Imagine the draw is underway. You filled out and paid for exactly one grid for this draw (hopefully not more than €1.80; otherwise see our Lotto price comparison!) and the first two balls drawn match your numbers! Great start, right?
Now the key question: From this situation, what is the probability of winning anything at all? That is, either at least 2 correct plus Superzahl (=prize class 9 with the fixed €6.00 payout), or 3 correct — whichever is more likely. For 4 or more correct numbers you can compute the probabilities yourself using the suggested approach. Also see the
calculation of the probability for 2 correct plus Superzahl.
A layperson might answer: Very likely! After all, you already have 2 correct! And there are still 4 more numbers to be drawn, plus the extra chance of the correct Superzahl!
Let’s solve it the simple way. We already have 2 correct. For prize class 9 you “only” need the correct Superzahl. There are 10 possibilities (0–9, typically the last digit of your playslip number), and you’ve marked one. The probability is exactly 0.1 (10%): p = 1/10 = 0.1.
What about the other Lotto balls? There are 47 balls left in the drum; 4 of them will be “the remaining winners,” so 43 are “non-winners.”
To get a total of 3 correct numbers (since you already have 2) you need exactly one more correct. There are 4 ways to draw exactly one of the 4 remaining winning balls (any one of the four).
At the start you marked the usual 6 numbers. Thus the remaining 3 you marked must be non-winners. Use combinations directly:
= COMBIN(43,3) = 12,341. Therefore, our “3 correct” case (i.e., exactly one additional correct number, ignoring the Superzahl) corresponds to 4 * 12,341 = 49,364 combinations.
Now compute the total number of ways to choose the remaining 4 numbers out of 47:
=COMBIN(47,4) = 178,365.
We can now compute the sought probability for exactly 3 correct numbers: p = 49,364 / 178,365 ≈ 0.276758 or 27.6758%. This is the probability that a single grid will hit exactly one additional winning number. Here we still ignore the Superzahl (if the Superzahl is correct, you’ve already won — see above).
As you can see, the probability of getting one more regular winning number is almost three times higher than the chance of the correct Superzahl. Since these probabilities are independent, they can be added (10% + ≈27.68% ≈ 37.68%). We leave it at that (for a fully rigorous calculation of “any win” in this situation you would also include prize classes 1–7; the impact is marginal — cf. probabilities in Lotto 6aus49).
And finally, a direct link to the latest Lotto numbers! Good luck!
