Keno
Keno is a lottery-like or bingo-like gambling game played at most modern
casinos, and at many bingo halls. A player chooses between 1 and 20 numbers and
marks them on a keno ticket of 80 numbers (1 to 80). The casino then draws 20
numbers at random. The player is paid proportional to his original wager as
opposed to the base rate of the paytable and based on how many numbers drawn
match the ones he marked on his ticket.
As a casino game, it is notable because in many gaming jurisdictions keno is
one of the only casino games not required by gaming authorities to maintain a
theoretical house hold percentage less than 25% of the wager. Keno is also one
of the only casino games in many gaming jurisdictions for which the house can
modify paytables at will without notifying or being granted approvals from
gaming authorities. Therefore and because keno is labor intensive, casinos
sometimes use this loophole to their advantage and set house hold percentages
for their keno paytables between 25% and 33% or even more. As a result, Keno has
gotten a bad rap as the worst bet in the house. The truth, however, is that to
the player, a keno game is only as good as the paytables the house sets for the
game, which vary greatly from casino to casino. Additionally, each casino can
offer a large number of different paytables and specialty keno bets for
customers to choose from. No two casinos' keno paytables are identical. There
are several Reno and Las Vegas casinos offering as many as 20 or 30 different
paytables from which the player can choose.
The house edge ranges from less than 4%
to 66%. The typical house edge for non-slot casino games is between 0% and 5%
It is unfortunate that Keno has received bad press as to being a “bad bet”.
In reality, there are many casinos whose keno games have very reasonable house
hold percentages as compared with other casino games. Yet there are still other
keno games who take advantage of the “no limit” house hold potential and offer
what most of us would consider “sucker bets” in their keno paytables. It would
therefore behoove the keno player to educate himself and to shop around for the
best keno paytable bargains.
Keno history
Keno is believed to have originated in ancient China in the Han Dynasty
between 205 and 187 B.C. The game was brought to America in the 19th century by
Chinese immigrants.
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 over 2000
years ago. 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. According to one source, results of Keno games in great cities were sent
to outlying villages and hamlets by carrier pigeon. Eventually, Chinese
immigrants introduced Keno to the West when they sailed across the Pacific to
help build the American trans-continental railroad in the 19th century.
Keno odds
The payouts for keno are based on how many numbers the player choses and how
many 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 from casino to
casino. Most casinos allow paytable
wagers of between 1 and 20 numbers, but some limit the choice to only 1 through
10, 12 and 15 numbers, or "spots" as keno aficionados call the numbers picked.
The probability of a player hitting all 20 numbers on a 20 spot ticket is
approximately 1 in 3.5 quintillion (1 in 3,535,316,142,212,180,000 to be exact).
If every person now alive played one keno game every single second of their
lives, there would be about one solid 20 jackpot-winning ticket to date. If all
these possible keno tickets were laid end to end, they would span the Milky Way
galaxy -- and only one of them would be a winner.
