This outcome, 2 correct plus Superzahl, corresponds to the smallest possible win in German Lotto 6aus49.
The payout for this prize class IX has recently (as of 23.09.2020) been a fixed amount of €6.00. You can verify this yourself:
on our page with the latest Lotto results you will find
in this “prize class NINE” exactly €6.00 week after week, not a cent more or less.
That is what’s unique about 2 correct with SZ: the special prize class in which the payouts do not vary.
From various sources, such as math forums or Wikipedia,
you’ll quickly find the probability of this win stated as odds of 1 in 75.54 or 1.32%.
But how is this value derived?
1) First note that exactly 6 winning numbers are drawn. They are treated equally; draw order does not matter
(for beginners, see the current Lotto rules).
This means there are multiple ways to obtain exactly 2 correct from the 6 winning numbers.
Assume 1, 2, 3, 4, 5, 6 are the six winning numbers of a hypothetical draw. From these, there are exactly 15 distinct
two-number combinations:
1) 1,2
2) 1,3
3) 1,4
4) 1,5
5) 1,6
6) 2,3
7) 2,4
8) 2,5
9) 2,6
10) 3,4
11) 3,5
12) 3,6
13) 4,5
14) 4,6
15) 5,6
For the probability calculation you don’t need the explicit list; the count alone (here 15) suffices.
In Microsoft Excel: =COMBIN(6,2).
2) Next, count the ways to choose the remaining 4 “wrong” numbers.
You select 4 numbers from the remaining 43 numbers (49 total numbers; 6 are the winners; 49−6=43 wrong numbers).
Using combinations gives 123,410: =COMBIN(43,4). Thus our “2 correct” case (still ignoring Superzahl) corresponds to
15 × 123,410 = 1,851,150 combinations.
3) Now determine the total number of six-number selections from 49:
=COMBIN(49,6) = 13,983,816. Among these ~14 million combinations (again ignoring Superzahl),
exactly one matches the 6 winners—a value you’ll see often.
4) We can now compute the probability of exactly 2 correct (still without Superzahl):
p = 1,851,150 / 13,983,816 ≈ 0.132378 or 13.2378%.
This is the probability that a single grid produces exactly 2 correct hits (without Superzahl).
5) And what about the Superzahl? We must include it because only 2 correct alone is not a win.
There are 10 possibilities for the Superzahl: 0–9. One ball is drawn; the probability is 0.1 or 10%.
Thus, our final result is:
p(2 correct with Superzahl) = 1,851,150 / (13,983,816 × 10) = 0.0132378 or 1.32378%
You can also express this as odds, the reciprocal of the probability: 1 in 1/0.0132378 ≈ 1 in 75.5412.
And finally, a direct link to the latest Lotto numbers! Good luck!
