Keno (gambling)
Keno is a game of chance that originally came from the Chinese Empire .
etymology
The name Keno is not of Chinese origin, but is derived from the French quine , the abbreviation for the quintern , that is, five correct numbers in the classic lottery 5 out of 90 (according to Merriam-Webster's Collegiate Dictionary ), this becomes clear when you talk about Keno in English and pronounce quine in French.
history
Legend has it that the Han Dynasty, ruled by Cheung Leung, was embroiled in a long and hard war that depleted the city's funds. Cheung Leung could no longer get any money from the townspeople because he had taxed them as much as he could. So he came up with the idea of a new game - Keno. Keno was invented as a lottery to raise money to complete the Han Dynasty War. Years later, keno was used again to raise money for the Great Wall of China, according to legend. However, according to historical records, the Chinese lottery was not licensed until the 19th century. So whether these legends are true is not known for sure.
Instead of numbers, a selection of 120 Chinese characters had to be guessed at. The drawing was carried out in such a way that white doves picked a few from a pile of letters with the corresponding symbols - this type of drawing is still used today in many regions of Asia. The game was therefore called the White Pigeon Game , but the name may also be derived from the fact that the results were brought by carrier pigeons to distant villages.
Chinese workers brought it to the United States in the early 20th century . The Chinese characters were replaced by numbers and the number was reduced from 120 to 80.
Situation in Germany
Today it is played in different variations all over the world. Keno also came to Germany via the USA . It is currently played in all federal states, in Saxony-Anhalt only since March 4, 2013, and offered through the regional lottery companies.
From 70 numbers (in the USA 80) 20 are drawn, the player can type two to ten numbers. A stake of 1, 2, 5 or 10 euros results in a profit of up to 1,000,000 euros according to fixed odds (with a stake of 10 euros and 10 correct numbers). The chances of winning the maximum are much better than with the lottery - 1: 2,147,179 for Keno (10 correct numbers) compared to 1: 139,838,160 (6 correct numbers plus super number for the lottery 6 out of 49).
With Keno Type 9 and Keno Type 10, the maximum winnings can be lower if these winnings are distributed multiple times.
The first keno drawing in Germany took place on February 2nd, 2004. At that time, players in the federal states of Hesse, Rhineland-Palatinate and Saarland could submit tickets. The Keno numbers were determined Monday through Saturday. Since June 13, 2010, the keno numbers have been determined daily, including on Sundays. The drawing will take place at 7:10 p.m. on the premises of Lotterie-Treuhandgesellschaft mbH Hessen in Wiesbaden and is open to the public. The drawing will be broadcast on the Keno homepage.
Profit opportunities
| typed numbers (n) | Correct (k) | possible Combinations | probability | Profit factor |
|---|---|---|---|---|
| 2 | 0 | 1,225 | 50.72464% | 0 |
| 2 | 1 | 1,000 | 41.40787% | 0 |
| 2 | 2 | 190 | 7.86749% | 6th |
| 3 | 0 | 19,600 | 35.80563% | 0 |
| 3 | 1 | 24,500 | 44.75703% | 0 |
| 3 | 2 | 9,500 | 17.35477% | 1 |
| 3 | 3 | 1,140 | 2.08257% | 16 |
| 4th | 0 | 230,300 | 25.11738% | 0 |
| 4th | 1 | 392,000 | 42.75299% | 0 |
| 4th | 2 | 232,750 | 25.38459% | 1 |
| 4th | 3 | 57,000 | 6.21663% | 2 |
| 4th | 4th | 4,845 | 0.52841% | 22nd |
| 5 | 0 | 2,118,760 | 17.50605% | 0 |
| 5 | 1 | 4,606,000 | 38.05664% | 0 |
| 5 | 2 | 3,724,000 | 30.76920% | 0 |
| 5 | 3 | 1,396,500 | 11.53845% | 2 |
| 5 | 4th | 242,250 | 2.00157% | 7th |
| 5 | 5 | 15,504 | 0.12810% | 100 |
| 6th | 0 | 15,890,700 | 12.11957% | 0 |
| 6th | 1 | 42.375.200 | 32.31887% | 0 |