However, the situation is not as dire as these statistics suggest. Although 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 as a
solid 20. 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:
20 Spots 0 Hits: 1 In 843.380 Or 0.11857057%
20 Spots 1 Hits: 1 In 86.446 Or 1.15678605%
20 Spots 2 Hits: 1 In 20.115 Or 4.97142576%
20 Spots 3 Hits: 1 In 8.009 Or 12.48637168%
20 Spots 4 Hits: 1 In 4.877 Or 20.50318987%
20 Spots 5 Hits: 1 In 4.287 Or 23.32807380%
20 Spots 6 Hits: 1 In 5.258 Or 19.01745147%
20 Spots 7 Hits: 1 In 8.826 Or 11.32954556%
20 Spots 8 Hits: 1 In 20.055 Or 4.98618021%
20 Spots 9 Hits: 1 In 61.420 Or 1.62814048%
20 Spots 10 Hits: 1 In 253.801 Or 0.39401000%
20 Spots 11 Hits: 1 In 1423.822 Or 0.07023351%
20 Spots 12 Hits: 1 In 10968.701 Or 0.00911685%
20 Spots 13 Hits: 1 In 118084.920 Or 0.00084685%
20 Spots 14 Hits: 1 In 1821881.628 Or 0.00005489%
20 Spots 15 Hits: 1 In 41751453.986 Or 0.00000240%
20 Spots 16 Hits: 1 In 1496372110.872 Or 0.00000007%
20 Spots 17 Hits: 1 In 90624035964.712 Or 0.00000000%
20 Spots 18 Hits: 1 In 10512388171906.553 Or 0.00000000%
20 Spots 19 Hits: 1 In 2946096785176811.500 Or 0.00000000%
20 Spots 20 Hits: 1 In 3535316142212173800.000 Or 0.00000000%
Modern keno
The balldraw occurs at the "keno booth". The balldraw is typically determined
by one of four devices:
1. Standard “Rabbit Ear” blower
2. "AKV": Automated blower in which the balls are encoded and a computer reads
them and sends them to the keno system for processing
3. Random Number Generator: an electronic number selection device approved by
gaming authorities
4. “Hand Cage”: A spinning the metal ball cage which rolls the numbers into a
slot where they are validated by a person.
"Keno runners" walk around calling, "keno!" and offer to carry players'
wagers to the keno booth for processing. The keno runner is handed the wager
payment and the “inside ticket” (keno wager forms filled out by the customer)
and then returns with an "outside" ticket, which is the official wager receipt.
It is incumbent on the player to check the ticket for errors before the game
balldraw is drawn. Any errors not corrected before the balldraw can and will not
be corrected and the "outside" ticket with the error will govern in any
disputes.
In modern keno, players are offered the option of playing multi-race keno,
which books a keno ticket for a number of sequential keno races up to 1000. The
races must always start on the next race to be drawn and must run sequentially.
When the number of wagered games is finished, the player can then redeem any
winnings within the time constraints specified by the casino.
After picking wager numbers, recording them at the keno booth and obtaining
the “keno ticket” (official wager receipt), the player watches the balldraw in
progress as the chosen numbers light either on an electronic keno board or on a
video monitor. Keno displays are typically found throughout the casino and
sometimes even appear on a television channel in casino hotel rooms. Nowadays,
after playing keno at a participating casino, keno players can even take their
multi-race keno tickets out of the casino to watch the live balldraw or check
historical draw results anywhere there is a computer and an Internet connection
on [www.kenousa.com].
In the past, a winning ticket needed to be taken to the keno booth for
collection immediately after the race results were posted, and drawings usually
took place approximately every five or six minutes. In days of old, if the
player tried to redeem a winning ticket after the beginning of the balldraw that
followed their own wager's last game, the ticket was declared expired and no
money was paid out even if it won. Nowadays most casinos set their "late pay"
window to accommodate the player, however there is great variation in the
published late pay window from casino to casino. For tickets played for 1
through 20 races, typical late pay settings range anywhere between 5 games to as
much as 200 days after the last game on the ticket is drawn. After the late pay
window ends, a winning ticket is considered expired and precludes collection of
any wins. Typically, a winning ticket played for 21 races or more is collectible
for one full year. But even the "split" defining "short term" or "long term"
multi-race varies greatly from casino to casino. There are casinos that allow a
one full year payout window on tickets played for 2 races or more. The valid
payout window is totally configurable by the casino and varies greatly from
casino to casino.
An embellishment of keno is “Way” keno or “Combination” keno. When playing a
way or combination keno ticket, the player circles groups of numbers within the
spots marked and specifies combinations of groups which combine together to make
different "ways". For example, if a player marks four numbers, and circles two
groups of two spots each, a combination ticket could be made in which the
gambler plays one 4 spot and two 2 spots (2-2). If an additional group of two
were added and circled, the player could play ways 1/6, 3/4 and 3/2 (2-2-2),
which at $1.00 per way would equal a $7.00 per race wager. Serious keno players
use great imagination on their keno ticket to make complex combinations of
groups and ways with varying numbers of spots in each group. There is literally
no limit to the way players can circle spots of like or a differing number of
spots and in the resulting “ways” they can choose to play on a keno ticket.
