arbitrage betting

Betting arbitrage or 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. Bookmakers dislike people who use arbitrage and will often limit their stakes if identified.
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 profitThere 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 modelsThis 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 you bet at 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, you could collect r1 = $100 * 1.43 = $143 from bookmaker 2. In case outcome 2 comes out, you could collect r2 = $36.67 * 3.9 = $143 from bookmaker 1. You 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 . You wish to place stake s1 at outcome 1, then you 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 you have two outcomes a 2/1 and a 3/1, by covering the 2/1 with $500 and the 3/1 with $333, you are guaranteed to win $1000 at a cost of $833, giving a 16% profit. More often profits exists around the 4% mark or less.
In practice it is very hard to find bets with this property and due to the small discrepancies of a few percent (you will be very unlikely to find higher) you will need to invest large sums to receive a profit of any real size. Which can be very dangerous as mentioned in the introduction of this article.
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.