Arbitrage betting

Example of arbitrage betting

Betting arbitrage, miraclebets, 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. When conditions allow, by placing one bet per each outcome with different betting companies, the bettor can make a profit regardless of the outcome. Mathematically arbitrage occurs when there are a set of odds, which represent all mutually exclusive outcomes that cover all state space possibilities (i.e. all outcomes) of an event, whose implied probabilities add up to less than 1. [1] In the bettors' slang an arbitrage is often referred to as an arb; people who use arbitrage are called arbers.

Arbitrage betting involves relatively large sums of money for 98% of arbitrage opportunities return less than 1.2%.[2] The practice is usually detected quickly by bookmakers, who typically hold an unfavorable view of it, and this can result in half of an arbitrage bet being canceled. Arbitrage betting is almost always insufficiently profitable due to detection, unreliable betting websites, limiting of stakes, hackers, and scammers that use high percentage arbitrages to trick bettors into providing security credentials.

Bookmakers generally disapprove of betting arbitrage, and restrict or close the accounts of those who they suspect of engaging in arbitrage betting. Although arbitrage betting has existed since the beginnings of bookmaking, the rise of the Internet, odds-comparison websites and betting exchanges have made the practice easier to perform. On the other hand, these changes also made it easier for bookmakers to keep their odds in line with the market, because arbitrage bettors are basically acting as market makers.

In Britain, a practice has developed in which highly experienced "key men" employ others to place bets on their behalf, so as to avoid detection and increase accessibility to retail bookmakers and allow the financiers or key arbitragers to stay at a computer to keep track of market movement.

Arbitrage is an extremely fast-paced process and its successful performance requires lots of time, experience, dedication and discipline, and especially liquidity.

Theory

There are a number of potential arbitrage deals. Below is an explanation of some of them including formulas and risks associated with them. 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

Using bookmakers

This type of arbitrage takes advantage of different odds offered by different bookmakers. For an example of an event with only two possible outcomes (e.g. a tennis match - either Federer wins or Henman wins), the two bookmakers have different ideas of who has the best chances of winning. They offer the following Fixed-odds gambling on the outcomes of the event:

Bookmaker 1 Bookmaker2
Outcome 1 1.25 1.43
Outcome 2 3.9 2.85

For an individual bookmaker, the sum of the inverse of all outcomes of an event will always be greater than 1. 1.25^{-1} + 3.9^{-1} = 1.056 and 1.43^{-1} + 2.85^{-1} = 1.051

The bookmaker's return rate is 1- (1.25*3.9)/(1.25+3.9)= 5.34\%, which is the amount the bookmaker earns on offering bets at some event. Bookmaker 1 will in this example expect to earn 5.34% 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 bettor a profit.

In case outcome 1 comes out, one could collect r_1 = $100 * 1.43 = $143 from bookmaker 2. In case outcome 2 comes out, one could collect r_2 = $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 o_1 and o_2, where o_1^{-1} + o_2^{-1} < 1. If one wishes to place stake s_1 at outcome 1, then one should place s_2 = s_1 * o_1 / o_2 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 1/1 and a 2/1, by covering the 1/1 with $500 and the 2/1 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. For example, arbitrage calculators can handle calculations for both book arbitrage ("back/back" or "lay/lay") and "back/lay" arbitrage opportunities on an intra-exchange or inter-exchange basis, and is free.

For arbitrages involving three outcomes (e.g. a game which can be won, lost or drawn) having the odds o_1 for Outcome 1, o_2 for outcome 2 and o_3 for outcome 3 with their respective bids being b_1, b_2 and b_3 and sum of the bids being B.

The amount required to bet on each possibility in order to ensure profit can be calculated by

b_1 = B / (1 + (o_1/o_2) + (o_1/o_3) )

b_2 = B / (1 + (o_2/o_1) + (o_2/o_3) )

b_3 = B / (1 + (o_3/o_1) + (o_3/o_2) )

Back-lay sports

Betting exchanges such as Smarkets have opened up a new range of arbitrage possibilities since on the exchanges it is possible to lay (i.e. to bet against) as well as to back an outcome. 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 on one exchange provides shorter odds than a back bet on another exchange or bookmaker. However, the commission charged by the bookmakers and exchanges must be included into calculations.

Back-lay sports arbitrage is often called "scalping" or "trading". Scalping is not actually arbitrage, but short term trading. In the context of sports arbitrage betting a scalping trader or scalper looks to make lots of small profits, which in time can add up. In theory a trader could turn a small investment into large profits by re-investing his earlier profits into future bets so as to generate exponential growth. Scalping relies on liquidity in the markets and that the odds will fluctuate around a mean point. A key advantage to scalping on one exchange is that most exchanges charge commission only on the net winnings in a particular event, thus ensuring that even the smallest favorable difference in the odds will guarantee some profit.

Bonus sports

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 the bettor hedges or backs their bets as usual, but since they received the bonus, a small loss can be allowed on each wager (2–5%), which comes off their 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.

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.

By signing up to various bookmakers, it is 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 arbitrages, which is where a middleman service is useful. As many bookmakers require a certain turnover of the bonus amount, matching money from different bookmakers against each other enables the player to in effect quickly "play free" the money of the losing bookmaker and in effect transfer it to the winning bookmaker. By avoiding most of the turnover requirements in this way the player can usually expect a 70-80% return on investment.

As well as spending time physically matching odds from various bet sites to exchanges, the other draw back with bonus bagging and arbitrage 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 minimised.

Shop arbitrage (sharbing)

Shop arbitrage (also known as sharbing) is the process of using a betting shop's coupons and a betting exchange to create an arbitrage position. This is made possible because online prices change quickly to close these positions and betting shops are slower to change the prices on their printed coupons.

Risks

While often claimed to be "risk-free", this is only true if an arbitrage is successfully completed; in reality, there are several threats to this:

Other potential problems include:

See also

References

  1. Cortis, Dominic (2015). Expected Values and variance in bookmaker payouts: A Theoretical Approach towards setting limits on odds. Journal of Prediction Markets. 1 9.
  2. Keynes, Milton. "Reward without Risk? An Introduction to Arbitrage Betting and the Asian Handicap". TBR. Retrieved 19 March 2014.
  3. "How quickly is temporary market inefficiency removed?" Ben R. Marshall The Quarterly Review of Economics and Finance 49 (2009) 917–930
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