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. As long as different Bookmakers are used for arbitrage betting the Bookmakers do not have a problem with this. Each Bookmaker will still make profit due to their calculations.

In the bettors' slang an arbitrage is often referred to as an arb; people who use arbitrage are called arbers. 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 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.

Arbitrage using bookmakers

This type of arbitrage takes advantage of different odds offered by different bookmakers. Assume the following situation:
We consider an event with 2 possible outcomes (e.g. a tennis match - either Federer wins or Henman wins), the idea can be generalized to events with more outcomes, but we use this as an example.

The 2 bookmakers have differing ideas of who have the best chances of winning, they offer the following Fixed-odds gambling on the outcomes of the event

For an individual bookmaker, the sum of the inverse of all outcomes of an event will always be greater than 1.

As they are in this case: 1.25 − 1 + 3.9 − 1 = 1.056 and 1.43 − 1 + 2.85 − 1 = 1.051
The fraction above 1, is the bookmakers return rate, the amount the bookmaker earns on offering bets at some event. Bookmaker 1 will in this example expect to earn 5.6% on bets on the tennis game. Usually these gaps will be in the order 8 - 12%.
The idea is to find odds at different bookmakers, where the sum of the inverse of all the outcomes are below 1. Meaning that the bookmakers disagree on the chances of the outcomes. This discrepancy can be used to obtain a profit.

For instance if one places a bet on outcome 1 at bookmaker 2 and outcome 2 at bookmaker 1:
1.43 − 1 + 3.9 − 1 = 0.956
Placing a bet of 100$ on outcome 1 with bookmaker 2 and a bet of $100 * 1.43 / 3.9 = 36.67 on outcome 2 at bookmaker 1 would ensure the bettee a profit.
In case outcome 1 comes out, one could collect r1 = $100 * 1.43 = $143 from bookmaker 2. In case outcome 2 comes out, one could collect r2 = $36.67 * 3.9 = $143 from bookmaker 1. One would have invested $136.67, but have collected $143, a profit of $6.33 (%4.6) no matter the outcome of the event.
So for 2 odds o1 and o2, where . If one wishes to place stake s1 at outcome 1, then one should place s2 = s1 * o1 / o2 at outcome 2, to even out the odds, and receive the same return no matter the outcome of the event.
Or in other words, if there are two outcomes, a 2/1 and a 3/1, by covering the 2/1 with $500 and the 3/1 with $333, one is guaranteed to win $1000 at a cost of $833, giving a 20% profit. More often profits exists around the 4% mark or less.
Reducing the risk of human error is vital being that the mathematical formula is sound and only external factors add "risk". Numerous online arbitrage calculator tools exist to help bettors get the math right.

Back-lay sports arbitrage
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. (Of course, the commission of the bookmaker must be included into calculations.)

  Bonus sports arbitrage
Many bookmakers offer first time users a signup bonus in the range $10 - $200 for depositing an initial amount. They typically demand that this amount is wagered a number of times before the bonus can be withdrawn. Bonus sport arbitraging is a form of sports arbitraging where you hedge or back your bets as usual, but since you received the bonus, a small loss can be allowed on each wager (2-5 %), which comes off your profit. In this way the bookmakers wagering demand can be met and the initial deposit and sign up bonus can be withdrawn with little loss. See also matched betting.

The advantage over usual betting arbitrage is that it is a lot easier to find bets with an acceptable loss, instead of an actual profit. Since most bookmakers offer these bonuses this can potentially be exploited to harvest the sign up bonuses.

Making money:
By signing up to various bookmakers, it's possible to turn these 'free' bets into cash fairly quickly, and either making a small arbitrage, or in the majority of cases, making a small loss on each bet, or trade. However, it is relatively time consuming to find close matched bets or arbs, which is where an arb / close matched bet service is useful.

Drawbacks:
As well as spending time physically matching odds from various bet sites to exchanges, the other draw back with bonus bagging / arb trading in this sense is that often the free bets are 'non-stake returned'. This effectively reduces the odds, in decimal format, by 1. Therefore, in order to reduce 'losses' on the free bet, it is necessary to place a bet with high odds, so that the percentage difference of the decrease in odds is minimalised.