Casino Game With 80 Numbered Balls

4/8/2022by admin

Algebra -> Probability-and-statistics-> SOLUTION: n one version of the game Keno, the house has a pot containing 80 balls, numbered 1 through 80. A player buys a ticket for $1 and marks one number on it (from 1 through 80). The Log On

Casino Game With 80 Numbered Balls
Casino Game With 80 Numbered Balls Crossword
Casino Game With 80 Numbered Balls Crossword
Casino Game With 80 Numbered Balls Crossword
Game With Numbered Balls

Casino game with numbered balls (4) Synonyms, crossword answers and other related words for GAME WITH 80 BALLS keno We hope that the following list of synonyms for the word keno will help you to finish your crossword today. Game with 80 balls is a crossword puzzle clue. Clue: Game with 80 balls. Game with 80 balls is a crossword puzzle clue that we have spotted 3 times. There are related clues (shown below). Roulette drinking game - great way to get the party started. Features a black plastic base and gold toned spinner. This game can be played with beer for a longer game, or with hard liquor for a shorter game. Each set comes with 16 numbered shot glasses (eight red, eight black), two roulette balls and a.

Question 357978: n one version of the game Keno, the house has a pot containing 80 balls, numbered 1 through 80. A player buys a ticket for $1 and marks one number on it (from 1 through 80). The house then selects 20 of the 80 numbers at random. If the number selected by the player is among the 20 selected by the house (the management), the player is paid $3.20. Find the expected net winnings for this game.

Answer by solver91311(24713) (Show Source):

You can put this solution on YOUR website!

The probability of catching exactly spots when you have bet on out of 80 spots is given by:
Where is the number of combinations of things taken at a time and is calculated by
And the expected payout for a bet on out of 80 spots is given by:
where is the payout for catching spots when you have bet on out of 80 spots and is the amount bet.
For your problem, you only have to count from 0 to 1, your amount bet is $1, and the payout for 1 out of 1 is $3.20, so:
Of course, since there is zero payout for not hitting the number, this reduces to:
Still, you are faced with what looks like a nasty bunch of arithmetic.
But because we know that , this becomes:
And because we know from the definition of factorials , we can write:
And finally:
This is actually a big payout. Most Vegas casinos get 25 cents from every dollar played.
John
My calculator said it, I believe it, that settles it

A set of Finnish keno betting slips

Keno/kiːnoʊ/ is a lottery-like gambling game often played at modern casinos, and also offered as a game by some state lotteries.

Players wager by choosing numbers ranging from 1 through (usually) 80. After all players make their wagers, 20 numbers (some variants draw fewer numbers) are drawn at random, either with a ball machine similar to ones used for lotteries and bingo, or with a random number generator.

Each casino sets its own series of payouts, called 'paytables'. The player is paid based on how many numbers were chosen (either player selection, or the terminal picking the numbers), the number of matches out of those chosen, and the wager.

There are a wide variety of keno paytables depending on the casino, usually with a larger 'house edge' than other games offered by that casino. The house edge ranges from less than 4 percent^[1] to over 35 percent.^[2] The typical house edge for non-slot casino games is under 5 percent.^[3]

History[edit]

Casino Game With 80 Numbered Balls

The word keno has French or Latin roots (Fr. quine 'five winning numbers', L. quini 'five each'), but by all accounts the game originated in China. Legend has it that the invention of the game saved an ancient city in time of war, and its widespread popularity helped raise funds to build the Great Wall of China. In modern China, the idea of using lotteries to fund a public institution was not accepted before the late 19th century.^[4]

Casino Game With 80 Numbered Balls Crossword

Chinese lotteries are not documented before 1847 when the Portuguese government of Macau decided to grant a license to lottery operators. According to some, results of keno games in great cities were sent to outlying villages and hamlets by carrier pigeons, resulting in its Chinese name 白鸽票 báigē piào, literally 'white dove ticket', pronounced baak-gap-piu in Cantonese (on which the Western spelling 'pak-ah-pu' / 'pakapoo' was based).

The Chinese played the game using sheets printed with Chinese characters, often the first 80 characters of the Thousand Character Classic, from which the winning characters were selected.^[5]^[6] Eventually, Chinese immigrants introduced keno to the US in the 19th century,^[7] where the name was Westernized into boc hop bu^[6] and puck-apu.^[5] By 1866, it had already become a widely popular gambling game in Houston, Texas, under the name keno.^[8]

Probabilities[edit]

Keno payouts are based on how many numbers the player chooses and how many of those numbers are 'hit', multiplied by the proportion of the player's original wager to the 'base rate' of the paytable. Typically, the more numbers a player chooses and the more numbers hit, the greater the payout, although some paytables pay for hitting a lesser number of spots. For example, it is not uncommon to see casinos paying $500 or even $1,000 for a 'catch' of 0 out of 20 on a 20 spot ticket with a $5.00 wager. Payouts vary widely by casino. Most casinos allow paytable wagers of 1 through 20 numbers, but some limit the choice to only 1 through 10, 12, and 15 numbers, or 'spots' as the numbers selected are known.^[9]

The probability of a player hitting all 20 numbers on a 20 spot ticket is 1 in 3,535,316,142,212,174,320.^[10]

Even though it is virtually impossible to hit all 20 numbers on a 20 spot ticket, the same player would typically also get paid for hitting 'catches' 0, 1, 2, 3, and 7 through 19 out of 20, often with the 17 through 19 catches paying the same amount as the solid 20 hit. Some of the other paying 'catches' on a 20 spot ticket or any other ticket with high 'solid catch' odds are in reality very possible to hit:

Hits	Probability
0	1 in 843.380
1	1 in 86.446
2	1 in 20.115
3	1 in 8.009
4	1 in 4.877
5	1 in 4.287
6	1 in 5.258
7	1 in 8.826
8	1 in 20.055
9	1 in 61.420
10	1 in 253.801
11	1 in 1,423.822
12	1 in 10,968.701
13	1 in 118,084.920
14	1 in 1,821,881.628
15	1 in 41,751,453.986
16	1 in 1,496,372,110.872
17	1 in 90,624,035,964.712
18	1 in 10,512,388,171,906.553
19	1 in 2,946,096,785,176,811.500
20	1 in 3,535,316,142,212,174,320.000

Probabilities change significantly based on the number of spots that are picked on each ticket.

References[edit]

Casino Game With 80 Numbered Balls Crossword

^Online Keno odds
^Shackleford, Michael. 'Keno - Strategy and Odds by The Wizard of Odds'. Wizard of Odds Consulting, Inc. Retrieved 21 July 2010.
^Casino advantages for various games
^'Keno History'. kenoonline.org. Retrieved 9 June 2015.
^ ^a^bMelanie Yap, Dianne Leong Man. Colour, confusion and concessions, pp.240-241.
^ ^a^b'Chinese Gambling Games; Mysteries of Fan Tan And Boc Hop Bu. Two Popular Games in the Chinese Quarters of American Cities-- Superstitions of the Players. Boc Hop Bu. Superstitions'(PDF). The New York Times. 5 February 1888.
^History of Keno. Transl. from German, 2017.
^'The New York Times'. 29 July 1866.Cite journal requires journal= (help)
^'Tutorial - How to play Keno'. Gambling Info. Retrieved 27 June 2011.
^Mark Bollman (2014). Basic Gambling Mathematics: The Numbers Behind the Neon. CRC Press. pp. 40–41. ISBN9781482208931.

Game With Numbered Balls

Retrieved from 'https://en.wikipedia.org/w/index.php?title=Keno&oldid=996539331'