# lotto

Monument to a ticket seller in Bairro Alto , Lisbon

Lotto (from Italian lotto from French lot "share", "lot", "fate", also "game of chance", "lottery") is a lottery and thus a game of chance in which the player for a financial stake on the draw previously tapped Sets numbers from a limited set of numbers.

In many countries such as Germany or Austria there is a so-called lottery monopoly .

## Concepts

A distinction is made between two concepts. In active lotteries , the player selects a limited number of numbers from a predetermined series of numbers. The best-known example in Germany is the game "6 out of 49": In the game, six numbers from a series of numbers from 1 to 49 are ticked on a ticket. In the later drawing, six winning numbers are determined; Previously, the profit level was based solely on the number of correctly predicted numbers - the so-called "hits". The amount of money to be paid out for each prize level is usually calculated using a quota system : Each prize level has a certain share of the total stake paid in for the drawing.

The second variant is the passive lottery (example: the Spanish Christmas lottery ). By purchasing a ticket with a multi-digit ticket number printed on it, the player is entitled to participate in the bet. So no numbers have to be actively ticked. One or more winning numbers or winning numbers are then determined in the drawing. The different profit levels usually determine the amount of the payout in advance.

In practice, there are variations and mixed forms of the two concepts. In the case of the German 6 out of 49, the super number, which determines the promotion from an even prize class to the next better odd prize class, is given as the last digit of the ticket number on the selected ticket.

## History of the lottery game

### Europe until the 19th century

The philosopher Samuel von Pufendorf (1632–1694) defined the term “lottery” as a means that promises the achievement of a profit “by pulling one or more pieces of paper out of a vessel containing a number of written and blank slips of paper and gets what is described on the slip of paper for himself. ”He compared the lottery with a collection “ because you get the money from people in a manner that they either not at all, or only if you impose one on them with grumbling and impatience. ”But he also saw the disadvantages that can be associated with these practices. He turned down lotteries organized out of pure profitability.

The author of the article “Lottery” in Johann Heinrich Zedler's Complete Universal Lexicon of All Sciences and Arts dealt with the question of the extent to which God's “caution and government have to do with lotteries” and describes various views of the time that God “with the settlement of the Lottery luck [...] not those natural means and tools, thereby [...] letting one get a good, another a mediocre, and the third an empty lottery; but have the hand with a very special provision [...] directly in the game ”, or that God otherwise“ would have to rule either the hands of those who mix the Zettul before the lottery is drawn, or the hands of those who draw such afterwards ” , "That they could of necessity so, and not otherwise, amount and take hold of what might be difficult to make out".

The Lotto was discovered by the Genoese in the 15th century as a practical means of raising money . Originally, the lot was used to determine the new council members every year. For this purpose the Genoese wrote ninety names on pieces of paper and secretly drew five out of these ninety. From the appointment of the new city council, a lively betting business developed , from which the lottery later developed, in which the names were replaced by numbers, the first "5 out of 90". The Genoese Benedetto Gentile is the first to offer this number lottery privately as a pure game of chance . Even then there were many enthusiastic lottery players and generated high sales . Since this simple business principle generated large profits for the organizer, the right to organize lotteries passed to the respective rulers or governments . It was a nice source of income at the royal and princely courts . This regulation is still common worldwide today. At most, licenses for lotteries are granted to private operators .

The raffle for first in England conducted lottery began on 11 January 1569 at the west door of St Paul's Cathedral in London . The proceeds should be used to mobilize money for public contracts such as port expansion or bridge construction.

One of the first big lotteries on German soil was played in Hamburg in 1614, the process of which was described as follows in 1707:

“There were two large baskets placed / from which the notes of names and profits / were taken out by a Waysen boy / and then recorded by the gentlemen and citizens who were present by the authorized notary used at the time. On the basket / inside the names were these verses:

Who can recognize in the ossuary
A poor man for a rich man
The can place in this basket
Meet Heintzen here / Cuntzen there.

On the / inside the winning slip was / it said:

In this basket are the profits
For large / medium and also small.
Are the profit and there the Nydt. "
- Peter A. Lehmann : Historical Remarques on the Latest Things in Europe , 1707
Public lottery drawing in Hamburg by children in front of senators

A lottery that was held in England in 1694 enjoyed a particularly large influx. The idea for their direction was born out of necessity, “because when the king needed a good sum of cash in a hurry and Parliament spent the whole of Jenner thinking about where to get it, one of them suggested a lottery from one Million pounds sterling to wreak ”. Indeed, the desired success was not long in coming. Within less than half a year, the desired sum was raised and even exceeded by far.

Lotteries and lucky pots were also held in Holland , namely in Amsterdam , Utrecht and Amersfoort . No fewer than 16,000 tickets are said to have been issued for the lottery in Amersfoort, each with a value of 25 guilders. The drawing, which began on February 25, 1695, lasted over four weeks. The highest price is said to have been 75,000 guilders. The city itself was left with a profit of at least 30,000 guilders, which - according to Zedler - "was a small one, but the good food from the very unbelievable influx of strangers, since all the houses were packed under the roofs, brought in a much larger one . ”More lotteries followed, in such a large number that one got the impression that there weren't even 1,000 people in this populous country who didn't try their luck in the lottery game (Zedler). Because many lotteries were held without the permission of the state and numerous abuses occurred (some lotteries contained almost nothing but rivets), they were eventually banned in Holland. However, this did not affect the game of chance, because you continued to play in France . There in May 1700 a lottery of ten million French pounds, consisting of four hundred thousand tickets, each for 2 Louis d'or , was organized to pay the royal debts  . At least this lottery did not have the desired success, "although every college was forced to take a certain number."

In Austria , under the government of Empress Maria Theresa, a lottery with 90 numbers with the official name “Lotto di Genova” was introduced and auctioned in 1751. In the beginning there was a complete lack of applicants and it took a full year for Count Cataldi to finally acquire the privilege. On November 21, 1752 the first drawing took place in Vienna at 11 o'clock in the morning at Augustinerplatz. According to a note in a local Viennese newspaper, “there was a lot of profit for those playing.” A local paper published a list of the lucky winners, including the first Shoemaker's apprentice Ulrich Huber was listed with 600 ducats.

Nevertheless, business was very sluggish at first. After the end of the ten-year lease term, Cataldi agreed to an extension only on condition that the subjects were forbidden to play in foreign lotteries with the threat of fines and physical punishment. The reasons for these initial difficulties were probably that among the nobility and the army it was still often considered dishonorable to play the lottery, while the working population had nothing to gamble with the poor wages at the time.

Public lottery drawing in Braunschweig, 1771

In Braunschweig , Duke Karl I introduced a number lottery in 1771, which took place as a public event with up to 50 annual drawings on the Aegidienmarkt . His son and successor, Karl Wilhelm Ferdinand , abolished the lottery in 1786 out of moral reservations about gambling and out of concern for his subjects.

In 1773 the large banking house Barara & Comp. entered the lottery business and made significant profits after a short time, which were immediately invested in new branches. By spreading targeted rumors of fairy-tale winnings, the "common people" became more and more appropriated for this type of gambling.

The addiction to money and wealth was immeasurable, but at the same time superstition also increased. The lottery prophets - so wrote a renowned Austrian newspaper at the time - resort to star Germanism, necromancy, swindle and deception in order to divest the people of the pennies they had badly earned. A leaflet distributed in 1774 with the headline “Excellent, mysterious arithmetic practices for finding numbers of the lottery art, along with notes and instructions for the glorious discovery of the root of happiness”, which found great sales at the Vienna fair, is known. The lottery game became a moral contagium, which produced the strangest social phenomena. A critical observer of the lottery wrote in the late 19th century: “Gallows wood was a sought-after item and a bitter argument arose over the rope of a hanged man, because - so the simple-minded population believed - placed under the head cushion, such props could be the lucky numbers in conjure the brain of the hopeful sleeper. "

With the increasing popularity of the lottery game, the rent for the concession also went up. In 1778 it was already twelve thousand guilders, which were paid to the universal chamber pay office and partially distributed to the coffers of the poor, orphanages and correctional houses. Emperor Joseph II thought about canceling the lottery game entirely. Since the financial counter-arguments did not allow this, however, he finally limited himself to curbing the gambling frenzy and the superstition associated with it. Emperor Leopold II, however, was anything but averse to the lottery, he and his court are said to have been one of the best clients of the general leaseholder. Under Emperor Franz II , the lottery passed into the administration of the state and from then on formed a branch of the Ministry of Finance, which generated enormous profits. Nonetheless, opponents of gambling fought against the continued existence of the small lottery decades later, because - so was one of their justifications - "the formation of capital should always progress only through increased labor, the lottery game is not a suitable means of economic progress favor. Wherever it is not the interest earned on income, but the income itself that is risked, the economic loss is the most likely consequence. Even the most profitable, no matter how considerable, do not compensate for it, because a property not acquired through work lacks moral value and wherever it is not incorporated into a solid, solid enterprise, it melts away as easily as it was won ".

### Germany in the 19th and 20th centuries

In the German Empire , a large number of state lotteries such as the Grand Ducal Hessian state lottery were formed . In order to reduce the competition between these, the state lotteries were merged into a smaller number of providers at the beginning of the 20th century. At the end of the Empire there were seven state lotteries such as the Hessian-Thuringian State Lottery or the Central German State Lottery .

