Today I want to talk about those accumulator bets that casinos offer so happily.
In particular, the bet to 6 results. The casino tells us that if we bet one euro and we win, we will obtain 31.31 times what we have bet.
Anyone can do the math and think:
If I bet 2 €, I will obtain 62.61€. If I bet 5, I will get 156.53 €. And finally, if I risk 10 €, I will win 313 € and I can retire some time. What an opportunity!!!
The problem is that the probability of winning this kind of bets is about 3.19%. Which means that if you bet 100 times to different offers like this, you can only beat 3 times casino odds. In other words you will risk 1000 € to win (if you win) € 939. So, you return home with a loss of 61€.
A quick summary is that the bet can be seen as a very good opportunity, but absolutely everything is against you.
Now the mathematical part:
The probability of winning a bet is the inverse of the odds. For example 1 / 2.45 gives a probability of 40.82% for Arsenal. The same for the rest.
But as the bet is an accumulator bet, we have to calculate the cumulative probability. That is to multiply all the probabilities together.
The bar graph shows the individual probability of winning each bet and the line shows that with each bet won, the probability of winning the next will decline drastically.
We begin with a probability of 40.82%. However, after four won bets, we only have a 10% chances of winning. Finally, we end up with 3.6%.
The best thing is to make one bet at a time and change (increase or decrease) the amounts of the bet according to the results. I also always recommend to bet with a chance of winning of at least 60% (casino payouts of 1.66).