Arbitrage is using the difference in markets in such a way that a risk-free profit can be guaranteed whatever the outcome of an event. In Sports Betting Arbitrage we are taking advantage of bookmakers differing opinions about the outcome of a sporting event to ensure a certain profit.

COUNTERPARTIES

There has been a huge growth of counterparties due to the success of the Internet. They are made up of traditional high street bookmakers who have made use of the new technology to compliment their shop based business; Internet based bookmakers who trade exclusively on the web and peer to peer exchanges ("P2P"). A new development, which allows punters to trade amongst each other bypassing both the traditional bookmaker and web based bookmaker entirely. Each has its own methods and psyche, which has to be "handled" accordingly.

THE TRADITIONAL HIGH ST COUNTERPARTY
These counterparties came about in the 1960's due to a change in the gambling legislation. They vary in size from the "big three" namely Ladbrokes, William Hill and Coral who hold the largest market share, to the smaller independents such as Vickers.

These have the advantages (for us) of being:

1. U.K. based.
2. English speaking.
3. Deal in sterling.
4. Transactions are swift, easy to execute with minimal costs attached.
5. Well established.
6. Guaranteed liquidity.
7. Excellent lines of communication.
8. Good customer support.
9. Wide range of sports and trades available.

However, they are:

1. Adverse to risk with successful accounts quickly closed or "limited".
2. They are very efficient at spotting unusual trading patterns. Examples being unusual stake amounts, trading more than one outcome of an event and repeat trades.
3. Unwilling to accept "relatively" large trades.
4. Have differing rules governing the same individual sports.

In order to keep up a successful relationship with traditional bookmakers, great care is needed when trading with them. This has to be done with a great deal of precision and subtlety but if implemented properly can be very successful. There are a few basic rules to this:

1. Keep stakes to a "round" number.
2. Use multiple accounts for individual bookmakers.
3. Never trade the maximum allowed stake.
4. Vary the amounts traded for each account per counterparty.
5. Never repeat a trade with the same account.
6. Rotate accounts as much as possible.
7. When "price arbing", calculate stakes using the bookmaker price first and round the stakes either up or down.

INTERNET BASED COUNTERPARTIES
It is the rise of these internet only counterparties has led to the proliferation of arbitrage opportunities that we find ourselves able to take advantage of. A much wider range of odds are now available over the complete sporting calendar. The competition is fierce with their margins being cut as a result. These counterparties have led to the market being truly global. These counterparties provide both similar and different challenges to the more traditional bookmakers.

The main challenges connected with this form of counterparty are:

1. Currency.
2. Liquidity.
3. History.
4. Communications / Language barriers.
5. Ability to place large trades.
6. Money laundering laws.
7. Retrieval of monies.
8. Transaction costs and methods.
9. Have differing rules governing the same individual sports.

Currencies most commonly used are Sterling, Dollar and Euro. When trading in a foreign currency, account has to be taken of the exchange rate, (if a trade is completed in Euros then that currency falls in value against Sterling before we can reclaim our return, our profit may well have been wiped out). Currency transactions always carry a cost so should be minimised where alternatives are available. As these counterparties are relatively new entities, many based in foreign countries, we have little information on their size and liquidity.

Caution should be taken with dealing with them until a good track record can be established. Language barriers can be a problem, along with e-mail only customer support, low stake and deposit limits and high transaction costs. The latter is due to deposit and withdrawal methods relying on either credit cards or third parties such as Neteller who all charge for their services. It can take a good deal of time as well as expense to retrieve returns from some of these counterparties which has to be taken account of before trading with them.

PEER TO PEER EXCHANGES
The introduction of the Peer to Peer exchange such as "Betfair" has revolutionised the gaming industry. People can now be both punter and bookmaker, bypassing the traditional bookmaker altogether. This ultra competitive environment tends to push the odds within it to a higher level than the bookmaker can manage because the bookmaker, amongst other things, has larger overheads so needs to protect his profit margin whereas the exchange player by in large just wants to have his trade matched so will offer a higher price to achieve this. The "average" punter who uses these exchanges is generally less familiar with "probability" than a bookmaker so will offer an odd that doesn’t represent the actual chance of the success or failure of any particular team / participant in an event. There are well over twenty such exchanges in the market. The largest of these being, Betfair and Betdaq.