In the time of National Socialism , the right of approval of the federal states was transferred to the Reich Minister of the Interior by the lottery ordinance of March 6, 1937 (RGBl I, p. 283). The consent of the Reich Treasurer of the NSDAP was always required. Its office for lotteries of the NSDAP with ten branch offices was the largest lottery organizer. The Reich Winter Aid Lottery in favor of the Winter Aid and the Reich Lottery for Employment Creation (later the Reich Lottery for National Labor ) were carried out throughout Germany ; the latter as street lotteries and drawing lotteries.

After the Second World War , Berlin announced its first city lottery on August 16, 1945 to promote reconstruction, which brought in 350,000 Reichsmarks . Lottery systems have been prepared for this in all occupation zones . The Saxon state lottery also began in the Soviet occupation zone in 1945 . On January 11, 1953, the German Class Lottery Berlin introduced the lottery with the game formula “5 out of 90”.

From January 1954 nationwide number lottery game offers were introduced in the German Democratic Republic with a legal ordinance of March 4, 1954. Responsible in the GDR was the VEB numbers lottery based in Leipzig under the supervision of the Ministry of Finance. Around 60% of the stakes paid in were supposed to be distributed as winnings and 10% had to be paid as lottery tax.

On June 30, 1955, the states of Hamburg , Schleswig-Holstein , Bavaria and North Rhine-Westphalia founded the lottery company Deutscher Lottoblock .

The first joint drawing of lottery numbers in the Federal Republic of Germany - possibly in response to the GDR measure - took place publicly on Sunday, October 9, 1955 in the Hamburg hotel “Mau” with “6 out of 49”. Two orphan girls took turns drawing the six numbers in the order 13-41-3-23-12-16. It was not until a few months later that the first million dollar profit was awarded to the construction worker Willi Strauch from Aachen. The other federal states followed successively: Bremen from May 13, 1956, Lower Saxony from June 10, 1956, Hesse from September 2, 1956, Rhineland-Palatinate from December 2, 1956, Saarland from January 6, 1957, Baden- Wuerttemberg from April 13, 1958, Berlin from October 4, 1959. In the GDR and in the new federal states from 1954 to 1992, the game types sports festival pools 6 out of 49, lottery pools 5 out of 45, number lottery 5 out of 90 (up to 1985) and Tele-Lotto 5 out of 35 (from 1972). From 1992 the new federal states took over the offers of the German lottery block.

Once a Saturday drawing failed in the Federal Republic of Germany, namely the one on December 30, 1956. Therefore, the number of Saturday draws to date differs from the number of weeks that have elapsed. In the first few years the tickets were evaluated manually. Since it was not possible at the time to estimate exactly how long it would take, the drawing was canceled due to New Year's Eve and New Year's. In the following years, however, the draws took place in these constellations.

The so-called additional number was introduced on June 17, 1956 in order to achieve more precise control of the profit distribution through more profit categories. On September 4, 1965, the drawing of the lottery numbers was broadcast live on television for the first time. Lotto on Wednesday followed on April 28, 1982 initially with the game formula "7 out of 38", from June 4, 1986 then with the formula "6 out of 49".

### Germany from 1990

The so-called super number was introduced on December 7, 1991 so that the higher number of players due to the reunification resulted in a more effective advertising jackpot by not filling the top prize category. This number is the last digit of the ticket number on the ticket and in Germany is determined at the end with another drawing machine. By introducing the number, the previously rather low chances of winning the highest prize category (jackpot) have been reduced by 90%. The additional lotteries Spiel 77 and Super 6 with fixed winnings can also be played using the ticket number. However, participation costs an additional stake.

After lottery games had been operated exclusively by state companies for almost 50 years, the last GDR government granted several lottery licenses in 1990. Whether these are only valid for individual federal states or for the whole of Germany has been the subject of several legal proceedings. In 1994, the Environment and Development Foundation, supported by several non-profit organizations, applied for licenses for its own lotteries in all federal states, but these were initially rejected. After several administrative court proceedings, the lottery “Our World” was approved under strict conditions in North Rhine-Westphalia in 2003, but was discontinued after 15 months.

With regard to naming, the Federal Court of Justice ruled on January 19, 2006 [1 ZB 11/04] that lottery is a collective term for number games and therefore cannot be protected as a word mark.

On the basis of the State Treaty on Gambling of January 1, 2008 and after the end of the transition period of one year stipulated therein, gambling was no longer permitted on the Internet from January 1, 2009.

On December 15, 2011, all federal states with the exception of Schleswig-Holstein signed an interstate gaming treaty . He finishes u. a. the ban on selling the lottery on the Internet.

Since the end of September 2012 it has been possible to play online again in some federal states such as Baden-Württemberg.

### Internet lotteries

Internet lotteries have also been around for a number of years; these are not to be confused with tip entry services. Internet lottery providers hold their own draws that have nothing to do with the state lottery. Depending on the provider, 7 out of 49, 6 out of 49, 6 out of 32 or 7 out of 50 are drawn, for example. Some providers also organize several different draws with different prices in parallel.

The chance of winning per drawing is not greater or perhaps even less than with the state lottery, but most internet lotteries are ad-financed and therefore free of charge. Also, most internet lotteries hold daily draws. To participate, you have to be of legal age and register once, you can then log in daily with your e-mail address and / or a password to submit a tip. There are usually three options for submitting a tip:

• You choose the tip numbers manually
• You can generate pseudo random numbers, called quick tips or random tips.
• You save a typing combination, which you have to call up manually every day.

The prizes can be material or cash prizes. In addition, some providers offer weekly or monthly special prices. Proof of identity is mandatory in order to receive a prize. Some internet lotteries offer additional services that are subject to a fee, such as automatic entry of bets or other competitions.

## Lottery systems

There are different country-specific systems:

 Belgium 6 out of 45 (until September 2011: 6 out of 42) Bulgaria 6 out of 49, 6 out of 42, 5 out of 35 Denmark 7 out of 36, 6 out of 48 Germany 6 out of 49 plus 1 out of 10 Finland 7 out of 39 France 5 out of 49 plus 1 out of 10 Greece 6 out of 49 Italy 6 out of 90 Liechtenstein (until August 5, 2011) 6 out of 49 Lithuania 6 out of 30 Netherlands 6 out of 45 plus 1 out of 6 Austria 6 out of 45 5 out of 90 (number lottery 1-90 ) Poland 6 out of 49, 5 out of 42 Portugal 5 out of 49 plus lucky number 1 out of 13 Québec / Canada 6 out of 49 Romania 6 out of 49, 5 out of 40 Sweden 7 out of 35 Switzerland 6 out of 42 plus lucky number 1 out of 6 Spain 6 out of 49 Turkey 6 out of 49 Hungary 5 out of 90, 6 out of 45 United States 5 out of 69 plus 1 out of 26 ( Powerball ) 5 out of 75 plus 1 out of 15 ( Mega Millions ) United Kingdom 6 out of 59

### 6 out of 49 in Germany

Logo of Lotto 6 out of 49 in Germany
Normal lottery ticket in Saxony

In Germany, the German Lotto and Totoblock operates the lottery game as an amalgamation of the state lottery companies.

The winning numbers are on Wednesday and Saturday night via internet live stream (until June 29, 2013 via television broadcast, Wednesday in ZDF and Saturdays in the First ) pulled . After the six winning numbers have been drawn, a super number is also drawn from the numbers 0 to 9. The player's participating super number is the last digit of the seven-digit ticket number. If there are two or more correct winning numbers, a correct super number increases the prize category.

You can also take part in the games Super 6 , Spiel 77 and the Glücksspirale . When participating in game 77 and the Glücksspirale, the entire ticket number serves as the ticket number, with Super 6 the last six digits.

Since May 4, 2013, a lottery betting field has cost one euro (previously 75 cents). 50% of the amount paid will be distributed again. In addition, a processing fee is charged for every ticket issued, which varies from 20 cents to one euro depending on the federal state (each state lottery company can determine the amount at its own discretion).

The conditions of participation are regulated in each individual federal state, because the lottery in Germany is a matter for the federal states. Commercial providers often play in the sense of syndicates with the lottery companies, but charge additional fees for this.

#### Regulations since May 4, 2013

On May 4, 2013, the following changes came into effect for the Lotto 6 out of 49 product:

• The super number replaces the additional number. This made Lotto 6 out of 49 easier. The chances of winning also increased, as the super number is only drawn from the numbers 0 to 9. The additional number, however, was drawn from 43 (49 minus 6) numbers.
• Introduction of the new prize class IX for "2 correct numbers plus super number"
• The stake per tip is one euro.
• By increasing the dividend share for prize class I “6 correct plus super numbers”, higher jackpot prizes can be expected in the top prize class.
• With the introduction of the new prize class IX for “2 correct numbers plus super number”, the probability of winning anything at all increased to 1:31 (3.125%); previously it was 1:54 (1.82%). On the other hand, the probability of achieving at least a profit equal to the sum of the stakes for these twelve picks (previously € 9, now € 12, plus around € 0.50 processing fee) when submitting all twelve picks on a normal lottery ticket has decreased because The winnings in class VIII were often over € 9.50, but it is to be expected that they will rarely exceed € 12.50 and only € 5 in the new class IX.
• While the expected profit percentages in classes II and IV-VIII have changed only moderately thanks to the 25 cents higher stake and the selected dividend shares, the expected amount of a profit in profit class III "5 correct and super numbers" is less than a quarter compared to the previous winning class III “5 correct and additional number”. Winning tens of thousands of euros has therefore become very unlikely.

