Keno

From Wikipedia, the free encyclopedia

Keno is a lottery-like or bingo-like gambling game played at most modern casinos, and at many bingo halls. A player chooses anywhere from 1 to 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 out against his original wager based on how many numbers match the ones he marked on his ticket.^[1]

As a casino game, it is notable because it provides the casino with an advantage against the player greater than any other gambling game -- on some bets up to 66%.^[2] The normal house advantage for a casino game is between 1% and 5%.^[3]

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.^[4]

1 Keno odds
2 Modern keno
3 Detailed mathematical analysis
4 References

[edit] Keno odds

The payouts for keno are based on how many numbers the player chose and how many numbers "hit", multiplied by the player's original wager. The more numbers a player chooses, and the more numbers hit, the greater the payout. Payouts vary widely from casino to casino.^[5] Some casinos allow the player to pick up to 20 numbers, but most limit the choice to only 15 or 10. The probability of a player hitting the "jackpot" 20 numbers from 20 chosen is 1 in 3,535,316,142,212,180,000.^[6] If every person who ever inhabited planet Earth played one keno game every single second of their lives, there would be about one 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.^[7]

[edit] Modern keno

Numbers are picked at the "keno booth". "Keno runners" will walk around shouting "keno!" and offering number selection cards to anyone interested in playing.

After picking numbers and recording them at the keno booth, the player will then watch either a "big board" in which winning keno numbers will light up or on a video monitor showing the selected numbers found throughout the casino. As the winning numbers light up, the player usually marks them on his or her card with a bright-colored marker. A winning ticket needs to be taken to the keno booth immediately if it is an individual game ticket, as drawings usually take place every five minutes. If the player tries to redeem a winning ticket when the next drawing starts, it is void and no money is paid out.

To avoid having a void ticket, a keno player can purchase a "multi-race" ticket with the same picked numbers on anywhere from 2 to 20 tickets. When the maximum number of games (matching the number of tickets) is finished, the player can then redeem any winnings and avoid the peril of a void ticket. Another option is the "stray and play" ticket, which is usually a number of games greater than 30. Unlike standard keno tickets, the "stray and play" doesn't have to be redeemed immediately and is often good for up to a year after purchase.

In the State of Nevada many Las Vegas casinos have introduced their own keno games. The odds of winning are about the same as in traditional keno games, except a keno player may select from a very large number of so called "special" games. These games are often changed and revised to introduce an element of newness and excitement, yet basic principals always remain the same – the house always has a tremendous advantage over the player.

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.

[edit] 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.,

P n (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:

$P_n (k) = \frac{{n \choose k} {80-n \choose 20-k}}{{80 \choose 20}}$

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:

W n (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:

$\sum\limits_{i=0 or 1}^{n}P_n (i) W_n (i)$

which could alternatively be represented as the inner product ("dot product") of the vector of probabilities and the vector of payouts for vector-happy people.

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.