# EuroJackpot

EuroJackpot is a multinational number lottery currently operated in 18 European countries. As the name of the game suggests, the jackpot is common for all the participating countries and can grow rapidly to sky high levels. The minimum guaranteed jackpot is €10 million.

**The Eurojackpot lottery** is played in 18 countries: Croatia, Czech Republic, Denmark, Estonia, Finland, Germany, Hungary, Iceland, Italy, Latvia, Lithuania, Netherlands, Norway, Poland, Slovakia, Slovenia, Spain, Sweden.

## How to play EuroJackpot

In the **Eurojackpot** lottery, you choose **five (5) main numbers out of fifty (50) and two (2) additional euro numbers out of twelve (12).** The drawing of 2 additional numbers out of 12 (instead of 10) occurred due to **rule changes from 19/03/2022.**

For curiosity: 2 numbers out of 10 were drawn from 04/10/2014. Before that, 2 numbers were drawn only from 8. The change is likely related to the increasing number of countries participating in the lottery. However, as we will see, these inconspicuous changes reduce the probability of winning the highest prize.

**The second change from 19/03/2022** is the number of drawings. It will be drawn twice a week on Tuesday and Friday (previously only on Friday), with the first Friday drawing under the new rules taking place on 25/03/2022 and the first Tuesday on 29/03/2022.

There are a total of **twelve prize categories** – depending on how many main numbers and euro numbers the bettor manages to guess correctly.

**To win the highest prize in Eurojackpot,** it is, of course, necessary to correctly guess all 5 main numbers out of the 5 drawn (out of a total of 50 numbers) and 2 additional euro numbers out of 2 (out of a total of 12 numbers).

A ticket or a betting line costs €2. This price can be perceived very differently in the participating countries due to their purchasing power. However it is compesated for by potentially massive jackpot that can reach up to €120 million (until recently, when there have been 12–16 participating countries, the maximum jackpot was €90 million). The jackpot and its division will be dealt with in one of the following chapters.

## Probability & Odds of Winning

All important **characteristics and calculations related to the EuroJackpot lottery** are shown in the Table 1. The meaning of the headings is described in more details on the EuroMillions webpage. Let us just go through it briefly, so that we can quickly jump to **the probability (or the odds) of winning the EuroJackpot** top prize and to the long-term expected return from a player’s perspective.

We can see that there are 12 *Prizes* and the related conditions that need to be met to get them (*Match*). For instance 5 + 2 means the necessity to match 5 main numbers (out of 5) and 2 additional Euro numbers (out of 2), of course, one cannot forget that there are 50 main numbers and 12 Euro numbers in total.

The *Prize Fund* shows the percentage allocation for each prize. If you sum up the figures, you arrive at the value 91%. It may seem strange, but the remaining 9% is used as a guarantee fund. As for lotteries, **traditionally the biggest part of the funds is allocated to the highest and lowest prizes**, so that (1) the jackpots can grow quickly and (2) players are motivated to keep on betting (and aiming for the upper prizes) as they do not leave empty-handed all the time.

The *Average Prizes* are published and updated after each draw by the lottery operator. Together with the probabilities they are used for the calculation of a player’s expected return (long-term average outcome) as it is addressed further in the text.

Prize | Matched | Quota | Average Net Win | …as a multiple | Probability | 1 in … | EV | ||
---|---|---|---|---|---|---|---|---|---|

1st | 5 | + | 2 | 36.00% | €34,548,539.00 | 17 274 269× | 0.0000000072 | 139,838,160 | 0.1235 |

2nd | 5 | + | 1 | 8.60% | €888,918.87 | 444 458× | 0.0000001430 | 6,991,908 | 0.0636 |

3rd | 5 | + | 0 | 4.85% | €148,253.54 | 74 126× | 0.0000003218 | 3,107,515 | 0.0239 |

4th | 4 | + | 2 | 0.80% | €4,800.87 | 2 399× | 0.0000016090 | 621,503 | 0.0039 |

5th | 4 | + | 1 | 1.00% | €265.23 | 132× | 0.0000321801 | 31,075 | 0.0042 |

6th | 4 | + | 0 | 0.80% | €111.93 | 55× | 0.0000724051 | 13,811 | 0.0040 |

7th | 3 | + | 2 | 1.10% | €88.16 | 43× | 0.0000707961 | 14,125 | 0.0030 |

8th | 2 | + | 2 | 2.55% | €22.11 | 10× | 0.0010147445 | 985 | 0.0102 |

9th | 3 | + | 1 | 2.85% | €19.21 | 9× | 0.0014159225 | 706 | 0.0122 |

10th | 3 | + | 0 | 5.40% | €15.59 | 7× | 0.0031858257 | 314 | 0.0216 |

11th | 1 | + | 2 | 6.75% | €10.98 | 4× | 0.0053274085 | 188 | 0.0239 |

12th | 2 | + | 1 | 20.30% | €8.54 | 3× | 0.0202948895 | 49 | 0.0664 |

At least some winnings | x | x | 0.0314162529 | 31.8 | x | ||||

Loss | Others | x | -€2.00 | -1× | 0.9685837471 | 1.03 | -0.9686 | ||

Expected value | x | x | x | x | -60.82 % |

Data source: Prizes, matches, prize fund allocations and average prizes – see the https://www.euro-jackpot.net/statistics/prizes [quoted 2023-12-26], own data processing, calculations and design.

The probabilities are shown in two formats: (1) decimally and (2) as the odds (one in …). In terms of lotteries there are usually very low probabilities (especially as regards the main prize) and therefore it is clearer to use the second format, *the Odds*.

**How many unique combinations there are in EuroJackpot?** We know that there are 5 main numbers and 2 additional Euro numbers drawn in this lottery. We can easily use the Excel function `=COMBIN(50,5)*COMBIN(12,2)`

and arrive at the result `139,838,160`

. This is the count of the total unique possibilities that can be created. And since there is only one winning combination of 5 main and 2 Euro numbers, **the odds of winning the EuroJackpot are 1 in approx. 140 million.**

The odds of winning the other (lower) prizes are also shown in the Table 1. If we add them up, we get the probability of winning any of the prizes approx. `0.0314`

(or `3.14%`

), in other words the odds are `1:31.8`

. The probability or the odds of winning nothing can be calculated indirectly by deduction from 1 (the total of probabilities must equal 1 or 100%).

## Player's Expected Long-term Outcome

The odds of winning the main prize in EuroJackpot, and similarly in a vast majority of lottery games, are often quite low. At the same time it is possible to win one of the lower prizes, whose odds are growing (in the opposite direction). However **the odds are not the only point of interest.** It is also important to know, **how much can we win.** If we weight (multiply) possible prizes (and the loss of the bet as well) by their probabilities and add them up, we arrive at the average expected outcome of betting in the long run.

**The player’s expected outcome in the EuroJackpot lottery** is `-60.82%`

. This figure with the plus instead of minus is *the margin of the lottery company* (the player’s loss is the lottery operator’s gain). The player is going to be losing about 60 cents out of each wagered euro.

## Jackpot Creation & Division

As it was mentioned the EuroJackpot is raised by lost (or undistributed) bets. The minimum guaranteed jackpot is 10 million euros, the average jackpot is €34,548,539.00 and the maximum so far achieved jackpot has been €120,000,000.00 – source, as of 26 December 2023. If the jackpot reaches the maximum and is not hit, the overflow feeds the lower prizes.

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Other resources: hazardni-hry.eu/loterie/eurojackpot.html (original Czech article).