New winning probabilities (from May 4, 2013):

Prize class Number of correct predictions Chance of winning Distribution share Theoretical quota
(in €)
1 to ... in %
I. 6 correct and super numbers 139,838,160.00 0.00000072% 12.8%² (00.0% ³) 8,949,642.20
II 6 correct 15,537,573.33 0.0000064% 10.0% ² (7.4% ³)0 574,596.50
III 5 correct and super numbers 542,008.37 0.00018% 05.0% ² (3.7% ³)0 10,022.00
IV 5 correct 60,223.15 0.0017% 15.0% ² (11.1% ³) 3,340.60
V 4 correct and super numbers 10,323.97 0.0097% 05.0% ² (3.7% ³)0 190.80
VI 4 correct 1,147.11 0.087% 10.0% ² (7.4% ³)0 42.40
VII 3 correct and super number 566.56 0.18% 10.0% ² (7.4% ³)0 20.90
VIII 3 correct 62.95 1.56% 45.0% ² (33.2% ³) 10.40
IX 2 correct and super numbers 75.54 1.31% Fixed profit amount (13.2% ³) 5.00
Classes I – IX 31.00 3.13% 50% stake (100%) 15.70
²: The stated percentages relate to the remaining profit distribution after deduction of the fixed profit amount in profit class IX and the allocation to 1st class.
³: The percentages in brackets are the rounded theoretical average dividend shares of the total winnings (if the probable 1.31% of all bets actually achieve profit class IX)

A jackpot is also possible for each prize class . This occurs if no winner has been determined for the class in the previous draws. The winnings will then be added to the same prize class in the next drawing. The jackpot is the sum of the carryover from the previous draw and the normal, expected winnings. Due to the totalizator principle, the exact amount of the jackpot can only be determined once the odds are fixed.Exception: If there is no win in class 2, but in class 1 (i.e. if all winners with six correct numbers also have the correct super number), the prize money from class 2 is not added to a jackpot, but to prize class 1 of the same drawing.

There are some special features to consider. If an individual win in a lower prize class exceeds that of a higher prize class, the winnings are combined and the prizes are evenly distributed between the two prize classes. If, after twelve consecutive draws in a prize class, no winnings are determined in the next drawing, a so-called compulsory distribution is made . This means that the prize money is carried over to the next lower prize class in which at least one winner is determined. A sequence can therefore contain a maximum of 13 draws. Before 2009, a sequence of a maximum of 15 draws was possible, the longest sequence so far was 13 draws. After around 60 years, the first compulsory distribution took place on May 14, 2016.

#### Regulations until May 1, 2013

The stake was 75 cents per tip and drawing. In addition, a processing fee was charged for every ticket or quick tip.

In addition to the six numbers, an additional number and a super number were drawn. The bonus number was drawn as the seventh number from the remaining 43 balls after the first six numbers. It increased the profit by one level in the lower profit classes. For example, if exactly four numbers typed by the player matched four of the six first numbers drawn, but neither of the two remaining numbers typed is the bonus number, he fell into prize category 6 (4 correct numbers with no bonus number). However, if one of the two remaining numbers matched with the bonus number, the prize category improved to class 5 (4 correct numbers and bonus number).

class required probability in% (rounded) Share of the
winnings note.
Average individual
win (Euro) Note.
Class I. 6 correct and super number correct 00,000.001 / 139.838.160 000.000000715% 010% 5,243,931.000
Class II 6 correct and wrong super number 00,000.009 / 139,838,160 ≈ 1 / 15,537,573 000.00000644% 008th % 466,127.200
Class III 5 correct and additional numbers 00,000.006 / 013,983,816 = 1 / 2,330,636 000.0000429% 005% 43,699.430
Class IV 5 correct numbers without additional numbers 00,000.252 / 013,983,816 ≈ 1 / 55,491 000.00180% 013% 2,705.200
Class V 4 correct and additional numbers 00,000.630 / 013,983,816 ≈ 1 / 22,197 000.00451% 002% 166.470
Class VI 4 correct numbers without additional numbers 00.012,915 / 013,983,816 ≈ 1 / 1,083 000.0924% 010% 40.600
Class VII 3 correct and additional numbers 00.017,220 / 013,983,816 ≈ 1/812 000.123% 008th % 24.360
Class VIII 3 correct numbers without additional numbers 00.229,600 / 013,983,816 ≈ 1/61 001.64% 044% 10.050
Class I – VIII at least 3 correct numbers 00.260,624 / 013,983,816 ≈ 1/54 001.86% 100% 20.120
Rivet less than 3 correct numbers 13,723,192 / 013,983,816 ≈ 53/54 098.1% 000% 0.000
all Nothing 13,983,816 / 013,983,816 = 1 100% 100% 0.375
Note August 2, 2003 to May 1, 2013

### 6 out of 45 in Austria

 Logo of the Austrian lottery Lottery ticket

The game will be run by Österreichische Lotterien GmbH , initially until September 30, 2027 .

For each tip, the participant has to pay the price of 1.20 euros, which is made up of the stake of 0.948 euros and an administrative fee of 0.252 euros.

In Austria, every Wednesday and Sunday, the ORF broadcast “ Lottery drawing 6 out of 45 with joker ”. The first drawing took place on September 7, 1986.

With the lottery in Austria, 48.8% of the amount paid is distributed again. These are divided into the following prize categories:

rank required probability in% (rounded) Share of the
winnings
average individual profit (rounded)
1st rank 6 correct 0.000.001 / 8.145.060 000.0000123% 40.0% 1,748,907.280
2nd rank 5 correct and additional numbers 0.000.006 / 8.145.060 = 1 / 1.357.510 000.0000737% 5.5% 40,079.130
3rd rank 5 correct numbers without additional numbers 0,000.228 / 8,145,060 ≈ 1 / 35,724 000.00280% 6.0% 1,150.600
4th rank 4 correct and additional numbers 0,000.570 / 8,145,060 ≈ 1 / 14,290 000.00700% 2.1% 161.080
5th rank 4 correct numbers without additional numbers 0.010,545 / 8,145,060 ≈ 1/772 000.129% 9.9% 41.050
6th rank 3 correct and additional numbers 0.014,060 / 8,145,060 ≈ 1/579 000.173% 4.8% 14.930
7th rank 3 correct numbers without additional numbers 0.168,720 / 8,145,060 ≈ 1/48 002.07% 17.6% 4.560
8th rank 0 correct and additional number 0.501.942 / 8.145.060 ≈ 1/16 006.16% approx. 12.6% (fixed) 1.200
1-8 rank one of the conditions is met 0.696.072 / 8.145.060 ≈ 1/12 008.55% approx. 98.5% 6.190
Rivet none of the conditions met 7,448,988 / 8,145,060 ≈ 11/12 091.5% 0.0% 0.000
all Nothing 8.145.060 / 8.145.060 = 1 100% approx. 98.5% 0.529

1.5% of the winnings is paid into an equalization pot, which is used to top up one or more prize categories in certain rounds or for additional raffles at the company's discretion. This ensures, for example, that a total of at least one million euros is always paid out in 1st place in each round, and you win an average of 0.5856 euros for each stake of 1.20 euros.

If no profit is determined in a rank, the winnings are added to the same rank in the next round (jackpot). In this case, the minimum sum of one million euros does not apply to 1st place, but it is calculated exclusively with 40% of the prize money.

This is regulated in the lottery terms and conditions.

On August 12, 2015 there was the tenth fivefold jackpot, which brought the winner with a solo six the record sum of 9,643,151.70 euros. The first six-fold jackpot was played on December 24, 2017 and this brought the two winners 6,118,478.40 euros each. The first sevenfold jackpot was won on November 14, 2018, and in the next round on November 21, 2018, around 14.9 million euros were paid out to a single winner in first place.

