Odds of the Jackpot in Six Games — a Comparison

The odds of the jackpot in Lotto stand at 1 in 13,983,816. In Mini Lotto they are sixteen times higher — 1 in 850,668. The lowest odds among the six games run by Totalizator Sportowy belong to Eurojackpot: 1 in 139,838,160, ten times lower than Lotto. All these values come from a single formula for the number of combinations and can be calculated in a matter of seconds.

Below is a breakdown for each game together with an explanation of where the given number comes from. There are no estimates here — the number of combinations is an exact quantity, the same for every draw and independent of what came up before.

Table: odds in six games

Game	You pick	Pool	Combinations	Odds
Kaskada	12	24	2,704,156	1 : 2,704,156
Mini Lotto	5	42	850,668	1 : 850,668
Lotto	6	49	13,983,816	1 : 13,983,816
Lotto Plus	6	49	13,983,816	1 : 13,983,816
Eurojackpot	5 + 2	50 + 12	139,838,160	1 : 139,838,160
Multi Multi	10 of 20	80	—	1 : 8,911,711

The „Combinations” column gives the number of all possible sets for a given pool. Multi Multi has a different structure and requires a separate calculation — explained below.

Where these numbers come from

All the values come from the binomial coefficient, the formula for the number of k-element subsets of an n-element set. For Lotto, this means choosing 6 numbers out of 49: 49 × 48 × 47 × 46 × 45 × 44 divided by 6 × 5 × 4 × 3 × 2 × 1. The numerator is 10,068,347,520, the denominator is 720, and the result is 13,983,816.

Dividing by the factorial is necessary because the order of the drawn numbers does not matter. The set 3-11-24-31-38-49 and the set 49-38-31-24-11-3 are the same ticket, and without dividing we would count it 720 times. That is the most common mistake when calculating odds on your own.

Mini Lotto is calculated the same way, just with smaller values: 5 numbers out of 42 gives 850,668 combinations. Kaskada — 12 out of 24 — comes out to 2,704,156. It is worth noting that Kaskada has the smallest pool of all the games, yet a harder jackpot than Mini Lotto, because it requires picking exactly half of all the numbers.

Why Eurojackpot is so hard

Eurojackpot has two independent pools, and the number of combinations must be calculated for each separately, then multiplied. Choosing 5 numbers out of 50 gives 2,118,760 possibilities. Choosing 2 additional numbers out of 12 gives 66. The product of these two values is 139,838,160.

The main pool of Eurojackpot alone — 5 out of 50 — is easier than the six numbers in Lotto: 2.1 million versus almost 14 million. It is the two additional numbers that raise the difficulty sixty-six-fold and determine the overall result. A full breakdown of frequencies for both pools can be found in the Eurojackpot statistics.

Multi Multi — a different kind of calculation

In Multi Multi, the machine draws 20 numbers out of 80, and the player picks between 1 and 10. There is no single „jackpot” here in the sense used in Lotto — there are ten separate game variants, each with its own prize table. The value 1 : 8,911,711 in the table refers to the highest variant, that is, hitting all ten picked numbers among the twenty drawn.

The calculation looks different than in the other games: we count in how many ways 10 numbers can be chosen out of the 20 drawn, and divide that by the number of all ways to choose 10 numbers out of 80. The first value is 184,756, the second is 1,646,492,110,120. The quotient gives roughly 1 : 8.9 million.

Kaskada works similarly in the sense that hitting part of the picked numbers also brings a prize, but it has a fixed number of selections. In both games it is worth looking not only at the top tier but at the whole distribution — details for individual tiers are given in the game rules.

What these numbers mean in practice

A probability of 1 : 13,983,816 means that if someone filled in one Lotto ticket for every draw — three times a week, about 156 times a year — they would wait, on statistical average, nearly 90,000 years to hit the six numbers. Buying ten sets on a single ticket cuts that time tenfold and raises the odds to 1 : 1,398,382, but it does not change the order of magnitude.

Every draw is independent of the previous ones. A number that has not come up for a hundred draws has exactly the same probability in the next one as any other number — the drawing machine has no memory. The history of results describes only the past, and no combination of numbers pulled from the Lotto statistics increases the chance of winning.

For the same reason, every set of six numbers is equally likely. The ticket 1-2-3-4-5-6 has the same odds as any other. The only practical difference concerns the size of a potential prize: sets popular among players — birth dates, arithmetic sequences — are more often hit by several people at once, and the pool is then split between them. If you have no preference, you can use the random-pick generator.

The jackpot is not the only prize

The numbers in the table apply only to the top tier. The lower tiers are much easier: three matches in Lotto occur roughly once in 57 tickets, four matches roughly once in about a thousand. The prizes from these tiers are small, but they occur regularly and make up most of the payouts in every draw.

It is also worth remembering the tax threshold: a prize up to 2,280 PLN is tax-exempt, above that a flat 10 percent applies to the whole amount. Calculations for different thresholds are shown by the prize tax calculator.