As alternatives to the traditional paytables which offer the selection of 1
to 20 spots, a number of special paytables are available and are often offered
for wagering. For example, with the Top/Bottom paytable the Keno player does not
select any spots. Rather, the player is betting that the balldraw top 40 and
bottom 40 ball distribution will be uneven. Top/Bottom typically begins paying
on a 7/13 or 13/7 ball distribution between the top half (1 to 40) and bottom
half (41 to 80) of the keno grid and the payouts increase with each higher
balldraw distribution disparity. The same principle is applied for the
Left/Right or Odd/Even paytables. Other specialty paytables are Top Only, Bottom
Only, Left Only, Right Only, Odd Only, Even Only, Parlay, Exacta, Edge, Square,
or eXtra Million, which is proprietary to XpertX Keno Systems. However the
traditional 1 though 20 spot pick is by far the most popular variety of live
keno.
Lottery versions of Keno are now used in many National Lotteries or state
licensed Lotteries around the world. The games have different formulas depending
on the wanted price structure and whether the game is slow (daily or weekly), or
if it is a fast game with just minutes between the draws. The drawn numbers are
typically published on TV for the slow games and on monitors at the point of
sale for the fast games. A video keno machine typically has a far greater payout
and win-rate than a traditional keno game.
Detailed mathematical analysis
The version of Keno played in Maryland serves as a case study in the precise
calculation of win probabilities and expected return—the latter referring to the
result to be realized in the long run from each unit invested.
In Maryland, anyone may play keno at any of thousands of establishments that
are wired with a television screen and an impossible-to-overlook, hot pink
machine resembling a cash register. The player uses a pencil to complete a small
slip; the attendant feeds the slip to the machine, which generates a
computer-printed ticket that is protected from tampering via cryptographic
checksum. Games—which are played every four minutes or so—can be viewed over the
accompanying television monitor. The computer selects twenty numbers between one
and eighty. The payout is calculated based upon how many numbers were chosen and
how many were matched. Intriguingly, for the nine-spot and ten-spot games, there
is a payout if the player fails to match any numbers—it obviously being an
unusual event for zero of nine or ten selected numbers to match any of the
twenty "dealt," so to speak, from the pool of eighty.
The probability that k of the n numbers chosen by the player, i.e.,
- Pn(k)
occur in the twenty numbers chosen by the computer can straightforwardly be
derived:
1. The number of possible outcomes equals the number of combinations of
eighty numbers taken twenty at a time.
2. The number of ways in which k of the n numbers selected by the player
occur in the twenty numbers selected (putatively at random) by the central Keno
computer is equal to the number of ways in which k numbers can be chosen from a
set of n numbers.
3. The number of ways in which the remainder of the numbers do not occur in
the twenty numbers selected is given by the number of ways in which 20-k numbers
can be chosen from a set of 80-n numbers.
Combining the foregoing, one finds that:
-
The payouts for each result can be read from the Maryland keno Web site. For
the purposes of our discussion, if the player participates in the n-spot game
and ends up matching k of the twenty numbers selected, we will refer to that
payout as:
- Wn(k).
The expected payout for the n-spot game can be determined by summing, over
all values of i from one to n (from zero to n if the game pays out in the case
of zero numbers matched), the product of the payout for that result and the
probability of occurrence of that result:
which could alternatively be represented as the inner product ("dot product")
of the vector of probabilities and the vector of payouts.
One finds that the best game for the player is the three-spot game, which
realizes an expected return of approximately 62 cents for every dollar invested,
or approximately a 38% loss. The seven-spot game ranks close behind, returning
just over 60 cents per dollar. Perhaps not surprisingly, despite the
astonishingly high payoff for strong performance, the ten-spot game is by far
the poorest from the player's perspective.
