Arbitrage Betting

Arbitrage betting is the system of betting on “sure bets” or bets that will guarantee the bettor a profit whatever the outcome of a certain sporting event. Arbitrage betting exploits the fact that bookmakers may have different opinions, or at times have errors, in calculating the probability of a certain event happening. Usual profit of the people who use arbitrage betting (called arbers) is 2%.

How to Spot Arbitrage Bets

You can spot an arb, or an arbitrage bet, by looking at the highest odds given among several bookmakers. There are several websites where you can see the latest odds given by several bookmakers. An example is oddschecker.com. In Figure 1, the compilation of the odds available for the West Brom vs. Everton match (1×2 market) on 20-Jan-14 is shown.

Figure 1. Compilation of odds available for the West Brom Vs. Everton (1×2) match on 20-Jan-2014

From Figure 1, the best odds for the said match is tabulated in table 1. First, we find the total market value of the odds using this formula:

Market = 1/Outcome 1 + 1/Outcome 2+ 1/Outcome 3

Market = 1/2.25 + 1/3.5 + 1/3.6 = 100.79%

As of the moment, the total market value of the odds is 100.79%. If the market value drops below 100%, it creates an arb and will be a sure profit for the bettor if he bets on all events. If for example, Paddy power, Stan James or Winner add 0.1 on their current odds of Everton winnning, the Market value becomes:

Market = 1/2.35 + 1/3.5 + 1/3.6 = 98.60%

This gives the bettor a 1.10% profit margin, no matter the result of the game. This is the called the arbitrage percentage. We may write this condition in a formula for an event with N event outcomes:

1 / O1 + 1 / O2 + ... + 1 /ON < 1

where O1 is Outcome 1, O2 is Outcome 2 and ON is Outcome N. For a sporting event with only two outcome, we can easily derive a formula that we can use to spot an arb (assuming that the odds are always positive):

1 / O1 + 1/O2 < 1

1 / O1 < 1 - 1/O2

O1 < (1 - 1/O2)^-1

Plotting this formula in Figure 2, we can see that all Odds combination under the curve are non-arb bets. In contrary, all odds combination over the curve are arbitrary bets.

Calculating Profit and Individual Bets

After spotting an arbitrage, one must place a bet in order to profit from this. We may calculate the individual bets using this formula:

Individual Bet = (Investment / ON) / Total Market %

For our initial example, we use the 1×2 odds = 2.25-3.5-3.6 which is a non-arbitrage bet. The calculator will indicate that this is a non-arbitrage bet and will tell the loss (negative profit) that will occur. If in case that the market moves and the Home Odds improve to 2.35, we can see that the profit will be 1.10% and the total win for a $1000.00 investment is $11.10 dollars. The individual bets is calculated using the formula above.

Potential Pitfalls of Arbitrage Betting

There are several pitfalls that may not guarantee a profit in arb bets. Here are some potential pitfalls in arbitrage betting:

1. Mispriced Odds - If in case that the odds difference is due to errors of the bookmaker (i.e., the odds placed was 7/3 instead of 3/7), the bookmaker may not honor the bets placed.
   
2. Betting Rules - Different bookmakers offer different rules in betting. Also, different sports also offer different betting rules. The lack of knowledge of these rules may hinder a sure profit for the arber.
   
3. Stake Restrictions (Limited Accounts and Maximum Bets) - There are bookmakers that limit the users to a certain number of bets and has betting interval limit. Knowing these bookies are crucial in arbitrage betting since this may limit your chances of betting on them if the need arises. Also, the arber must also know the maximum betting limit. There is really no point of betting $1000 on one side of the arb, and then knowing that the other bookmaker has a $100 bet limit.
   
4. Commissions - Bookmakers like BetFair has a commission fee and must be incorporated in the calculations.
   
5. Odds Change - Odds change very quickly. It may be possible that you have already placed an odd in one side of the arb then the odds on the other side of the arb already change.