The maths of the EuroMillions

My uncle is very engaged in this game, and I've found a little inspiration to write about it. Lottery... I hate it. However, lets see what science has to say about this.

The player must choose 5 numbers between 1 and 50 and 2 stars (stars are numbers as well) between 1 and 11. Numbers cannot be repeated.

Let's see how many combinations of 5 numbers and 2 stars can we make:

We can choose 5 numbers in 50*49*48*47*46 = 254251200 different ways, but the order doesn't matter. There are 5! = 120 ways of ordering 5 numbers, so there are 254251200/120 = 2118760 ways of selecting the numbers without taking into account the order of selection.

We can choose 2 stars in 11*10 = 110 different ways, but (again) the order doesn't matter. There are 2! = 2 says of ordering 2 stars (which are also numbers), so there are 110/2 = 55 ways of selecting the numbers without taking into account the order of selection.

Combining those numbers and stars, there are a total of 116531800 ways of betting in EuroMillions.

Taking this as a starting point, I've made a simple program (a script written in Python) that outputs the following:

If I've made it correctly, as the output says you need to play 80773689 times in a row to make your chances higher than 50%. In Spain, each ticket costs 2€, which means that if you want to avoid losses, you should only play when the jackpot is 161547378€ or higher (162 million in easy terms).

Notes:
- Actually, chances of winning are higher, since there are other prices, perhaps I should do the maths in another post, but here you can get a general idea.
- When I say that you should play for those jackpots, chance is still very little and you should buy quite a lot of tickets. You may need several million years to make profit playing lottery.
- Every lottery company expects to make money, so it's not a surprise if you end up with losses.
- Some people play because when they buy a ticket, they're buying a dream.
- Maths know nothing about dreams, just numbers.