#### Lotto system with 0 bank numbers - costs and coverage

This table shows the 6 out of 45 lottery system when no bank numbers are played. The official system only goes from 0-7 to 0-12, everything above is theoretically playable.

system Number of tips Costs (euro) Coverage in%
0-6 1 1.20 0.000012%
0-7 7th 8.40 0.000086%
0-8 28 33.60 0.000344%
0-9 84 100.80 0.001031%
0-10 210 252.00 0.002578%
0-11 462 554.40 0.005672%
0-12 924 1,108.80 0.011344%
0-13 1,716 2,059.20 0.021068%
0-14 3,003 3,603.60 0.036869%
0-15 5,005 6,006.00 0.061448%
0-16 8.008 9,609.60 0.098317%
0-17 12,376 14,851.20 0.151945%
0-18 18,564 22,396.80 0.227917%
0-19 27,132 32,558.40 0.333110%
0-20 38,760 46,512.00 0.475871%
0-21 54.264 65,116.80 0.666220%
0-22 74,613 89,535.60 0.916052%
0-23 100,947 121,136.40 1,239365%
0-24 134,596 161,515.20 1.652486%
0-25 177,100 212,520.00 2.174324%
0-26 230.230 276,276.00 2.826621%
0-27 296.010 355,212.00 3,634227%
0-28 376.740 452,088.00 4.625380%
0-29 475.020 570,024.00 5.832001%
0-30 593.775 712,506.00 7.290002%
0-31 736.281 883,537.20 9.039602%
0-32 906.192 1,087,430.40 11.125664%
0-33 1,107,568 1,329,081.60 13.598034%
0-34 1,344,904 1,613,884.80 16,511898%
0-35 1,623,160 1,947,792.00 19.928153%
0-36 1,947,792 2,337,350.40 23.913783%
0-37 2,324,784 2,789,740.80 28.542258%
0-38 2,760,681 3,312,817.20 33.893931%
0-39 3,262,623 4,035,147.60 40.056464%
0-40 3,838,380 4,606,056.00 47.125251%
0-41 4,496,388 5,395,665.60 55.203866%
0-42 5,245,786 6,294,943.20 64.404510%
0-43 6.096.454 7,315,744.80 74.848485%
0-44 7,059,052 8,470,862.40 86.666667%
0-45 8,145,060 9,774,072.00 100.000000%

With the system 0-45 you would play all possible combinations and would have a 100% hit. However, this - apart from the very high stake - would not really make sense to play due to the low profit distribution (because the lottery company also wants to earn) and the possibility that someone else hits the main goal and you have to share the profit.

### Numbers lottery 1-90 in Austria

Numbers lottery betting slip

The number lotto 1-90 was introduced in 1752 under Maria Theresa and is thus the oldest licensed game of chance in Austria. The first drawing took place on October 21, 1752 on Lobkowitzplatz in Vienna. The drawing of 5 out of 90 numbers is carried out weekly on Tuesday, Thursday and Saturday. In the number lottery, one to five numbers can be selected from seven game types ( Extrakt, Ruf, Ambo, Terno, Ambo-Terno 3, Ambo-Terno 4, Ambo-Terno 5 ), the stake can be 0.75 euros, 1.50 euros, EUR 3, EUR 5, EUR 10, EUR 50, EUR 100 or EUR 500. If you guess the correct numbers, you win a fixed multiple of the stake, regardless of the participation of other players.

### 6 out of 42 plus 1 out of 6 in Switzerland

With the drawing on January 12, 2013, the game formula was changed in Switzerland. The 6 out of 45 system in effect since January 4, 1986 was replaced by the formula 6 out of 42. In addition, a lucky number between 1 and 6 must now be ticked for each tip. A tip costs CHF 2.50 per drawing, whereby at least two tips must be submitted. This already includes possible fees. The additional game "Plus" with the "Jackpot Plus" and the additional number are no longer available with the changes made in January 2013. This means that there is only one jackpot that is paid out for six correctly typed numbers combined with the correct lucky number. If the “rePLAY” number printed as standard on the betting slip, which is drawn at the same time as the lottery numbers (free 1-out-of-13 system), will be reimbursed for the next game in the form of free quick tips. This information applies to the two national lottery companies Swisslos and Loterie Romande .

Probabilities of winning:

Prize class Number of correct predictions Chance of winning Average expected profit
1 to ... in %
I. 6 correct and lucky numbers 31,474,716, 00 0.0000032%
II 6 correct numbers without a lucky number 6,294,943.20 0.000016% CHF 1,000,000 4
III 5 correct and lucky number 145,716.28 0.00069% CHF 5,000
IV 5 correct numbers without a lucky number 29,143.26 0.0034% CHF 1,000 4
V 4 correct and lucky number 3,330.66 0.030% CHF 150
VI 4 correct numbers without a lucky number 666.13 0.15% CHF 75
VII 3 correct and lucky number 220.41 0.45% CHF 25
VIII 3 correct numbers without a lucky number 44.08 2.27% CHF 10
Classes I-VIII 34.41 3.19%
4 : Maximum prize amount of the prize class

### 6 out of 45 plus 1 out of 6 in the Netherlands

The stake per tip is 2.00 euros. The amount of the distributed profit does not depend on the stake, as the winnings are fixed in profit classes III to VIII and are distributed in the fixed amount. Prize class I is set at one million euros, but this will be split if there are several winners. It is the same in prize class II, which is endowed with 100,000 euros. The prize money in the jackpot prize category is won by the player or players who correctly predicted the six numbers drawn from 45 numbers and the correct color from six colors. The right color is called the "jackpot color" and corresponds to the super number in the German Lotto. The jackpot in the Dutch Lotto always starts at 7.5 million euros. From drawing to drawing, the prize money will be increased by 500,000 euros. If the jackpot is not hit within twelve months, there will be a compulsory distribution to profit class I, as last happened on October 16, 2010. The last big jackpot in the amount of 26 million euros was distributed on October 15, 2011.

### 6 out of 90 in Italy

In Italy, the Sisal Spa operates the lottery game. This game is called SuperEnalotto . It is drawn on Tuesday, Thursday and Saturday. You can also take part in the superstar. In addition to the six numbers and the Jolly (corresponds to the additional number), a superstar is also drawn.

Since the Italian lottery does not have a compulsory payout, the jackpot contains e.g. B. after more than 100 unsuccessful draws in the top prize category, occasionally more than 150 million euros.

### EuroMillions / EuroMillions

ULF Tramway of Wiener Linien as an advertising medium for Euro million

In contrast to the traditional country-specific lotteries, EuroMillions (EuroMillions, EuroMillones, EuroMilhões ) was designed as a multi- country lottery from the start. On February 13, 2004, the first drawing took place, for which one could place tips in Spain, France and Great Britain. In the course of 2004 Austria, Belgium, Ireland, Liechtenstein, Luxembourg, Portugal and Switzerland were added.

Since September 27, 2016, the game formula has been “5 out of 50 plus 2 out of 12”, and a tip costs 2.20 euros, of which 1.10 euros are added to the winnings. The stakes from all countries go into a common pool, and there is a single drawing for all participating countries every Tuesday and Friday.

rank required probability in% (rounded) Share of the
winnings
average individual
profit (rounded)
01st rank 5 numbers and 2 stars 000,000.001 / 139.838.160 000.000000715% 43.20% / 27.00 %² 66,451,093.63 /
41,531,933.52 0²
02nd rank 5 numbers and 1 star 000.000.020 / 139.838.160 ≈ 1 / 6.991.908 000.0000143% 03.95% 303,798.400
03rd rank 5 numbers and 0 stars 000.000.045 / 139,838,160 ≈ 1 / 3,107,515 000.0000322% 00.92% 31,448.050
04th rank 4 numbers and 2 stars 000,000.225 / 139.838.160 ≈ 1 / 621.503 000.000161% 00.45% 3,076.440
05th rank 4 numbers and 1 star 000.004,500 / 139,838,160 ≈ 1 / 31,075 000.00322% 00.48% 164.080
06th rank 3 numbers and 2 stars 000.009,900 / 139,838,160 ≈ 1 / 14,125 000.00708% 00.67% 104.100
07th rank 4 numbers and 0 stars 000.010.125 / 139.838.160 ≈ 1 / 13.811 000.00724% 00.38% 57.730
08th rank 2 numbers and 2 stars 000.141,900 / 139,838,160 ≈ 1/985 000.101% 01.75% 18.970
09th rank 3 numbers and 1 star 000.198,000 / 139,838,160 ≈ 1/706 000.142% 01.85% 14.370
10th rank 3 numbers and 0 stars 000.445,500 / 139,838,160 ≈ 1/314 000.319% 03.50% 12.080
11th rank 1 number and 2 stars 000.744.975 / 139.838.160 ≈ 1/188 000.533% 04.95% 10.220
12th rank 2 numbers and 1 star 002,838,000 / 139,838,160 ≈ 1/49 002.03% 14.85% 8.050
13th rank 2 numbers and 0 stars 006,385,500 / 139,838,160 ≈ 1/22 004.57% 18.25% 4.400
1st - 13th rank one of the conditions is met 010,778,691 / 139,838,160 ≈ 1/13 007.71% 95.2% / 79.0 %² 13.59 / 11.27 0²
Rivet All conditions not met 129,059,469 / 139,838,160 ≈ 12/13 092.2% 00.0% 0.000
all Nothing 139.838.160 / 139.838.160 = 1 100% 95.2% / 79.0 %² 1.0472 / 0.869 0²
²: For drawings 1 to 6 of a jackpot cycle, the share of prize class 1 is 43.20% (booster fund 4.80%). For further draws in the jackpot cycle (and for super jackpots and jackpots with minimal guaranteed winnings), the share of prize class 1 is 27.00% (booster fund 21.00%).
Receipt for Austria with JOKER participation

Depending on whether the drawing is at the beginning of a jackpot cycle (cycle 1 to 6) or has already progressed further (see note on the table), 47.6% or 39.5% of the income is played out again. With a stake of 2.20 euros, the average individual win is 1.0472 euros or 0.869 euros. The missing cents for 1.10 euros are paid into the so-called booster fund. This is used “at the company's own discretion” to occasionally top up winnings or carry out additional draws. In total, 50% of the income is played out again, and you win an average of 1.10 euros for each stake of 2.20 euros.

