Understanding Superenalotto Odds

Explore different aspects of Superenalotto probabilities. Click on a section to jump directly to the content.

If you play a single ticket (6 numbers out of 90), the probability of guessing all 6 drawn numbers is 1 in 622.6 Million. In percentage terms: about 0.0000001606%. This means that Superenalotto is a game with extremely low odds for the jackpot.

To put this probability in perspective: you're more likely to be struck by lightning (about 1 in 1 Million) or by a meteorite (1 in 1.6 Million), or to win an Olympic gold medal (about 1 in 662,000) than to win the Superenalotto jackpot with a single ticket.

The problem is a classic combinatorics question, namely answering:

How many possible combinations of 6 numbers can be formed by choosing from 90?

To calculate this, we use the formula for combinations without repetition C(n, k) = n! / (k! × (n−k)!) where:

• n is the total number of elements to choose from (90 numbers)
• k is the number of elements to choose (6 numbers)
• ! indicates the factorial of a number (e.g. 5! = 5 × 4 × 3 × 2 × 1 = 120)

Calculating the probability of winning 6 numbers

To win the jackpot, you must guess exactly the 6 drawn numbers. Since there is only one winning combination among all possible ones, the probability of guessing all 6 numbers with a single ticket is given by: P(6 su 6) = 1 / C(90, 6)

Calculating C(90, 6):

C(90, 6) = 90! / (6! × 84!) = 622.614.630

Therefore:

P(6 su 6) = 1 / 622.614.630 ≈ 1.6061 × 10⁻⁹

So in percentage terms, the probability of guessing all 6 numbers is about 0.0000001606%.

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Probability of getting 3, 4 or 5 numbers

Besides calculating the probability of winning the jackpot, we can also calculate the probability of guessing exactly 3, 4 or 5 numbers out of 6. This is done using the hypergeometric distribution.

We use the hypergeometric model: to get exactly k correct numbers (k = 3,4,5):P(k) = [C(6,k) × C(90−6, 6−k)] / C(90,6), where:

• C(6,k) is the number of ways to choose k correct numbers from the 6 drawn.
• C(84, 6−k) is the number of ways to choose the remaining numbers (not drawn) from the 84 remaining numbers.
• C(90,6) is the total number of possible combinations of 6 numbers from 90.

Numerical values (approximated):

• 6 exact: 1 way → P ≈ 1.6061e-9 → 1 in 622,614,630
• 5 exact: 504 ways → P ≈ 8.0949e-7 → ~1 in 1,235,346
• 4 exact: 52,290 ways → P ≈ 8.3985e-5 → ~1 in 11,907
• 3 exact: 1,905,680 ways → P ≈ 0.00306077 → ~1 in 327

Note: the calculations shown have minimal rounding, which doesn't significantly affect the final results.

Besides winning odds, it's important to know how much you can actually win in each category. Prizes vary from draw to draw based on the prize pool and number of winners, but we can calculate historical average winnings.

* Expected return is calculated as: (Prize × Winning probability). The main value uses the historical average prize, while the "Max" value shows the theoretical return if the maximum prize ever recorded occurred. It represents how much each category "returns" on average for each euro played. The total of ~€0.43 means that statistically SuperEnalotto returns about 43% of what is collected in prizes (the rest covers costs, taxes and margins).

Given the extreme difficulty of winning at Superenalotto, it's important to adopt a responsible and conscious gaming approach. Here are some practical tips on what to do and what to avoid.

• Wheeling System
• Group Purchase

Responsible gaming

Gaming is an entertainment activity, not a reliable source of income. If you feel gaming is becoming a problem, seek professional help