In the following article we already presented a detailed calculation of the winning probability for 2 correct plus Superzahl.
Naturally the question arises whether the calculation can be shortened and what values the winning probabilities for the remaining prize classes (e.g., 3 correct, 4 correct, etc.) take.
The calculation described in detail above is simply a hypergeometric distribution (Excel function HYPGEOMDIST, in newer versions: HYPGEOM.DIST). Thus we can compute the probability for 2 correct without considering the Superzahl from that article using a single function:
=HYPGEOMDIST(2, 6, 6, 49, FALSE) ≈ 0.132378 or 13.2378%
As explained, the probability of predicting the correct Superzahl is exactly 0.1 or 10% (there are 10 balls for Superzahl 0–9, only one is correct). Therefore, for a prize class with Superzahl we multiply the corresponding formula by 0.1; for the variant without Superzahl we multiply by 0.9.
So here are the probabilities for the individual prize classes in Lotto (you can always check the current payout amounts per class here):
Prize class 9, 2 correct with Superzahl:
=0.1 * HYPGEOMDIST(2, 6, 6, 49, FALSE) ≈ 0.0132378 or ≈1.32378%
This corresponds to the odds (reciprocal of probability):
≈ 1 in 75.54
Prize class 8, 3 correct:
=0.9 * HYPGEOMDIST(3, 6, 6, 49, FALSE) ≈ 0.0158854 or ≈1.58854%
Odds (reciprocal):
≈ 1 in 62.95
Prize class 7, 3 correct with Superzahl:
=0.1 * HYPGEOMDIST(3, 6, 6, 49, FALSE) ≈ 0.0017650 or ≈0.17650%
Odds (reciprocal):
≈ 1 in 566.56
Prize class 6, 4 correct:
=0.9 * HYPGEOMDIST(4, 6, 6, 49, FALSE) ≈ 0.0008718 or ≈0.08718%
Odds (reciprocal):
≈ 1 in 1,147.11
Prize class 5, 4 correct with Superzahl:
=0.1 * HYPGEOMDIST(4, 6, 6, 49, FALSE) ≈ 0.0000969 or ≈0.00969%
Odds (reciprocal):
≈ 1 in 10,323.97
Prize class 4, 5 correct:
=0.9 * HYPGEOMDIST(5, 6, 6, 49, FALSE) ≈ 0.0000166 or ≈0.00166%
Odds (reciprocal):
≈ 1 in 60,223.15
Prize class 3, 5 correct with Superzahl:
=0.1 * HYPGEOMDIST(5, 6, 6, 49, FALSE) ≈ 0.0000018 or ≈0.00018%
Odds (reciprocal):
≈ 1 in 542,008.37
Prize class 2, 6 correct:
=0.9 * HYPGEOMDIST(6, 6, 6, 49, FALSE) ≈ 0.00000006 or ≈0.000006%
Odds (reciprocal):
≈ 1 in 15,537,573.33
Highest prize class 1, 6 correct with Superzahl:
=0.1 * HYPGEOMDIST(6, 6, 6, 49, FALSE) ≈ 0.000000007 or ≈0.0000007%
Odds (reciprocal):
≈ 1 in 139,838,160
And finally, a direct link to the latest lotto numbers. Good luck!