Various factors (the low probability of winning “7 correct numbers”, the large number of players, the relatively high stakes and the type of allocation to the prize categories) quickly result in very high jackpots: A minimum jackpot of 17 million euros is guaranteed, which is increasing is now limited to 190 million euros. If the upper limit of 190 million euros is reached and no one cracks it, it will be retained for the next four drawings. If the jackpot of 190 million euros is not hit again, the winnings in the fifth drawing will be added to the next lowest winnings rank in the same round ("rolldown").

• The first record of 115.4 million euros was won by Dolores McNamara from Ireland on July 29, 2005.
• On February 3, 2006, three winners shared the record jackpot of 183 million euros after first place had not been taken for eleven draws. Two French and one Portuguese received 61,191,026 euros each.

In order not to let the jackpot rise any further, the rules of the game in the period from 2006 to 2009 provided that the jackpot would be divided between the next occupied rank after the twelfth drawing. This happened for the first time on November 17, 2006, after around 183 million euros had accumulated in the jackpot. The sum was distributed among the winners of the second tier (there were therefore 20 winners of 9.6 million euros each).

• The Bayford couple from England cracked the highest jackpot to date with 190 million euros on August 10, 2012, but due to the weakness of the euro, “only” 148.6 million pounds were paid out.
• A jackpot also filled with 190 million euros was cracked by a Portuguese on October 24, 2014, but only 152 million euros were paid out because of the gambling tax in Portugal of 20%.
• The third highest jackpot of 185 million euros (161.6 million pounds) was won on July 12, 2011 by the Weir couple from Scotland.
• On November 13, 2012, a Frenchman cracked the jackpot with 169.8 million euros and a Frenchman had already done so on 13 September 2011 with a jackpot filled with around 162.3 million euros.
• On June 13, 2014, a Spaniard won the jackpot of around 137.3 million euros. Previously, on May 8, 2009, a Spanish woman won a single win of 126.2 million euros.
• Further individual prizes were won on March 14, 2014 in the amount of 129.4 million euros (108 million pounds) to the Englishman Trotter, on May 13, 2011 in the amount of 121 million euros to the Spaniard Delgado Rodríguez and on October 7, 2011 in the amount of 117.7 million euros (101.2 million pounds) distributed to Englishman Dawes.

All in all, the concept of EuroMillionen is comparable to the German “6 out of 49 plus super number” and especially the US multi-state lotteries Powerball and Mega Millions : The trend is evidently towards ever lower chances of winning ever higher jackpots and at the same time comparatively low winnings in the other categories. The Italian SuperEnalotto continues to have the lowest chance of winning the main prize with its 6-out-of-90 principle (see above).

### Eurojackpot in Europe

Eurojackpot is a cross-border European lottery that offers a comparable, controlled range of state lottery companies as the cross-border lottery Euromillions in Western Europe. In addition to all German national lottery companies, the companies Danske Spil A / S (Denmark), Veikkaus Oy (Finland), Sisal SpA (Italy), De Lotto (Netherlands), Loterija Slovenije (Slovenia) and AS Eesti Loto (Estonia) took part at the start. at the Eurojackpot lottery.

• The first drawing took place on March 23, 2012.
• On July 6, 2012, the company Organización Nacional de Ciegos de España ( ONCE , Spain) was added.
• Since February 1, 2013 the companies Norsk Tipping AS (Norway), AB Svenska Spel (Sweden), Íslensk Getspá (Iceland), VAS Latvijas Loto (Latvia), UAB Olifėja (Lithuania) and Hrvatska Lutrija doo (Croatia) have also participated.
• Since October 10, 2014, the companies SAZKA as (Czech Republic) and Szerencsejáték Zrt. (Hungary) Eurojackpot on.

It is possible to join other European state lotteries at a later date. The Lottery Society of Slovakia has expressed its interest.

5 numbers are typed in field A from 1 to 50 and in field B 2 numbers from 1 to 10. The numbers in field B are called euro numbers. Each tip costs 2.00 euros plus the processing fee. Half of the stakes are distributed to the game participants as winnings. This is divided into twelve prize categories. A minimum jackpot of 10 million euros is guaranteed, which can grow to 90 million euros. If the maximum amount of 90 million euros is exceeded, the additional amount goes to the lower prize category. The chance of winning the main prize (class 1) in the Eurojackpot lottery is 1: 95,344,200. The winning numbers will be drawn weekly on Friday evenings at 9pm in Helsinki, Finland.

• The first main prize of 19,536,863.80 euros was won on May 11, 2012 by a syndicate from Germany.
• The highest jackpot in Germany of 90 million euros was won on October 14, 2016 by a player from Baden-Württemberg. This win is equal to a jackpot winner from the Czech Republic who also won 90 million on May 15, 2015.

### System games

In a lottery system game , more than the usual six numbers can be ticked off and thus many combinations can be commissioned at once, for example all possibilities to form combinations of six with seven specific numbers. The number of possible combinations with a system tip can be determined with the binomial coefficient , so with a system tip "3 out of 5", which covers all 3-way combinations of five numbers (5 over 3), so ten different three-way combinations are typed. The increased chance of winning goes hand in hand with a higher stake, increasing the win rate is not possible.

### Payout ratio compared to other games of chance

Playing all conceivable lottery series of the German lottery 6 out of 49 with super numbers at once (14 million betting options × 10 super numbers) would require a stake of around 120 million euros. In addition to a jackpot, most of the distributions from the other prize categories could be received in this way, but the winnings would only be in the double-digit millions. The fact that the profit balance is always clearly negative in the long term when playing the lottery is a result of the low profit distribution rate. While in roulette, for example, the players' losses per game averaged around 2.7% of the stake, in the normal lottery it is 50%.

## Number of tip combinations

With the help of combinatorics , the number of possible number combinations in the lottery can be calculated. In the game 6 out of 49 ( combination without repetition ) you can choose from 49 objects 6 without replacing and regardless of the order. There are exactly 49 for that! / (6! · (49–6)!) = 13,983,816 possibilities. In the German system with “super number” this number increases tenfold, ie 139,838,160.

system where in use options
5 out of 35 Bulgaria 324,632
6 out of 30 Lithuania 593.775
6 out of 42 Bulgaria 5,245,786
7 out of 35 Sweden 6,724,520
6 out of 45 Lotto , Austria
Belgium, Russia, Netherlands
8,145,060
6 out of 49 Bulgaria, Greece,
13,983,816
6 out of 47 Ireland 10,737,573
5 out of 49 plus 1 out of 10 France 19,068,840
6 out of 42 plus 1 out of 6 Swiss Lotto , Switzerland 31,474,716
5 out of 90 Numbers lottery 1-90 , Austria 43,949,268
6 out of 59 Great Britain 45.057.474
5 out of 50 plus 2 out of 8 Eurojackpot until October 3rd, 2014 59.325.280
5 out of 50 plus 2 out of 9 EuroMillions until May 6, 2011 76.275.360
5 out of 50 plus 2 out of 10 Eurojackpot from October 10, 2014 95.344.200
6 out of 48 plus 1 out of 8 Viking Lotto 98.172.096
5 out of 50 plus 2 out of 11 EuroMillions from May 10, 2011 116,531,800
5 out of 50 plus 2 out of 12 EuroMillions from September 27, 2016 139.838.160
6 out of 49 plus 1 out of 10 Lotto 6aus49 , Germany 139.838.160
5 out of 69 plus 1 out of 26 Powerball , USA 292.201.338
5 out of 70 plus 1 out of 25 Mega Millions , USA 302.575.350
6 out of 90 SuperEnalotto , Italy 622.614.630

## Winning probability

### Probability of winning the lottery

The hit probability in the lottery can be on the hypergeometric distribution determined by : ${\ displaystyle P_ {r} = {\ frac {{\ tbinom {6} {r}} {\ tbinom {N-6} {6-r}}} {\ tbinom {N} {6}}}, r \ in \ {0, \ ldots, 6 \}}$

 6 out of 49 (N = 49) 6 out of 45 (N = 45) H 49.6.6 H 45.6.6 r number Probability (P) in% r number Probability (P) in% 0 6.096.454 43,596 0 3,262,623 40.056 1 5,775,588 41,302 1 3,454,542 42,413 2 1,851,150 13.238 2 1,233,765 15.147 3 246.820 1.7650 3 182.780 2.2441 4th 13,545 0.096862 4th 11,115 0.13646 5 258 0.0018450 5 234 0.0028729 6th 1 0.0000071511 6th 1 0.000012277 ∑ 13,983,816 100.00 ∑ 8,145,060 100.00 Expected value 0.735 Expected value 0.800 scattering 0.578 scattering 0.615
 Probability in the German lottery Probability in the German Lotto scaled logarithmically

If you add up the numbers, you can see from the table that the chance of a rivet (0, 1 or 2 correct numbers out of 6) with the Austrian lottery is 97.6%, with the German lottery 98.1%.

