Arbitrage Training

Basic maths behind creating the odds

Do you know exactly what an odds of 1.50 means?

If you are a sports arbitrage beginner, it’s odds-on that you will surely improve your skills after reading this text. First, we would like to ask you a question: Do you know exactly what an odds of 1.50 means? In fact, even if you are an experienced sports bettor, do you know what it means? We believe you will find it interesting, so keep on reading.

See an example – maths behind the odds

Rafael Nadal oddsLet us introduce you again to an example of a tennis match. This time, however, we will choose different sportsmen, Rafael Nadal and Andy Murray. Pinnacle offers 1.50 for Rafael to win, and 2.85 for Andy to win. Now we move on to the explanation of the odds themselves.

The odd of 1.50 means that Pinnacle believes that Rafael has a 66.66% probability of winning the match. This has been very easily calculated as 1 divided by 1.50. On the other hand, 2.85 means that Andy has 35.08% (1/2.85) probability of winning the match. If you sum those probabilities you will get 101.74%.

Well, you are now probably interested in what the extra 1.74% means, right? It is a built-in profit, or to be precise, a margin set by the particular bookmaker. Normally this number varies at around 3–10%. As you can see, a margin of 1.74 was calculated from the odds offered by Pinnacle. Their margin is the smallest one among the other bookmakers, which means that they offer the best odds on the market.

Behind those odds – arbitrage opportunity

Maybe you’re thinking that this 1.74% is an opportunity for arbitrage – but no, it is not. To explain the maths behind it in even more detail , imagine that you place €100 at 1.50 on Rafael, and you have to calculate how much you need to bet at 2.85 on Andy so you can cover all the outcomes and win the same amount every time. You should already be able to calculate it. So you just find out the amount you can win when you bet on Rafael – which is 1.50*100 =150; and divide by 2.85, which equals 52.63. If you now calculate your “profit” you find that in both cases you lose €2.63, which is not exactly a profitable situation, right? The €2.63 equals the bookmakers’ margin of 1.74% (2.63/152.63). And now, just as an example, calculate a margin of 10% for some other bookmaker for the same stake as above, so you know how much they take from each bet. Right: it is 10/152.63, which is €6.50.

We believe that this now helps you to recognise a bookmaker with the best odds, and the opposite. But you are probably more interested in finding out when exactly there is an opportunity for surebets/sports arbitrage, right? It’s in the situation where the sum of the two (or more for more outcomes) probabilities equals less than 100%. This of course will not happen with two odds of a single bookmaker – they would soon be at a loss when offering such odds. Straightforwardly, this situation will occur only if you combine odds of two or more bookmakers with different odds.

Let’s get back to the tennis match. If Pinnacle offers odds of 1.50 and 2.85, it can happen that Unibet will offer odds of 1.35 and 3.10. You can now easily calculate that Unibet has a margin of around 6%. Anyway, the most important thing here is that if you combine the odds of those two bookmakers, a sports arbitrage opportunity appears. And in this case there is one! We will help you with the maths behind it, but it is nothing difficult. We have already calculated the probability of winning for Rafael if we decide to bet on him at Pinnacle – it is 66.66%. Now you just need to calculate the probability of Andy winning using the odds from Unibet, which is 1/3.10 = 32.25%. If you sum up those two numbers you get 98.91%, an opportunity for the surebet or sports arbitrage of 1.09%. You can try to calculate how much you need to bet on Andy if you, for example, choose to bet €100 at 1.50 on Rafael; and how much your profit is from this sports arbitrage, no matter who wins the match. You can find the correct answer at the end of this lesson.

We believe that it should give you an idea about how the odds are created by bookmakers. They estimate the probability of winnings for each sportsman. Bookmakers have to also calculate with some margin and adjust to the market situation and its changes. Generally speaking, the lower the margin of the bookmaker, the higher the probability of occurrence of sports arbitrage there is.


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