Current Eurojackpot probabilities
On 25 March 2022 (25.03.2022) the Eurojackpot rules were changed again; the following therefore applies to
the current Eurojackpot rules.
These changes can be summarized as follows:
1) Similar to German Lotto 6aus49, in addition to the regular Friday draw, a second weekly draw on Tuesday was introduced.
The first Tuesday draw took place on 29.03.2022.
2) As with Lotto (draw days: Saturday and Wednesday), any un-won jackpot now rolls over between
these two draw days: from Friday to Tuesday and from Tuesday to Friday.
3) The maximum permitted jackpot (before the so-called forced payout) increases from €90 million to €120 million.
4) The play matrix itself was adjusted. Instead of selecting 2 out of 10 Euro numbers (also called stars), from the 25.03 draw onward there are 2 out of 12 Euro numbers.
5) Consequently, all Eurojackpot probabilities change, and prize classes 6 and 7 were effectively “swapped.” With this change, the chance of exactly 4 correct regular numbers is now higher (compared to 3 correct with 2 Euro numbers):
new class 6 is 3 correct regular numbers and 2 correct Euro numbers (until 25.03.2022: class 7) and class 7 is 4 correct regular numbers (until 25.03.2022: class 6).
6) Due to changes in payout shares per class, some classes see higher payouts; see
theoretical Eurojackpot payouts.
For probability calculations, the key factor is the increase in Euro numbers from 10 to 12
(similar to the change on 10.10.2014).
Since 25.03.2022 the odds of winning the Eurojackpot jackpot are exactly 1:139,838,160
(now identical to “Lotto 6aus49”) and can be calculated in Microsoft Excel as follows:
= COMBIN(50,5) * COMBIN(12,2),
where the chance of selecting the 5 correct Eurojackpot numbers from a total of 50 balls remains 1:2,118,760 (first factor).
The probability of matching 2 Euro numbers is 1:66 (second factor).
Every lottery player knows that in regular Lotto 6aus49, six winning numbers are drawn from 49 balls.
Thus, the probability of winning the jackpot is exactly 1:139,838,160 (you can display all these combinations with our unique generators:
Lotto number generator and Eurojackpot generator).
In Microsoft Excel this can be computed, for example, as follows:
= COMBIN(49,6) * COMBIN(10,1), where the first
factor counts all ways to draw exactly 6 balls from 49
(13,983,816 possibilities), and the second factor is the correct Superzahl
(exactly one Superzahl out of 10 possible, i.e., 10 possibilities).
For EuroMillions there are also exactly 12 Euro numbers (stars). The odds of reaching the top prize class
are now the same for Eurojackpot and EuroMillions.
Therefore, statistically, the top-prize odds (highest class) of the three well-known lotteries—Eurojackpot, EuroMillions, and Lotto 6aus49—are identical. However, a Eurojackpot tip costs two euros plus a processing fee, nearly double the
regular Lotto price of €1.20.
Odds by individual prize class
In simplified terms, Eurojackpot runs two lotteries on one grid: predicting 5 correct numbers out of 50 (on the main playslip grid) and predicting two correct Euro numbers out of now 12 (usually below the Eurojackpot grid). If you have never dealt with probability calculations, we first recommend this post in our forum:
Detailed calculation of the probability for 2 correct plus Superzahl in Lotto.
Here we will perform a direct calculation using the hypergeometric distribution (Microsoft Excel function HYPGEOM.DIST / HYPGEOMVERT). Thus we can compute the entire probability of 2 correct without considering the Superzahl from the post above using a single Excel function:
=HYPGEOMVERT(2;6;6;49) = 0.132378 or 13.2378%
Applying Excel’s HYPGEOMVERT for the hypergeometric distribution yields the following probabilities for two, one, or zero correct Euro numbers:
Two correct Euro numbers: =HYPGEOMVERT(2;2;2;12) = 0.015151515 = 1/66
One correct Euro number: =HYPGEOMVERT(1;2;2;12) = 0.303030303 = 20/66
No (=zero) correct Euro numbers: =HYPGEOMVERT(0;2;2;12) = 0.681818182 = 45/66