The expected value corresponds to the average number of correctly guessed numbers. For example, if you play 6 out of 49 in 100 drawings, you can count on around 73 correctly guessed numbers in total. (A maximum of 600 would be possible, with a hundred times 6 correct ones.) It makes no difference whether the tip given is different every time or always the same.

With the Austrian Lotto you get a correct number more often than none, as the table above shows (6 out of 45, H 45,6,6 ). This also applies to the Lithuanian lottery (6 out of 30), in which 2 correct numbers occur even more often than 0 correct numbers.

The following applies to the lottery in Germany until May 2013:

The winning opportunities with an additional number were each division of the cases of 5, 4 and 3 correct numbers: an additional number was drawn from the 43 remaining numbers.

The following probabilities resulted:

Result number Probability
(rounded)
distribution mean individual
profit (euro)
0 correct numbers without additional numbers 5,245,786 037.513%
0 correct and additional number 850,668 006.0832%
1 correct number without an additional number 5,104,008 036.499%
1 correct and additional number 671,580 004.8026%
2 correct numbers without an additional number 1,678,950 012.006%
2 correct and additional numbers 172,200 001.2314%
3 correct numbers without additional numbers 229,600 001.6419% 22.0% 10.050
3 correct and additional numbers 17,220 000.12314% 04.0% 24.360
4 correct numbers without additional numbers 12,915 000.092357% 05.0% 40.600
4 correct and additional numbers 630 000.0045052% 01.0% 166.470
5 correct numbers without additional numbers 252 000.0018021% 06.5% 2,705.200
5 correct and additional numbers 6th 000.000042907% 02.5% 43,699.430
6 correct and wrong super number 910 000.0000064360% 04.0% 466,127.200
6 correct and super number correct 110 000.00000071511% 05.0% 5,243,931.000
total 13,983,816 100.00% 50.0% 0.375
Explanation: Of the 246,820 cases with 3 correct numbers, the additional number is also correct in 3/43 of all cases and incorrect in 40/43 of all cases.

The formula to determine the probability P r, z for r correct numbers including z correct additional numbers ( z {0, 1}) is ${\ displaystyle \ in}$

${\ displaystyle P_ {r, z} = {\ frac {{\ tbinom {6} {r}} {\ tbinom {1} {z}} {\ tbinom {49-6-1} {6-rz}} } {\ tbinom {49} {6}}} = {\ frac {{\ tbinom {6} {r}} {\ tbinom {42} {6-rz}}} {\ tbinom {49} {6}} } \.}$

Reminder for the formula on the left: Below the fraction line is the sum of the components above the fraction line. This formula uses binomial coefficients . Since only one additional number is drawn from 49 for 6, the term is always equal to 1 and can be omitted for the calculation (right formula). This formula does not take into account the independently drawn super number, which divides the chance of winning in the case of 6 correct numbers to 1/10 for prize class I and 9/10 for prize class II. All other prize categories remain unaffected. ${\ displaystyle {\ tbinom {1} {z}}}$

The probabilities for r correct ones, taking into account z correct or incorrect additional numbers, add up to the probability without considering an additional number, that is , since the relationship applies according to the calculation rules for binomial coefficients . The number in the numerator is therefore exactly the sum of the numbers with correct and incorrect additional numbers (e.g. 4 correct numbers = 630 + 12,915 = 13,545 possibilities). ${\ displaystyle P_ {r} = \ sum _ {z = 0} ^ {1} P_ {r, z}}$${\ displaystyle {\ tbinom {43} {6-r}} = {\ tbinom {42} {6-r}} + {\ tbinom {42} {5-r}}}$

The expected value for the prizes in the individual prize categories is independent of the number of tickets sold, because the higher the number of tickets, the more often each prize category is represented on average and the more winners the sum is distributed among. Only the spread of the amount of winnings (and thus, for example, the amount of a jackpot) depends on the number of tips.

The mathematical probability often contradicts the subjectively perceived chance, see Estimating Probabilities .

### Probability of winning for EuroMillions

Note: The following list refers to the variant "5 out of 50 plus 2 out of 12".

If all 139,838,160 possible tips were given before a drawing, the following picture would result after the drawing.

Result number Probability
(rounded)
distribution mean individual
profit (euro)
0 numbers and 0 stars 54.979.155 039.316%
0 numbers and 1 star 24,435,180 017.474%
0 numbers and 2 stars 1,221,759 000.87369%
1 number and 0 stars 33,523,875 023.973%
1 number and 1 star 14,899,500 010.655%
1 number and 2 stars 744.975 000.53274 2.475% 10.220
2 numbers and 0 stars 6,385,500 004.5664% 9.125% 4.400
2 numbers and 1 star 2,838,000 002.0295% 7.425% 8.050
2 numbers and 2 stars 141,900 000.10147% 0.875% 18.970
3 numbers and 0 stars 445,500 000.31858% 1,750% 12.080
3 numbers and 1 star 198,000 000.14159% 0.925% 14.370
3 numbers and 2 stars 9,900 000.007079613% 0.335% 104.100
4 numbers and 0 stars 10.125 000.0072405% 0.190% 57.730
4 numbers and 1 star 4,500 000.0032180% 0.240% 164.080
4 numbers and 2 stars 225 000.00016090% 0.225% 3,076.440
5 numbers and 0 stars 45 000.000032180% 0.460% 31,448.050
5 numbers and 1 star 20th 000.000014302% 1.975% 303,798.400
5 numbers and 2 stars 1 000.00000071511% 21.60% / 13.50 %² 66,451,093.63 /

41,531,933.520

total 139.838.160 100.00% 47.60% / 39.50% ² 0.914
The probability of a loss is 92.292%, which means that out of 100 tips submitted, around 8 tips are in the winning ranks.

The formula to find the probability P r, s for r numbers and s stars is

${\ displaystyle P_ {r, s} = {\ frac {{\ tbinom {5} {r}} {\ tbinom {45} {5-r}} {\ tbinom {2} {s}} {\ tbinom { 10} {2-s}}} {{\ tbinom {50} {5}} {\ tbinom {12} {2}}}} \.}$

This formula uses binomial coefficients .

## Record profits

### Germany

The first millionaire in the German lottery 6 out of 49 was chosen on September 2, 1956. He won exactly DM 1,043,364.50. Taking into account inflation , the amount today corresponds to EUR 2,593,592.

#### Biggest winnings (in jackpot)

National Lotto:

• On December 5, 2007, three players from Schleswig-Holstein, North Rhine-Westphalia and Thuringia shared the largest jackpot in German lottery history at EUR 45,382,458. All three had guessed the correct winning numbers 9, 10, 24, 28, 39, 42 and the matching super number 3 and each received around 15 million euros.
• The highest single win with 37,688,291.80 euros was achieved on October 7, 2006 by a player from North Rhine-Westphalia .
• The second highest single win was played out in the compulsory distribution described below.
• The third highest single win was 33.8 million and was played on July 8, 2015 in Berlin .
• The highest win for 6 correct numbers without a super number took place on May 14, 2016 through the regulation of the compulsory distribution of 37,050,634.80 euros. A player from North Rhine-Westphalia also achieved the second highest individual win.
• The second highest win for 6 correct numbers without a super number (but also through the regulation of the compulsory distribution) was achieved on September 14, 2016. It was EUR 32,759,747.40.
• The third highest win for 6 correct numbers without a super number (compulsory distribution) was reached on June 29, 2019. It amounted to EUR 31,482,812.60 million.
• The highest win for 6 correct numbers without a super number before 2009 was reached on December 4, 1999. It amounted to the equivalent of 4.1 million euros. This was not a jackpot payout.

#### Lowest winnings (in jackpot)

National Lotto:

• The lowest win in prize class 1 (7 correct numbers for “7 out of 38”) was achieved on April 25, 1984 by 69 winners with the numbers 1, 3, 5, 6, 9, 12, 25. It was DM 16,907.00 (EUR 8,644.41).
• The highest number of winners for 6 correct numbers were 222 winners on January 23, 1988 with a profit of 84,803.90 DM (the equivalent of 43,359.55 euros) - all of them had guessed the two triplets 24, 25, 26 and 30, 31, 32.
• 6 numbers in the arrangement of a U crossed 124 players on October 4, 1997. With the numbers 9, 13, 23, 27, 38 and 40 each won 53,982 DM.
• The winning numbers of the Dutch lottery from the previous week were taken over by 205 participants on June 18, 1977. For the 6 correct numbers there was DM 30,737.80.
• On April 10, 1999 the numbers 2, 3, 4, 5, 6 and 26 were drawn. As a result, 38,008 players with 5 correct numbers each won DM 379.90.
• The lowest win in prize class 3 (5 correct numbers with an additional number) in the lottery 6 out of 49 was achieved on February 15, 2003 by 25,141 winners. Since there were only 9,436 fives, both ranks had to be merged. The quota was EUR 201.30 each. Five of the winning numbers and the bonus number formed a continuous line on the ticket from top right to bottom left. The winning line was 4, 6, 12, 18, 24, 30, bonus number 36.
 1 2 3 4th 5 6th 7th 8th 9 10 11 12 13 14th 15th 16 17th 18th 19th 20th 21st 22nd 23 24 25th 26th 27 28 29 30th 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49
 1 2 3 4th 5 6th 7th 8th 9 10 11 12 13 14th 15th 16 17th 18th 19th 20th 21st 22nd 23 24 25th 26th 27 28 29 30th 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49
 1 2 3 4th 5 6th 7th 8th 9 10 11 12 13 14th 15th 16 17th 18th 19th 20th 21st 22nd 23 24 25th 26th 27 28 29 30th 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49
 1 2 3 4th 5 6th 7th 8th 9 10 11 12 13 14th 15th 16 17th 18th 19th 20th 21st 22nd 23 24 25th 26th 27 28 29 30th 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49

