The probabilities for the Glücksspirale lottery are very easy to calculate—almost like straight from a probability textbook! Glücksspirale has a total of 7 prize classes:
Glücksspirale prize classes
In each of the seven prize classes, separate winning numbers are drawn. Thus there are 7 winning numbers and likewise 7 winning chances per ticket (actually more, because in the top two classes, two winning numbers are drawn each). For this reason, probabilities can be computed completely independently. A ticket wins if one or more ending digits match the drawn number’s ending digits in the correct order. If a player wins in a higher class, a win in the lower class is automatically excluded. Therefore, strictly speaking, the probabilities should not be added as in standard probability theory for independent events. However, since the numbers in each class are drawn independently (and may coincide), we ignore this subtlety for simplification.
For the lowest class 1 it suffices that the last ending digit matches the class’s winning number’s ending digit. The fixed prize equals twice the stake, i.e., €10 for a full ticket with a €5 stake. Hence the probability is exactly one tenth: 1/10 = 0.1 or 10%.
For classes 2 to 5, which correspond to two, three, etc. correct ending digits, the probabilities are 0.01 (1%), 0.001 (0.1%), and so on.
Many ask why, for the two highest classes of Glücksspirale (classes 6 and 7), the odds are 1 in 500,000 and 1 in 5,000,000 (and not 1:1,000,000 or 1:10,000,000 as the naive continuation would suggest). Fortunately, this is not a special probability formula; it’s simply due to the
Glücksspirale rules
namely:
In these two top prize classes, two winning numbers are drawn!
With this, the overall probability of any win—that is, the probability that a single Glücksspirale ticket wins something at all—can be calculated as the complement of “no win in any class”:
p = 1 − ((1 − p_C1) × (1 − p_C2) × (1 − p_C3) × (1 − p_C4) × (1 − p_C5) × (1 − p_C6) × (1 − p_C7)) = 1 − (0.9 × 0.99 × 0.999 × 0.9999 × 0.99999 × 0.999998 × 0.9999998) = 1 − 0.89000913 = 0.109990869, i.e., 10.99909%.
And finally, a direct link to the latest lotto numbers. Good luck!
