2.10 with 47% of your stake. You would have a 100% return for staking just under 100% of your money for something that will certainly happen - i.e. the match will have over or under 2.5 goals.
The trick of course is finding bookmakers to take your bet at the right price and finding the opportunity. Services such as Oddschecker.com allow you to see that whole betting market at a glance and instantly spot any arbitrage opportunities. There are also specialist services which exist to purely serve this market.
If you are watching a horse race on-course and see a horse offered at 3/1 but spot that the price lower than that on an exchange, there is no reason why you should not back on course and lay off on the exchange. All you do is take up one price and lay the same amount on the exchange.
Just browsing the financial markets can often throw up opportunities if you are quick enough. In the illustration, you can see we are watching the FTSE hourly up or down market and on Binarybet are able to lay the index to close down for the hour at 1.50 while over on Betfair it is trading at 1.53 to back. This means we can lay £221 at 1.50 and back it at 1.53 to net the difference as profit.
The only thing you need to remember is to lay a price lower than your back price, therefore at a lower liability, and to back above any lay price. If you are using an exchange you will also need to ensure you account for your commission rate. To fail to do so may leave you out of pocket. When looking at sports markets, services such as Oddschecker will allow you to preset your commission so you can be sure the price you are using is accurate.
While arbitrage involves fairly low risks, generally it is impossible to close two or three transactions at exactly the same instant. Therefore, there is the possibility that when one part of the deal is closed, a quick shift in prices makes it impossible to close the other at a profitable price. There is also counter-party risk, the risk that the other party to one of the transactions fails to deliver as agreed: though unlikely, this hazard is serious because of the large quantities one must trade in order to make a profit on small price differences.
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