### Switzerland

• On December 17, 2016, the biggest jackpot in the Swiss number lottery - around CHF 70 million - was cracked, with the sum divided between three winners.
• The largest single win was 48.6 million francs on August 23, 2014. The second largest win was achieved in May 2020 (45 million francs). The third largest was in March 2010 (35.8 million francs), the fourth largest (34.5 million) in November 2013. Swisslos maintains a list of the ten highest lottery wins of all time on its website; all have been implemented since 2009.
• On April 28, 1979 Werner Bruni became the first lottery millionaire in Switzerland. His life is the subject of a biography published in 2010.
• The highest win in the Euro Millions lottery was achieved on August 23, 2013 when a ticket issued in Valais was worth CHF 115.5 million.

### Austria

#### Highest profits

• In the Austrian Lotto there was the highest single win to date on November 2, 2018 at 14,926,157.30 euros.
• The second largest single prize was achieved on August 12, 2015 in the amount of 9,643,151.70 euros.
• The third largest single win came on August 15, 2012 in the amount of 9,437,932.50 euros.
• On June 9, 2013, the fourth largest single prize to date was achieved at EUR 9,231,788.80 and on December 22, 2010, the fifth largest single prize to date was achieved at EUR 8,905,907.20.

jackpot

• The first six-fold jackpot was played on Christmas Eve 2017. This was cracked by a Waldviertler and an Obersteirer each with a quick tip. The six correct numbers were 7, 8, 14, 33, 38 and 40. With these numbers, the two winners each achieved a total of 6,118,478.40 euros.
• The first Austrian five-fold jackpot was cracked on May 28, 2008 by two people who had bet the numbers 14, 30, 32, 39, 40 and 42. A sum of 4,918,840.20 euros was paid out to both winners. The second five-fold jackpot in the lottery history was cracked on October 23, 2011 by two women with the six correct numbers (2, 18, 27, 28, 37 and 38) and each won € 5,507,164.10 a.

In the European lottery EuroMillionen, on April 28, 2006, a betting slip handed in in Austria won the first place for "5 plus 2 correct". The specialty was that the correct numbers were shown twice on the ticket played in Vienna (total profit 13 million euros).

The highest profit in the EuroMillionen lottery was achieved on May 16, 2008, when a ticket issued in Carinthia was EUR 55.6 million.

#### Lowest Profits

In the drawing on May 21, 1989, 23 sixes were achieved. The reason for the extraordinary frequency of this winning tier was the line-shaped pattern (left illustration) that the winning numbers 2, 14, 16, 26, 28 and 40 formed. The additional number was the 12.

The right illustration shows the winning numbers from January 25, 1998 with exactly 6,110 fives. The single winner was only left with € 86.89. Here, too, a pattern (diagonal) was the reason for the many wins. The winning numbers in this case were 1, 15, 22, 29, 36 and 41 (bonus number: 10).

 1 2 3 4th 5 6th 7th 8th 9 10 11 12 13 14th 15th 16 17th 18th 19th 20th 21st 22nd 23 24 25th 26th 27 28 29 30th 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
 1 2 3 4th 5 6th 7th 8th 9 10 11 12 13 14th 15th 16 17th 18th 19th 20th 21st 22nd 23 24 25th 26th 27 28 29 30th 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45

### Europe and USA

• In Europe, the highest jackpot played in Europe of 190 million euros (148.6 million pounds) in the multi-country lottery EuroMillions was hit by a British couple on August 10, 2012. Due to the weak euro exchange rate, which is the basis for currency conversion, the aforementioned profit is only considered to be the second highest in Great Britain.
• On July 12, 2011, a British couple also managed to crack the highest ever jackpot in Europe of 185 million euros (161.6 million pounds) at EuroMillions. The conversion rate to US dollars on July 12, 2011 results in an amount of 258.5 million US dollars. It is therefore the second highest net individual win in the world, as the winnings are not subject to any tax in the UK, whereas lottery winnings are taxed in the USA.
• In Italy, at the end of October 2010, the highest single-state jackpot in Europe of over 178 million euros was cracked in the SuperEnalotto lottery by 70 lottery players. All 70 male winners had bought their tickets according to a game system with a stake of 24 euros each and won the equivalent of “only” 2.538 million euros per person. As early as August 2009, a single winner achieved the second-highest win in the history of Italy and the fifth-highest win in the history of European lotteries with 146.9 million euros.
• In Portugal, on October 24, 2014, a single winner achieved the highest prize of 190 million euros in the multi-country lottery EuroMillionen, but only 152 million euros were paid out because of the 20% gambling tax introduced in 2013.
• In France, in September 2011, a single winner achieved the fifth-highest win in the history of European lotteries with 162.3 million euros.
• The world's highest jackpot to date was on January 13, 2016 at around US $1,586,400,000 (more than US$ 1.5 billion) with an annual payout mode over a period of 29 years - or around US $983 million as a one-off payout - played in the US Powerball lottery . Three players from California, Florida and Tennessee had checked the correct combination of numbers. • Other top winnings were$ 656 million (spread over 26 years; with immediate payout 474 million) played on March 30, 2012 at the Mega Millions lottery after 18 previous draws in a row without a main prize. It was cracked by three players.
• The previous world record jackpot of $390 million was won in March 2007 by two players at Mega Millions. The world's highest single win of US$ 590.5 million in the Powerball lottery on May 18, 2013 was achieved by an 84-year-old American woman . Previously, two players also hit a jackpot at Powerball with 587.5 million US dollars. Since all winners chose the payoff option rather than the annuity payment option, the first case came after taxes of $331.5 million, the second case was$ 155.4 million, the third case was $278 million, and the fourth case was$ 277 Million dollars to be paid out.

## Use of the income

Caption of the painting "Resurrection" by Max Beckmann , with a reference to the purchase with lottery funds

In 2013, stakes in Germany totaled around seven billion euros per year. They are used as follows:

• Half of the income is paid out to all winners ( totalizator principle ), i.e. the payout ratio is 50%. It is this amount that players are speculating on.
• 23% is collected by the tax authorities as a concession fee or special- purpose income, i.e. this amount has to be spent by the state again for legally specified purposes, such as sports promotion, art purchases, the environment or youth projects.
• 16.7% go to the general state budget as lottery tax.
• 7.5% are paid to the acceptance points (tenants) as commission .
• 2.8% is retained for administration and as income for the lottery companies.

So if lottery tickets are sold for around 10,000 euros, 750 euros remain at the acceptance point and 1,670 euros at the Ministry of Finance. 5,000 euros of this will be distributed to the various prize categories (see above). The percentage distribution is different depending on the prize class. Within the individual prize categories, however, the winnings are distributed evenly over the number of prizes.

In Switzerland, a large part of the lottery net profit goes to the so-called lottery funds of the cantons.

## Influencing the chance of winning

### statistics

Statistics that show how many draws a number has not been drawn lead many people to the conclusion that a certain number selection can influence the chance of winning. But since chance has no memory, this is not possible.

For example, up to the German record jackpot (October 7, 2006), the number 49 in the Saturday lottery was drawn a total of 371 times and thus 1.4 times as often as the number 13 , which was drawn only 262 times. Anyone who avoided the 13 and favored the 49 in the past few decades would actually have made at least a smaller loss than usual. However, it would be a mistake to avoid the 13 in the future, as it has been drawn less often so far, or to favor it because it would have some catching up to do, because every drawing is statistically independent of the previous ones.

Draw statistics in the lottery are only retrospectively informative; they are worthless insofar as no recommendations for action for the future can be derived from them. However, these statements only apply to an actually completely random drawing. See also the main article player fallacy .

### strategy

The probability of a win cannot be influenced, but the amount of the win can; because the numbers are drawn at random, but not ticked at random. By typing other numbers than the crowd, you can win higher amounts if you win.

Strategies to increase the amount of winnings:

• Avoid the lucky numbers 7 and 3, the central number 25, the number 19 (part of the year of birth) and the 9
• Avoid graphic number patterns or entire rows of numbers lying directly next to each other
• Prefer the rarely typed numbers on the left, right and bottom with the exception of the lucky number 7

All winning numbers are equally likely, but since many people choose certain numbers, such as their own birthday, out of convenience or superstition, the amount of winnings is often divided among more winners when they are drawn and the amount of each individual win is then significantly lower. In Germany, for example, there was only the equivalent of 8,000 euros for 6 correct numbers in 1984 and less than 200 euros for 5 correct numbers for the number series 2, 3, 4, 5, 6 drawn in 1999 - around 38,000 tipsters had ticked these 5 numbers.

