When it comes to football and betting, we seldom think of 1X2 probabilities but consider only the odds of each event. Yet it would be much more informative if we knew what implied probabilities are behind these odds. But how can we extract probabilities out of odds?

Before we answer the question, we need to remember that there are probabilities inclusive bookie’s profit margin; and implied probabilities exclusive bookie’s profit margin. In the below article I will be referring to European football example and European odds format.

**Probabilities inclusive bookie’s margin**.

Consider the following football game.

Probabilities can be found simply by dividing 1 by the odds of an outcome.

Yet there is a little trick. If we sum up all the results we get the following:

Total = 45% + 31% + 28% = 104%.

It turns out that the summation doesn’t equal exactly 100% but surpass this threshold. The margin above 100 is simply called overround. Effectively this is the bookie’s profit for providing you the service and assuming the risk in the betting business. Therefore by cutting the odds across all three outcomes, the bookie creates unfair market for his own gain.

To grasp the concept of bookie’s profit let’s use the same example viewed from another perspective. Can we try to answer the question: How much shall we stake at each event, so that we return EUR 1 regardless of the outcome? Well, the above results 0.45, 0.31 and 0.28 can be exactly viewed as the euro amounts, we need to stake at each of the odds – 2.2, 3.2 and 3.6 in order to get a profit of EUR 1.

But if we do so then we will stake EUR 1.04 and the bookie will pay out just EUR 1 regardless of the outcome. As a result the bookie records a mark-up of EUR 0.04 each time he must pay EUR 1. We are destined to lose no matter what the outcome is.

**Probabilities exclusive bookie’s margin**

Now we get back to the probabilities exercise. In order to exclude the bookmaker’s overround from the equation we need to do some final manipulation. We figured that for each EUR 1.04 that the bookie receives he pays out EUR 1. This means simply that the bookie’s payout share is:

PO share = 1 / 1.04 = 0.96.

Therefore the bookie pays out EUR 0.96 for each EUR 1 received.

Furthermore if we multiply the payout share by the probabilities inclusive margin, we will arrive at the implied probabilities exclusive margin.

We make the check and sum the numbers:

Total = 43.5% + 29.9% + 26.6% = 100%.

That is how punters can extract probabilities out of odds and ultimately assess the game from another angle. Bookies’ profit margin is part of the game. Sometimes it may be much more than the example given here, sometimes less. But it is always there.

Above all, the example has huge implications on value betting comprehension and payout analysis. By slashing the odds to charge a mark-up the bookies are effectively creating unfair market. As a result we are on the losing side always when we place bets. Read more about payout and value betting analysis here.

Bookmakers have the edge by applying an over-round and in the long-term it’s not possible to make a profit in case odds are fair. Is it worth pursuing betting opportunities at all and can we ever consistently make profits?

Well the answer is yes. There are plenty of occasions when bookmakers do price selections incorrectly – occasions that are usually known as value bets. Read more why bookies deviate form fair odds here.

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