How to Calculate Arbitrage Betting

We explain why it’s a low-risk betting strategy, and how to calculate arbitrage bets to give you an understanding of the maths behind arbitrage betting. Learn how to calculate arbitrage bets between an exchange and bookmakers to maximize your potential arbitrage profit.

If you’re new to arbitrage betting we have already explained in detail what it is, but to offer context for this article, it is a trading strategy which benefits from price differentials between two or more bookmakers or betting exchanges to guarantee a profit whatever the outcome.

Arbitrage sports betting is the way of placing bets at chances that guarantee a profit regardless of the eventual outcome on all outcomes of an event.

Let’s explain this briefly. A fair market would be priced at 100 percent dependent on the probability of an event happening bookmakers will price their odds to go above a 100% likelihood giving an edge to them.

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Arbitrage opportunities are the opposite of the whereby an arber will bet on all eventualities across a number of gambling providers, giving them the chance to take advantage of discrepancies in price so the probability of the odds they have bet on is lower than 100% – hence in their favour.

It’s fundamental when making an arbitrage bet to comprehend the maths behind arbitrage betting, however in the event you will need to compute an arbitrage bet our arbitrage calculator is free and easy to use.

Arbitrage calculator

Just follow the below directions:

Input the complete stake you want to risk.
Input the odds for outcome 1 and the commission if on a betting exchange (if you are arbing between bookmakers set the commission value to 0).
Repeat for the other results you want to arb (add new outcome if you require more than 4 results on a market).
The arb calculator will then automatically inform you how much you will need to stake on each outcome and your gain. 

How to Compute arbitrage betting between a bookmaker and exchange

The most frequent arbitrage bet is created by taking positions in the market across a bookmaker and a exchange – laying the outcome on the betting exchange and then backing at the bookmaker.

For instance let’s say you want to bet on a tennis game between Player A and Player B. The odds on the bookmaker and the market indicated probabilities in brackets – learn how to compute margins – are displayed below:

Market margin


2.20 (45.45%)


You now examine the lay price on Player A to win – gambling he won’t win – which is 1.98 together with the Smarkets exchange. The table below highlights this can be an arbitrage opportunity as the joint implied probability for bets is 95.96%.

Player A to win at bookmaker

Player A not to win at markets

Combined market margin


2.20 (45.45%)

1.98 (50.51%)


Now you stake #200 on Player A to win on the bookmaker with odds of 2.2. To calculate your stake that is lay about the Smarkets exchange you use the following calculation:

(back price x back bet ) / (current lay odds – exchange commission)

Example: (2.2 * 200) / (1.98 – 0.02) = #224.49

You would then make a #224.49 lay bet on Player A to win at odds of 1.98 on the betting exchange.

Calculate your gain if you win in the bookmaker

If your bet wins with the bookmaker is simple calculating your gain:

Gain = (back odds – 1) * back stake – (lay odds -1) * lay stake

Example: Gain = (2.2 – 1) * 200 – (1.98 -1) * 224.49 = #20.00

Calculate profit if the lay bet wins in the exchange:

Next, if your bet with the market is effective, you calculate your gain:

Profit = (lay stake * (1 – commission)) – bookmaker bet

Example: Profit = (224.49 * (1-0.02)) -200 = #20

Overall arbitrage profit

Your arbitrage profit regardless of the outcome is displayed below:



Smarkets exchange


Player A wins




Player A loses


  • #220 (includes 2% commission)


So if you placed this arbitrage bet, you’d guarantee a profit of #20 no matter Player A winning or not.

The Way to calculate arbitrage between two bookmakers

Arbitrage bets were made between two or more bookmakers before betting exchanges – because bookmakers have chances that were quite 24, these are becoming less prevalent. Having said they do still happen.

For an arb you need to identify both bookmakers offering the highest chances on each outcome. The table below can help you recognise if there is a possible arb across bookmakers. If you find odds similar to outcome 1 would present an arbitrage opportunity:

Outcome 1 odds

Outcome 2 odds



















For instance let’s say you want to wager on a darts match between Player A and Player B. The odds on the market and both bookmakers implied probabilities are displayed below:

Player B to win

Market margin

Bookmaker A odds

1.30 (76.92%)


Bookmaker B odds

2.98 (33.56%)


This shows an arbitrage opportunity between bookmaker A and bookmaker B. The table below combines the odds and probabilities and reveals they are – or in other words, in your favour – learn how to convert odds in to implied probability.

Player A to win at bookmaker B

Player B to win at bookmaker A

Combined market margin



By cross-matching the chances for every outcome across the two bookmakers the joint market margin is now in the bettor’s favour providing a guaranteed return of 1.57%.

Calculating how much to bet for arbitrage bets

Now you must calculate how much to stake with every bookmaker to ensure an equal return without consideration for the outcome. Let’s say you’re willing to bet #100 overall.

Example: Bookmaker A stake = (100*27 percent ) / 98.43% = #27.43

Example:Bookmaker B bet = (100*71.43%) / 98.43% = #72.57

Total arbitrage profit

Your overall arbitrage profit regardless of the result is displayed below:

Bookmaker A

Bookmaker B


Player A wins




Player B wins




The Way to Compute arbitrage on three-way betting markets

Now you understand how to calculate arbitrage opportunities for a two-way arbitrage bet that is simple, you can look at 1X2 arbs or three-way. Arbs are prevalent in football where is a possibility of a draw.

When arbing with a betting exchange there’s absolutely not any requirement for arbs as you could back Manchester United to win on the bookmaker against Liverpool and then put them to win the exchange – which covers anything aside from a Liverpool win.

This example is for a three-way arb involving three individual bookmakers. Let’s say you find the following odds on a match between Manchester United and Liverpool:


Liverpool to win

Market margin


Bookmaker B 3.55 (28.17%)


This highlights an arbitrage opportunity between both bookmakers as the table shows the market margin is below 100% and above unites the odds and probabilities that are implied.

Calculating how much to stake for arbitrage bets

You need to figure how much to stake with each bookmaker to guarantee an equivalent return depending on which bookmaker you win with. Let’s say you need to stake #1500 overall.

Stake at each bookmaker = (Overall stake * Bookmaker implied probability)/Combined market margin

Example: Bookmaker A stake = (1500*47.17%) / 93.86% = #753.84

Example: Bookmaker B bet = (1500*28.17%) / 93.86% = #450.19

Example: Bookmaker C bet = (1500*18.52%) / 93.86% = #295.97

Overall arbitrage profit

Your arbitrage profit regardless of the outcome is displayed below:


Bookmaker A

Bookmaker B

Bookmaker C


Man United win










Liverpool win





So for this example, as suggested, if you placed # 1500 bet across the bookmakers that are different you’d guarantee a profit of about #98.

Apply this to betting

You understand how to calculate arbitrage bets you are in the best position to take advantage of price discrepancies across bookmakers and betting exchanges. Remember Smarkets accept arbitrage bettors and also offer the best odds online – with our 2 percent commission.