Avoiding frequently typed numbers while at the same time preferring rarely typed number combinations is the only way to increase the expected value of the profit when playing the lottery.

## Drawing and announcement of the winning numbers in Germany

The winning numbers of the German Lotto block are drawn under the supervision of a legal officer of a finance or interior ministry, depending on which ministry of a federal state is responsible for supervising the lottery administration. The supervisory officers are sent on a rotation basis from all 16 federal states to the drawing lots. During the drawing, a drawing assistant ("Lottofee") and a drawing manager are also on site.

From 1965 to 2013 the drawing was broadcast on Saturday by the Hessischer Rundfunk (hr) as a supply for the joint program Das Erste ; thus the winning numbers were announced live nationwide on television. Most recently, the show drawing of the lottery numbers was produced in the Main Tower in Frankfurt am Main .

The ZDF broadcast from 1982 to 2013 live from the broadcasting center in Mainz-Lerchenberg the draw on Wednesday.

Since July 3, 2013, both drawings have been broadcast live on the Internet by the German Lotto and Totoblock. The numbers are taken from the Saarländischer Rundfunk (SR) in Saarbrücken . The live draws will be moderated alternately by Chris Fleischhauer and Miriam Hannah . This is the first time in the history of the German lottery that a man is moderating the drawing of the lottery numbers. Celina Fries and Patrick Klötzer act as representatives . Until June 2017, Nina Azizi was in Hannah's place. However, the winning numbers will continue to be announced at a fixed time on Erste and ZDF. The live drawing resulted in constant ratings in the seven-digit range for public television. The first Saturday draw on the Internet, however, only had 12,000 and the subsequent Wednesday draw only 10,000 viewers.

In earlier years before the introduction of live transmission , the numbers were recorded and transmitted with a time delay. The drawing has been carried out automatically since the 1970s with the help of a transparent drum in which there are normal table tennis balls with black numbers painted on; Previously, lots were used to determine winning numbers. Elvira Hahn was the first lottery fair in history on October 9, 1955 (as a twelve-year-old) in Hamburg, at that time in a public event, but not on television.

## Taxation of Profits

### Germany

In the German income tax, the winnings are not assigned to any type of income, in particular they do not fall under the catch-all offense of § 22 No. 3 sentence 1 EStG . The popular claim that gambling winnings are “tax-free” is not correct under tax law: Only income that is assigned to one type of income ( Section 2 (1) No. 1 to 7 EStG) can be tax-free . Rather, game winnings are “not taxable” in Germany. However, this tax theory difference has hardly any practical relevance. Income generated later with the capital gained, such as interest, is then taxable as income.

### Austria

In Austria, lottery winnings are not part of the income and are therefore not taxable.

### Switzerland

In Switzerland, withholding tax is automatically paid on lottery winnings from major games over 1,000,000 Swiss francs permitted under the Federal Law on Money Games, which is 35%. Up to this amount, lottery winnings are also free of income tax. According to Swisslos , only the amount in excess of the million is taxed. The withholding tax on interest, income from securities and also lottery winnings is offset by the tax office with the tax liability if this is stated in the tax return. In any case, most of the Swiss cantons as well as the federal government consider lottery winnings over CHF 1,000,000 from major games permitted under the Federal Law on Money Games as income, and therefore income taxes in excess of the withholding tax amount already paid may be due on winnings in the millions. The tax-free amount was increased from CHF 1,000 to CHF 1,000,000 with effect from January 1, 2019 for major games permitted under the Federal Law on Money Games. Some cantons levy their own tax on lottery winnings (at least before 2019), but no income tax.

Swiss Lotto players who are not domiciled in Switzerland are also subject to withholding tax (at least before 2019). There is also no possibility for them to have this withholding tax reimbursed or credited through a declaration in their home country. Article 2 of the double taxation agreement between Switzerland and Germany explicitly excludes this.

### Netherlands

In the Netherlands, the gambling tax (kansspelverbinding) is 29% on lottery winnings of more than 454 euros. Until December 31, 2005 the tax rate was 25%. The lottery company has to pay the gaming tax directly, which reduces the winnings paid out accordingly.

## Trivia

• On October 9, 1955, 13 was the first number drawn in the German lottery. The other numbers - they were drawn alternately by two orphan girls - were 41, 3, 23, 12, and 16. Overall, however, 13 is the least common number drawn.
• Since 2004, private companies have also offered lottery games on the Internet. Some of these lotteries were free for the players because they were sponsored by advertising. The winnings were not covered by betting stakes, but by sponsorship money and financial insurance. Therefore, this variant was not considered a game of chance, but a competition.
• In Germany 53% of the population at least occasionally play Lotto or Toto .
• In Israel , on September 21st in 2010 and eight draws later on October 16th, the same six numbers were drawn: 13, 14, 26, 32, 33 and 36. Only the additional numbers were different. The probability of such a repeat in the Israeli lottery 6 out of 37 is 1: 291,000.

## Gambling communities

Syndicates organize joint lottery tickets according to certain systems. Several players play a joint lottery ticket and share the winnings if necessary. In addition to privately organized syndicates, there are also various commercial providers who enable participation in syndicates on a larger scale for a fee.

## Number of participants and sales

Market data such as the number of participants and sales development of lotteries in Germany are collected, researched and published by the Federal Center for Health Education and the Gambling Research Center at the University of Hohenheim , among others . Studies and forecasts on market development are regularly collected by market research institutes on behalf of the German Lotto Association and published by it.

According to these sources, for example, 31.5% of the German population took part in the “6 out of 49” lottery in 2011. At Game 77 and / or Super 6 it was 21% of the population in the same period.

According to information from the German Lotto and Totoblock , the total stakes in Baden-Württemberg in 2007 amounted to 660.1 million euros for the 6 out of 49 lottery; 129.0 million euros for the game 77 and 91.9 million euros for Super 6.

## literature

• Lottery. In: Johann Heinrich Zedler : Large complete universal lexicon of all sciences and arts . Volume 18, Leipzig 1738, column 564-573.
• Lotterie , Oeconomische Encyclopädie von Krünitz, Volume 81, 1801, pp. 13-136
• Johann Heinrich Bender: The lottery. A legal treatise . Mohr, Heidelberg 1832 ( digitized version ).
• Klaus Lange: Numbers lottery. Theory and odds of a popular game of chance . Otto Maier, Ravensburg 1980, ISBN 3-473-43059-5
• Manfred Zollinger: History of Gambling. From the 17th century to the Second World War. Böhlau, Vienna a. a. 1997, ISBN 3-205-98518-4 .
• Peter J. Tettinger , Jörg Ennuschat: Basic structures of the German lottery law. Vahlen, Munich 1999, ISBN 3-8006-2503-2 ( Studies on Public Law and Administrative  Doctrine 66).
• Gerhard Strejcek (Ed.): Lotto and other games of chance. Considered legally, economically, historically and in the light of world literature. Austrian Lottery Society, Vienna. Linde, Vienna 2003, ISBN 3-7073-0392-6 .
• Stefan Korte: The state gambling system. Privatization of state monopolies using the example of the lottery, sports betting and casino sectors. Heymann, Cologne a. a. 2004, ISBN 3-452-25795-9 ( Studies on Public Commercial Law 63), (At the same time: Dissertation, University of Hamburg 2004).
• Karl Bosch: Das Lottobuch , Oldenbourg Wissenschaftsverlag, Munich 2004, ISBN 3-486-57615-1
• Christoph Lau, Ludwig Kramer: The relativity theory of happiness. About the lives of lottery millionaires. Centaurus-Verlag, Herbolzheim 2005, ISBN 3-8255-0605-3 ( contributions to social science research  24).
• Lottery players pay high taxes - others benefit , press release by the Max Planck Society, July 21, 2008
• Mark Lutter: Markets for Dreams. The Sociology of the Lottery Game . Frankfurt / Main: Campus, 2010.
• Werner Ogris : 250 years of lottery bans. Lotteries - yes or no? in: Historical Museum of the City of Vienna (Ed.): On the trail of luck. 250 years of the Austrian number lottery. Verlag des Historisches Museum, Vienna 2002, ISBN 3-85202-152-9 , pp. 84−99

Commons : Lotto  - collection of images, videos and audio files
Wiktionary: Lotto  - explanations of meanings, word origins, synonyms, translations
Wikisource: Lottery  Sources and Full Texts

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2. Peter A. Lehmann: Historical Remarques on the Latest Things in Europe (Volume 8), Johan Niclas Gennagel, Hamburg 1707, p.  55
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9. ↑ Amending State Treaty on Gambling, draft version October 6, 2011
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29. This figure was based on the template: Inflation determined and refers to the previous calendar year at most
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36. ^ Bruni, Werner, Markus Maeder: Lottokönig . Gockhausen: Wörterseh Verlag, 2010.
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49. RZ-Online GmbH: Theme of the day: ping-pong balls and a fairy ... . rhein-zeitung.de. October 7, 2006.
50. →… taxable income that falls under the types of income listed in the law. Lottery winnings, for example, are not taxable ... ( Memento from June 28, 2011 in the Internet Archive ) In: bmf.gv.at