The trading screen of an exchange is typically made up of two halves:

Oldenway	1.8 £577	1.81 £587	1.82 £17	1.83 £180	1.84 £62	1.86 £21
Millagros	3.2 £40	3.25 £1741	3.3 £138	3.35 £65	3.4 £200	3.45 £241
Leighton	8 £200	8.2 £30	8.4 £15	8.8 £16	9 £78	9.2 £7
Jamestown	29 £4	30 £3	32 £42	38 £6	40 £13	44 £2
Stepastray	90 £16	130 £16	150 £4	190 £5	200 £2	220 £11

The Odds which are 'available to back', to the left, have been placed by people who want to lay the outcome at those specific Odds. In other words, they are looking for other people to take the opposite side of their bet and to back the outcome. Likewise, the Odds which are 'available to lay', to the right, have been placed by people who want to back the outcome at those specific Odds. In other words, these customers are looking for other people to take the opposite side of their bet and lay the outcome.

This new trading environment has also provided both in conjunction with bookmakers and in isolation, a large amount of arbitrage opportunities which we can take advantage of.

The main differences between dealing with an exchange and a bookmaker are:

1. Exchange markets can be much more volatile leading to a need for faster execution of trades.
2. Volumes can vary wildly between different markets.
3. Exchanges charge commission on all winning trades. These can vary from 1% to 5% which must be included in all calculations.
4. There are no restrictions on the size of trade (other than the amount available in the market).
5. Repeat trades can be made.
6. Accounts are not limited or closed.
7. A competitor / team can be laid to loose as well as being backed to win.

TRADING

Arbitrage Models
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
s1	Stake in outcome 1
s2	Stake in outcome 2
o1	Odds for outcome 1
o2	Odds for outcome 2
r1	Return if outcome 1 occurs
r2	Return if outcome 2 occurs

Bookmaker only Arbitrage
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 Nadal 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:

	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.

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 punter 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 o₁^-1 + o₂^-1 < 1. 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.

Reducing the risk of human error is vital being that the mathematical formula is sound and only external factor add "risk". Numerous online arbitrage calculator tools exist to help bettors get the math right.

Quick version of calculating the percentages

Fractional odds:

• - When using fractional UK-style odds (e.g. 5/6), divide the right hand number by the sum of both numbers and times by 100.
• - Chelsea at 5/6 calculates as 6 / (5 + 6) x 100 = 54.54%
• - Liverpool at 7/5 calculates as 5 / (7 + 5) x 100 = 41.66%

Decimal odds:

• - When using decimal odds (e.g. 1.83), divide 100 by the odds.
• - Chelsea at 1.83 calculates as 100 / 1.833333 = 54.54%
• - Liverpool at 2.4 calculates as 100 / 2.40 = 41.66%

These percentages represent the cover of the event that the bookmakers have. Anything under 100% is an under-round and means that it is an arbitrage opportunity. So adding these percentages comes to 96.20% Subtract this from 100% and we have an arbitrage opportunity of 3.80%.

Quick version stakes calculation
Calculating how much money to stake on each selection is a vital part of the sports arbitrage process. If you don't stake your money proportionately you wont guarantee an even return no matter which selection wins. You must back each selection to a stake that is proportionate to their percentages that we calculated above. So in our case, stakes of £54.54 on Chelsea at 5/6 and £41.66 on Liverpool at 7/5 both return £100 no matter which selection wins and you only invested £96.20!

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.

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.

GOLDEN RULES FOR ARBITRAGE TRADING

1. Double check your figures before placing your trade.
2. Make sure you have enough money with counterparty to cover stake.
3. Make sure events can be traded as singles.
4. Work out all legs before placing any trades.
5. Make sure counterparty rules regarding event correspond with each other.
6. Minimise inter currency trades where possible.
7. Record all parts of a trade before beginning another.
8. Record all trades individually.
9. Never leave part of a trade unmatched.
10. Print a copy of every transaction once completed.
11. Always factor in commission charges.
12. Use exchange with lowest commission rate where possible.
13. If, by the time you go to place a leg of a trade, the price has changed. Return to the "back" screen to see the next best odds available. Recalculate the amounts required and continue with the trade as before. If you find that because of a price change the arbitrage opportunity is no longer profitable, calculate the lowest loosing position and complete the trade.