Multiplying these with the probability of the corresponding number of correct regular numbers on the Eurojackpot main grid (5 out of 50) gives the following probabilities for the individual Eurojackpot prize classes:
Prize class 12, 2 correct regular numbers (of 50) with 1 correct Euro number (of 12):
=20/66*HYPGEOMVERT(2;5;5;50) ≈ 0.02029488 or ≈ 2.029488%
This corresponds to odds (reciprocal of probability):
≈ 1 in 49.27
Prize class 11, 1 correct regular number (of 50) with 2 correct Euro numbers (of 12):
=1/66*HYPGEOMVERT(1;5;5;50) ≈ 0.005327408 or ≈ 0.5327408%
Odds:
≈ 1 in 187.71
Prize class 10, 3 correct regular numbers (of 50) without correct Euro numbers (of 12):
=45/66*HYPGEOMVERT(3;5;5;50) ≈ 0.003185826 or ≈ 0.3185826%
Odds:
≈ 1 in 313.89
Prize class 9, 3 correct regular numbers (of 50) with 1 correct Euro number (of 12):
=20/66*HYPGEOMVERT(3;5;5;50) ≈ 0.001415923 or ≈ 0.1415923%
Odds:
≈ 1 in 706.25
Prize class 8, 2 correct regular numbers (of 50) with 2 correct Euro numbers (of 12):
=1/66*HYPGEOMVERT(2;5;5;50) ≈ 0.001014744 or ≈ 0.1014744%
Odds:
≈ 1 in 985.47
Prize class 7, 4 correct regular numbers (of 50) without correct Euro numbers (of 12):
=45/66*HYPGEOMVERT(4;5;5;50) ≈ 0.00007240 or ≈ 0.007240%
Odds:
≈ 1 in 13,811.18
Prize class 6, 3 correct regular numbers (of 50) with 2 correct Euro numbers (of 12):
=1/66*HYPGEOMVERT(3;5;5;50) ≈ 0.000070796 or ≈ 0.0070796%
Odds:
≈ 1 in 14,125.07
Prize class 5, 4 correct regular numbers (of 50) with 1 correct Euro number (of 12):
=20/66*HYPGEOMVERT(4;5;5;50) ≈ 0.00003218 or ≈ 0.003218%
Odds:
≈ 1 in 31,075.15
Prize class 4, 4 correct regular numbers (of 50) with 2 correct Euro numbers (of 12):
=1/66*HYPGEOMVERT(4;5;5;50) ≈ 0.000001609 or ≈ 0.0001609%
Odds:
≈ 1 in 621,502.93
Prize class 3, 5 correct regular numbers (of 50) without correct Euro numbers (of 12):
=45/66*HYPGEOMVERT(5;5;5;50) ≈ 0.00000032 or ≈ 0.000032%
Odds:
≈ 1 in 3,107,514.67
Prize class 2, 5 correct regular numbers (of 50) with 1 correct Euro number (of 12):
=20/66*HYPGEOMVERT(5;5;5;50) ≈ 0.00000014 or ≈ 0.000014%
Odds:
≈ 1 in 6,991,908
Top prize class 1, 5 correct regular numbers with 2 correct Euro numbers (of 12):
=1/66*HYPGEOMVERT(5;5;5;50) ≈ 0.000000007 or ≈ 0.0000007%
Odds:
≈ 1 in 139,838,160
From this, the following theoretical payouts by Eurojackpot prize class follow.
Eurojackpot probabilities before 25.03.2022
On 10 October 2014 (10.10.2014) the Eurojackpot rules were changed so that
the number of Euro numbers increased from 8 to 10.
At first glance that may not seem important—what’s the difference between 8 and 10? In terms of odds this change was significant!
How do you compute the jackpot probability (i.e., top prize)?
Prize class 1 corresponds to 5 correct regular numbers + 2 correct Euro numbers.
Eurojackpot has 50 regular numbers and, after this change, 10 Euro numbers. What do we do with that?
Consider a typical probability example—a fair die with faces 1–6.
We all know the probability of rolling a 6 is 1/6.
Similarly for Eurojackpot:
1) Probability to draw one of five remaining “correct balls” from 50: 5/50,
2) from the remaining 49: 4/49,
3) from the remaining 48: 3/48,
4) from the remaining 47: 2/47,
5) from the remaining 46: 1/46.
Multiplying gives the probability of all 5 correct regular numbers:
5/50 * 4/49 * 3/48 * 2/47 * 1/46 = 1/2,118,760
Instead of the step-by-step, use combinations (Excel: =COMBIN(50,5) → 2,118,760).
For the two Euro numbers (stars):
=COMBIN(8,2) = 28 (original rules at launch, before 10.10.2014),
=COMBIN(10,2) = 45 (with 10 Euro numbers).
Thus jackpot odds are:
1:[2,118,760*45] = 1:95,344,200.
With only 8 Euro numbers the jackpot before 2014 was much easier to hit:
1:[2,118,760*28] = 1:59,325,280.
So this small change from 8 to 10 Euro numbers had a very large effect—reflected in typical jackpot sizes.
Eurojackpot probabilities before 10.10.2014
At the initial launch of Eurojackpot on 23 March 2012, the matrix was 5 out of 50 regular numbers and only 8 Euro numbers (stars).
An experienced reader can apply the methods described above and compute the jackpot probability:
= COMBIN(50,5) * COMBIN(8,2),
i.e., exactly 1:59,325,280. Further details omitted.
All information without guarantee