| 6th | 2 | 43,757,000 | 33.37274% | 0 |
| 6th | 3 | 22,344,000 | 17.04140% | 1 |
| 6th | 4th | 5,935,125 | 4.52662% | 2 |
| 6th | 5 | 775.200 | 0.59123% | 15th |
| 6th | 6th | 38,760 | 0.02956% | 500 |
| 7th | 0 | 99.884.400 | 8.33221% | 0 |
| 7th | 1 | 317,814,000 | 26.51157% | 0 |
| 7th | 2 | 402.564.400 | 33.58132% | 0 |
| 7th | 3 | 262,542,000 | 21.90086% | 0 |
| 7th | 4th | 94,962,000 | 7.92159% | 1 |
| 7th | 5 | 18,992,400 | 1.58432% | 12 |
| 7th | 6th | 1,938,000 | 0.16167% | 100 |
| 7th | 7th | 77,520 | 0.00646% | 1,000 |
| 8th | 0 | 536.878.650 | 5.68706% | 1 |
| 8th | 1 | 1,997,688,000 | 21.16116% | 0 |
| 8th | 2 | 3,019,233,000 | 31.98221% | 0 |
| 8th | 3 | 2,415,386,400 | 25.58577% | 0 |
| 8th | 4th | 1,115,803,500 | 11.81951% | 1 |
| 8th | 5 | 303.878.400 | 3.21893% | 2 |
| 8th | 6th | 47,481,000 | 0.50296% | 15th |
| 8th | 7th | 3,876,000 | 0.04106% | 100 |
| 8th | 8th | 125,970 | 0.00133% | 10,000 |
| 9 | 0 | 2,505,433,700 | 3.85253% | 2 |
| 9 | 1 | 10,737,573,000 | 16.51083% | 0 |
| 9 | 2 | 18,978,036,000 | 29.18193% | 0 |
| 9 | 3 | 18,115,398,000 | 27.85547% | 0 |
| 9 | 4th | 10.265.392.200 | 15.78477% | 0 |
| 9 | 5 | 3,570,571,200 | 5.49035% | 2 |
| 9 | 6th | 759,696,000 | 1.16816% | 5 |
| 9 | 7th | 94,962,000 | 0.14602% | 20th |
| 9 | 8th | 6,298,500 | 0.00969% | 1,000 |
| 9 | 9 | 167.960 | 0.00026% | 50,000 |
| 10 | 0 | 10.272.278.170 | 2.58940% | 2 |
| 10 | 1 | 50,108,674,000 | 12.63123% | 0 |
| 10 | 2 | 102.006.943.500 | 25.71358% | 0 |
| 10 | 3 | 113,868,216,000 | 28.70353% | 0 |
| 10 | 4th | 76.990.441.500 | 19.40750% | 0 |
| 10 | 5 | 32.849.255.040 | 8.28053% | 2 |
| 10 | 6th | 8,926,428,000 | 2.25015% | 5 |
| 10 | 7th | 1,519,392,000 | 0.38300% | 15th |
| 10 | 8th | 154.313.250 | 0.03890% | 100 |
| 10 | 9 | 8,398,000 | 0.00212% | 1,000 |
| 10 | 10 | 184,756 | 0.00005% | 100,000 |
The probability results from the hypergeometric distribution and thus corresponds to the calculation principle of the well-known Lotto 6 out of 49 . It is the population of possible numbers, the number of samples taken. denotes the number of typed numbers and corresponds to the kenotype, a natural number between 2 and 10. By inserting it you will find the probability that there are exactly the right ones among these . E.g. for the probability of getting exactly 3 correct numbers out of 10 typed: as can also be seen in the table above.
The general formula for all probabilities of kenotype n is:
Expected value
Below is a table with the exact values for a game with a stake of € 1 and € 10 with a fee of € 0.25 each.
| typed numbers | Expected value of € 1 stake | Expected value of € 10 stake | Total loss probability |
|---|---|---|---|
| 2 | −0.777950311 € | € −5.529503 106 | 92.13% |
| 3 | −0.743240775 € | € −5.182407746 | 80.56% |
| 4th | −0.755570431 € | - € 5.305704306 | 67.87% |
| 5 | −0.751020985 € | - € 5.260209854 | 86.33% |
| 6th | - € 0.752560653 | −5.275606527 € | 77.81% |
| 7th | - € 0.754334893 | - € 5.293348929 | 90.33% |
| 8th | € −0.760616291 | € −5.356162907 | 78.73% |
| 9 | −0.749546918 € | −5.245469180 € | 89.33% |
| 10 | −0.75600258 € | € −5.310025801 | 86.46% |
In practice, the expected values for 9 or 10 numbers typed are lower (i.e. worse) than stated here, because in the associated types 9 and 10 the maximum winnings can be reduced if they are distributed multiple times. It is difficult to calculate the actual expected values because the probabilities of multiple payouts of maximum winnings are not publicly known.
Web links
- Keno.de Official Keno website of the German Lotto and Totoblock with u. a. Information about the game and game rules; at the same time portal to the (state) companies of the respective federal states.
Individual evidence
- ↑ Keno History . In: KenoOnline.org .
- ↑ Casinonoxdeutsch .
- ↑ a b Official Conditions of Participation KENO. P. 14 , accessed on March 23, 2017 .