Keno

Keno is a popular game of chance, thought to be of ancient Chinese origin, somewhat like bingo, but more like the lottery. It often is played in a Keno parlor, or in a bingo hall. If there is a “Keno lounge,” the game will be played in a bar atmosphere. The name is thought to have its origin in Latin or perhaps French, for a “set of five” (quine) [winning numbers].

Keno is played in “games.” Bets are accepted up until a minute before a game begins, which is just about every four or five minutes. The Keno operator randomly selects 20 numbers from a universe of 80 and posts them (usually electronically) for the gamers to see and confer. The player’s objective is to match as many numbers as possible to those selected by the “house.” (There is usually a “consolation prize” for not getting any of your numbers.) Payoffs vary according to how many numbers the player had picked, and of those, how many matched the numbers drawn.

The traditional mode of playing Keno is for the player to fill out a ticket with any number of choices up to a limit. A common ticket is a “pick 5” but a player can choose to play any number from one through 10 or even 15 numbers. Some casinos will accept picks up to a “pick 20.” Keno is so profitable for casinos that they are very flexible in adapting to how Keno players want to bet the game.

The completed ticket is then handed to an attendant. “Keno runners” may be circulating, offering blank tickets. Bets must be hand carried to the Keno attendant at the Keno booth or desk. The attendant will register the bet and return the ticket, with a receipt, which is the official proof of the wager. It’s always a good idea to be sure the receipt and ticket match, particularly if the booth is very active during the last minutes before a game. Betting will close when the new game is a minute away.

Casinos like to use the “ping-pong-balls-in-the-air-chamber” method of selection, like some lotteries on the television. Sometimes the numbers are selected off-site and reported back by closed-circuit screens. Whatever the mechanism chosen, the numbers themselves must be random, according to Nevada Gaming Commission rules. As the Keno numbers are selected they are posted. Nowadays these numbers pop up on TV-like screens, either big ones, or individual monitors in a Keno lounge. Players confer the numbers displayed with those on the ticket or receipt to determine whether they have won anything or not. (Often a highlighter is provided for the player to indicate matching numbers.) Winning tickets on individual games should be cashed right away with the Keno attendant, before the next game begins, as they become void once a new game starts.

An example of a winning ticket might be a “pick 5” (five numbers were bet on) that had a “catch” of three – that is, three of the five numbers selected by the player match numbers reported by the Keno operator. No payments are made for a low number of matches. With higher picks, like 7 or 9, there will be a prize for “catching” anywhere from 3 or 4 numbers up to the maximum number picked.

Multi-game tickets (called “Multi-Race” in slang) are available up to 20 games, where the same numbers can be bet in one or more games, thus avoiding the risk of a void ticket. The “Stray and Play” tickets usually cover 30 or more games, and are valid for a long time, even several months or a year, after the last game closes.

In Las Vegas, most Keno operations are on-premises, run by the casino itself. Sometimes the game is operated from off-site, (through closed-circuit communication) for several (usually related or subscribing) venues at once. The customer really will not perceive much difference (other than showmanship, perhaps), as the bets are always placed and paid on-site.

Keno is popular because it does not require much effort and even less intelligence to play. After a hard day of serious gambling, a wagerer can fill out a ticket, have a cocktail, and see what happens. No one plays Keno professionally, and few poor souls play it seriously. The reason is that the house edge in Keno is anywhere from -4% (against the player) to -66%! Worse still, there are no decisions about strategy or betting variation that can moderate this edge. So, like the lottery, Keno should be for entertainment value only.

Just how bad a deal is a Keno bet? Start with the odds of hitting the biggest jackpot of all – the one for selecting the same 20 numbers as the computer did out of a universe of 80. The odds of that happening are 1 in 3.5 x 1018 (quintillion). This number is a little larger than the number of seconds that tick off in 100 billion years. There is not enough prize money on the planet to make this a positive expectation bet.

Consider next a “pick 1” bet. Many casinos will pay it off at 2:1, that is, the prize on a $1 bet will be $3. The odds that this number will be among the twenty casino picks is 25%, or 20 out of 80. Getting a 2:1 payoff on 3:1 odds is not a good deal. The house advantage is -25% (i.e., against the player). Some casinos frequently pay a “pick 1” winner at “true odds” or 3:1 as a promotional measure, but the other payouts will gravitate towards the strongly negative edge for the player.

This edge, more precisely, is calculated by multiplying the payout against the true odds, then dividing by the price of the bet and subtracting the total from 1. This calculation shows that most casinos in Las Vegas return from 60% to 80% to the player, with an unscientific estimate of an average of 75%. In other words, casinos enjoy an edge of anywhere from -20% to -40%. (The minus sign indicates that the edge is against the player).

Payouts will vary widely across casinos. The concept is that a complete match of the pick will be a reasonable prize (like 5 out of 5), and this prize goes up, naturally, as the number of picks in the set rises. For example, if someone has a “pick 5” ticket and selects all 5 numbers, the prize might be $1000 for a $1 bet. However the payout for 4 correct out of 5 will be much smaller, perhaps 10 or 20 for 1. The payout for 3 correct out of 5 might only be 1 for 1 (that is, a return of the bet with nothing more). Two or fewer matches in pick 5 will not win a prize at all. By comparison, a “pick 3” might pay 50 for 1 for three matches and 1 for 1 if 2 numbers match. The “pick 10” might go as high as 50,000 for 1, with a fast drop off for fewer than the maximum number of matches, like 10,000 for 1 when there are nine matches, 1,000 for 1 when there are eight matches, 250 for 1 when 7 match, and so on).

A Bit of Math

The way to calculate probabilities for any Keno combination is to figure out how many possible ways you can have combinations of x matches from within y picks (where y is usually 10 or less and x is any number up to and including y). These “ticket” combinations are then compared with the much larger number of possible combinations for extracting 20 numbers out of a universe of 80. These are the Keno “game” combinations.

The formula for calculating the number of possible combinations of x numbers in a universe of y is [y!]/[x!*(y-x)!] (“y” factorial divided by the product of “x” factorial and the factorial of “y” minus “x”) (The factorial of any integer “x” is the product “x” and “x-1” and “x-2”, etc., down to 1). This formula for the number of combinations of x instances in a field of y can be defined as a function for simplicity of notation. In spreadsheet programs it can be employed, just like any other math function, and is called “combin” in English versions of most spreadsheet software.

To illustrate, the combin(5,3) function would be calculated as 5! (y!) divided by the product of 3! (x!) and 2! ((y-x)!). This number is 10. So in short, “combin(5,3)” returns “10” as its answer.

The formula for the probability of having x catches out of y picks in a set of 20 numbers taken from an 80-number field is now fairly simple, using the “combin” function both for notation and calculation. The formula is: combin(y,x) times combin(80-y,20-x) divided by combin(80,20). This is fairly simple to set up on a spreadsheet. For example, the probability of selecting 4 numbers out of a “pick 7” would be combin(7,4) times combin(73,16) divided by combin(80,20). The answer is about 5.22%.

Now, assume the payment schedule for “pick 7” is as listed in the table that follows (8000, 250, 20, 2, 1). The above formula is used to calculate the probability of each winning outcome as well as the monetary expectation of each outcome. The total probability shows that a “pick 7” has about a 24% chance of having some kind of win, but the payoff amounts come to a total of only 83% of the “risk.” In other words, the house edge or advantage over the player is about -17% in the case of a pick 7 ticket with this payoff schedule.

Nevada permits casinos to concoct special Keno games that introduce some special “sizzle” or design feature for more playing excitement. The underlying math, however, remains the same.