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.

Game1Odds1/Odds
Tottenham3.20.3125
Draw3.80.263158
Bayern Munich2.10.47619
Total1.051848
Game2Odds1/Odds
Juventus1.450.689655
Draw4.50.222222
Bayer Leverkusen70.142857
Total1.054735
Game3Odds1/Odds
Red Star 30.333333
Draw3.30.30303
Olympiacos2.40.416667
Total1.05303

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 MunichJuventus vs Bayer LeverkusenRed Star Belgrade vs OlympiacosOdds1/Odds
13.21.45313.920.071839
23.81.45316.530.060496
32.11.4539.1350.109469
43.24.5343.20.023148
53.84.5351.30.019493
62.14.5328.350.035273
73.27367.20.014881
83.87379.80.012531
92.17344.10.022676
103.21.453.315.3120.065308
113.81.453.318.1830.054996
122.11.453.310.04850.099517
133.24.53.347.520.021044
143.84.53.356.430.017721
152.14.53.331.1850.032067
163.273.373.920.013528
173.873.387.780.011392
182.173.348.510.020614
193.21.452.411.1360.089799
203.81.452.413.2240.07562
212.11.452.47.3080.136836
223.24.52.434.560.028935
233.84.52.441.040.024366
242.14.52.422.680.044092
253.272.453.760.018601
263.872.463.840.015664
272.172.435.280.028345
Total1.168254

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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