Keno Random

KENO FAQs; KENO Booster! ® KENO drawings are available to view from August 2008 to present. Drawings prior to February 28, 2010 do not include Booster ®. KENO drawings are best viewed in the following browsers: Internet Explorer 11, Safari, Firefox and Google Chrome. Here’s a look at the Keno playslip. Every 4 minutes (except during system processing), the Lottery will select 20 winning numbers. The goal is to match your numbers to the ones selected by the Lottery. To understand how much your Keno ticket will cost, multiply the amount wagered per draw by the number of consecutive draws played.

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]

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]

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:

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

References[edit]

1. ^Online Keno odds
2. ^Shackleford, Michael. 'Keno - Strategy and Odds by The Wizard of Odds'. Wizard of Odds Consulting, Inc. Retrieved 21 July 2010.
3. ^Casino advantages for various games
4. ^'Keno History'. kenoonline.org. Retrieved 9 June 2015.
5. ^ ^abMelanie Yap, Dianne Leong Man. Colour, confusion and concessions, pp.240-241.
6. ^ ^ab'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.
7. ^History of Keno. Transl. from German, 2017.
8. ^'The New York Times'. 29 July 1866.Cite journal requires journal= (help)
9. ^'Tutorial - How to play Keno'. Gambling Info. Retrieved 27 June 2011.
10. ^Mark Bollman (2014). Basic Gambling Mathematics: The Numbers Behind the Neon. CRC Press. pp. 40–41. ISBN9781482208931.

To understand keno probabilities you must first fully understand the combinatorial function. For example, in the Maryland lotto the player picks 6 numbers out of 49. Then the lottery will draw 6 numbers out of 49, without replacement. The player wins the jackpot if all six numbers match (order does not matter). If you don’t know the probability of winning per game is 1 in 13,983,816 then you need to review the combinatorial function before going further.

In keno the casino, or game machine, will draw 20 numbers out of 80, without replacement. Before this happens the player may pick 1 to 15 (or more) numbers. A 'catch' is a number the player picked and was drawn by the casino. A 'miss' is a number of the player picked but was not drawn by the casino. The player is paid according to the number of picks made and catches.

Although the player picks first the combinations get very huge when calculation the number of ways the casino can match the player’s picks. To start with there are combin(80,20) = 3,535,316,142,212,180,000 ways the casino can draw 20 numbers out of 80. Many calculators don’t support numbers this big. So to keep the combinations smaller we will assume the casino draws first, but keeps the numbers secret, and player tries to match the numbers already drawn. I assure you the math is the same either way.

All the following images were taken from the Luxor keno rulebook. All pays are on a 'for one' basis. In other words the player never gets his original bet back, even if he wins.

1 Spot

Let’s examine the 1 Spot card first. Here the player just picks one number, from 1 to 80. Then the casino will draw 20 numbers. If one of these 20 match the player’s number then the player is paid $3 for a $1 bet.

There are 80 numbers the player can pick. 20 of these will result in a winning ticket. So the probability of winning is 20/80 = ¼. The expected return is thus ¼ * 3 = 75%.

2 Spot

We need to start using the combinatorial function for the 2 Spot card. The player picks 2 numbers and casino must draw both of them for the player to win. There is no consolation prize for only catching one. There are a total of combin(80,2) = 3160 ways the player can draw 2 numbers out of 80. However the player must draw 2 out of the casino’s 20 drawn numbers to win. So there are only combin(20,2) = 190 ways to draw 2 winning numbers. So the probability of winning is 190/3160 = 6.01%. A winning $1 ticket pays $12, so the expected return is (190/3160) * $12 = 72.15%.

Alternatively, the probability the player’s first pick will match one of the casino’s numbers is 20/80. If it does match the probability the second pick will match one of the casino’s other 19 numbers out of 79 is 19/79. So the probability of winning is (20/80)*(19/79) = 6.01%.

3 Spot

With the 3 Spot card we start having consolation prizes for not matching every pick. First let’s determine the probability of catching all 3 marks. There are combin(80,3) = 82,160 ways to draw 3 numbers out of 80. To catch all three the player must pick all 3 numbers from the casino’s 20 drawn numbers. There are combin(20,3) = 1140 ways to do this. So the probability of catching all 3 is 1140/82160 = 1.39%.

There is a consolation prize for catching 2 out of 3. Imagine the casino puts the 20 drawn numbers in a winning urn and the other 60 numbers in a losing urn. The number of ways to catch 2 out of 3 is the number of ways to draw 2 balls from the 20 in the winning urn, which is combin(20,2) = 190. The number of ways to draw one losing ball out of 60 is obviously 60. So the number of ways to catch 2 out of 3 is the product of the number of ways to pick 2 winning balls from the winning urn and 1 ball from the losing urn, or 190*60 = 11,400. We already know there are combin(80,3) = 82,160 total ways to draw 3 balls out of 80. So the probability of catching 2 out of 3 is 11,400/82,160 = 13.88%.

For any bet the expected return is the dot product over every possible event of the probability and what it pays. The following table shows every possible outcome, with the total in the bottom row.

The bottom right cell shows that over all 82,160 combinations the player will get back $59,280. So the expected return is 59280/82160 = 72.15%.

4 Spot

For the 4 Spot ticket the number of ways to catch all four is combin(20,4) = 4845. The number of ways to catch 3 and miss one is the product of the number of ways to choose 3 out of 20 and the number of ways to choose 1 out of 60, or combin(20,3) * 60 = 1140*60 = 68,400. The number of ways to catch 2 and miss 2 is the product of the number of watch to choose 2 out of 20 winners and 2 out of 60 losers, or combin(20,2)*combin(60,2) = 190 * 1770 = 336,300. The following table shows all the possible outcomes.

The return of the 4 Spot ticket is 1,122,900/1,581,580 = 71.00%.

4 Spot Special

Next, let’s look at the 4 Spot Special. We just worked out all the combinations, so we only need to apply them to a different pay table as follows, based on a $7 ticket.

The expected return of the ticket is 7,957,200/1,581,580 = $5.0312. However we must divide this by $7, the cost of the ticket, to get the expected return, which is $5.0312/$7 = 71.87%. So, if you don’t mind extra volatility, and were going to bet $7 anyway, the 4 Spot Special is a better bet than the regular 4 Spot.

5 Spot

For the rest of the tickets I will present just the return tables. Following is the return table for the 5 Spot.

5-Spot return = $17,037,300/24,040,016 = 70.87%

6 Spot

6-Spot return = 70.99%

7 Spot

The 7-spot has a return of $2237033400/3176716400 = 70.42%

8 Spot

8-Spot return = $20445589920/28987537150 = 70.53%.

9 Spot

9 Spot Return = 70.23%

10 Spot

Keno Random Numbers

For some reason there is a $2 minimum beginning with the 10-spot. Here is the return table for a $2 ticket.

Keno Random Numbers

Keno Random Number Picker

The $2 10-spot returns on average $1.4092. So the expected return is $1.4092/2 = 70.46%.

How To Beat Keno Random Number Generator

The Luxor keno rule book goes through a pick 15, plus a pick 20. However hopefully you understand how to do the math yourself by now.