Numbers the brain cannot picture
Matching all six numbers in La Primitiva has a probability of 1 in 13,983,816. It is so small that we have no intuition for it: it just feels “hard”, the same way something a thousand times more likely would. That is why it helps to translate it into time. Playing in every draw, it would take tens of thousands of years on average to win once.
Technical Exact probabilities (hypergeometric distribution)
For a 6/49 game, the probability of matching k numbers is:
P(k) = C(6, k) · C(43, 6 − k) / C(49, 6)With C(49, 6) = 13,983,816. EuroMillions multiplies two independent draws, 5 of 50 numbers and 2 of 12 stars: P(5+2) = 1 / (C(50, 5) · C(12, 2)) = 1 / 139,838,160. The 5 + bonus tier needs the number you missed to match the bonus ball, drawn from the remaining 43: P(5) · 1/43. The project’s tests check these figures.
Half the money never comes back
At roulette the house keeps less than 3 cents of every euro. With the lottery it keeps far more: EuroMillions pays out 50% of sales in prizes, La Primitiva and Bonoloto 55%, and the National Lottery 70%. In other words, out of every €10 spent on tickets, between €3 and €5 never comes back to players. The simulation above shows it: after a lifetime of playing, the usual outcome is never winning a big prize and getting back only part of what you spent.
Sources for prize shares: La Primitiva, EuroMillones, Lotería Nacional.
“Somebody has to win”
True: in almost every draw somebody wins. But somebody winning says nothing about your chances. When millions of people play, it is almost certain that one of them hits, and that person is on the news. The millions who do not win never are. Seeing only the winners makes the prize feel far closer than it is.