Predictive Hacks

# Bookmaker’s Margin in Multiple Bets

In the previous post we explained how to calculate the Bookmaker’s Margin for a single bet. Now, we are going to explain how we can calculate the margin when we are dealing with multiple bets at the same time (paroli).

Let’s consider the following 3 Champions League games with their corresponding odds and margins.

 Game1 Odds 1/Odds Tottenham 3.2 0.3125 Draw 3.8 0.263158 Bayern Munich 2.1 0.47619 Total 1.051848
 Game2 Odds 1/Odds Juventus 1.45 0.689655 Draw 4.5 0.222222 Bayer Leverkusen 7 0.142857 Total 1.054735
 Game3 Odds 1/Odds Red Star 3 0.333333 Draw 3.3 0.30303 Olympiacos 2.4 0.416667 Total 1.05303

As we can see in all three games the margin is around 5%. Let’s assume that the gambler would like to bet on the three games simultaneously in order to get higher returns. But what is the margin in this case?

## Calculate the Margin in Multiple Bets

In order to calculate the margin you will need to take the product of all possible events. In our case we have 3 x 3 x 3 = 27 possible events, and the product of those by row, is the odds that the bet pays off.

 Tottenham vs Bayern Munich Juventus vs Bayer Leverkusen Red Star Belgrade vs Olympiacos Odds 1/Odds 1 3.2 1.45 3 13.92 0.071839 2 3.8 1.45 3 16.53 0.060496 3 2.1 1.45 3 9.135 0.109469 4 3.2 4.5 3 43.2 0.023148 5 3.8 4.5 3 51.3 0.019493 6 2.1 4.5 3 28.35 0.035273 7 3.2 7 3 67.2 0.014881 8 3.8 7 3 79.8 0.012531 9 2.1 7 3 44.1 0.022676 10 3.2 1.45 3.3 15.312 0.065308 11 3.8 1.45 3.3 18.183 0.054996 12 2.1 1.45 3.3 10.0485 0.099517 13 3.2 4.5 3.3 47.52 0.021044 14 3.8 4.5 3.3 56.43 0.017721 15 2.1 4.5 3.3 31.185 0.032067 16 3.2 7 3.3 73.92 0.013528 17 3.8 7 3.3 87.78 0.011392 18 2.1 7 3.3 48.51 0.020614 19 3.2 1.45 2.4 11.136 0.089799 20 3.8 1.45 2.4 13.224 0.07562 21 2.1 1.45 2.4 7.308 0.136836 22 3.2 4.5 2.4 34.56 0.028935 23 3.8 4.5 2.4 41.04 0.024366 24 2.1 4.5 2.4 22.68 0.044092 25 3.2 7 2.4 53.76 0.018601 26 3.8 7 2.4 63.84 0.015664 27 2.1 7 2.4 35.28 0.028345 Total 1.168254

As we can see, although the margin of each single bet was around 5%, in the multiple bets of three games it becomes around 16.8% and as you add games, then the margin is becoming bigger and bigger.

## Suggestion

We know that some gamblers would like to go for high returns. It is better to go for single bets of high odds (go for the underdog) rather than go for many bets at the same time. As a rule of thumb, before you place any bet, try to calculate the margins.

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