Arbitrage betting

Betting arbitrage, surebets, sports arbitraging is a particular case of arbitrage arising on betting markets due to either bookmakers’ different opinions on event outcomes or plain errors. By placing one bet per each outcome with different betting companies, the bettor can make a profit.

In the bettors’ slang an arbitrage is often referred to as an arb. A typical arb is around 2%, often less, however 4%-5% are also normal and during some special events they might reach 20%.

Arbitrage betting is usually done on the web by researching prices (odds) on betting web sites or subscribing to one of the arb-hunting services. As an investment practice, it is not completely risk-free despite the commercially used terms ‘no-risk’ and risk-free betting. It involves relatively large sums of money (stakes are bigger than in normal betting) while another variety, betting investment, means placing relatively small bets systematically on overvalued odds most of which will lose but some win thus making a profit.

Arbitrage in theory

There are a number of potential arbitrage deals. Below is an explanation of some of them including formulas and risks associated with these arbitrage deals. The table below introduces a number of variables that will be used to formalise the arbitrage models.

Variable	Explanation
$s 1$	Stake in outcome 1
$s 2$	Stake in outcome 2
$o 1$	Odds for outcome 1
$o 2$	Odds for outcome 2
$r 1$	Return if outcome 1 occurs
$r 2$	Return if outcome 2 occurs

Arbitrage using bookmakers

This type of arbitrage takes advantage of different odds offered by different bookmakers. Assume the following situation:

The event to be bet on has only two distinct outcomes (e.g. a tennis match – either Federer wins or Henman wins).

	Bookmaker 1	Bookmaker2
Outcome 1	1.3	1.5
Outcome 2	4.3	3

Placing a back bet of $100 on outcome 1 with bookmaker 2 and of $35 on outcome 2 with bookmaker 1 covers both possible outcomes and provides a profit of $15 if outcome 1 occurs, and a profit of $20.5 if outcome 2 occurs.

Hedging the bets to one side or the other can provide the bettor with a ‘risk free’ winnings. For instance if $50 was bet on outcome 2 with bookmaker 1 instead of the $35 in the example above, nothing would be won or lost if outcome 1 was the result ($100 x 1.5 = $150, covering the total of the two bets), however if outcome 2 was the final result then the overall profit would be $65.

Let’s formalise this arbitrage model. $r 1$ and $r 2$ can be calculated as follows:

$r 1 = - s 1 * (o 1 - 1) + s 2$

$r 2 = s 1 - s 2 * (o 2 - 1)$

Plugging the numbers from the above example into the formulas gives:

$r 1 = - 100(1.3 - 1) + 30 = 0$

$r 2 = 100 - 30(3 - 1) = 40$

However, these calculations can be done for you with an arbitrage calculator.

Arbitrage using betting exchanges

Betting exchanges open up a new range of arbitrage possibilities since it is possible to back as well as lay an event. Arbitrage using only the back or lay side might occur on betting exchanges. It is in principle the same as the arbitrage using different bookmakers. Arbitrage using back and lay side is possible if a lay bet provides lower odds than a back bet.