Casino game

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Slot machines are a popular type of casino game. Vegas slots.JPG
Slot machines are a popular type of casino game.

Games available in most casinos are commonly called casino games. In a casino game, the players gamble cash or casino chips on various possible random outcomes or combinations of outcomes. Casino games are also available in online casinos, where permitted by law. Casino games can also be played outside casinos for entertainment purposes like in parties or in school competitions, some on machines that simulate gambling. Over a hundred mobile casinos apps were operating as of December 2013, with most of the big casino operators in gambling now providing a mobile platform for their player base.

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Overhead view of a casino floor with table games (bottom) and slot machines DSC29095, Atlantis Casino Hotel, Reno, Nevada, USA (5477998844).jpg
Overhead view of a casino floor with table games (bottom) and slot machines

There are three general categories of casino games: gaming machines, table games, and random number games. Gaming machines, such as slot machines and pachinko, are usually played by one player at a time and do not require the involvement of casino employees to play. Tables games, such as blackjack or craps, involve one or more players who are competing against the house (the casino itself) rather than each other. Table games are usually conducted by casino employees known as croupiers or dealers. Random number games are based upon the selection of random numbers, either from a computerized random number generator or from other gaming equipment. Random number games may be played at a table or through the purchase of paper tickets or cards, such as keno or bingo.

Some casino games combine multiple of the above aspects; for example, roulette is a table game conducted by a dealer, which involves random numbers. Casinos may also offer other type of gaming, such as hosting poker games or tournaments, where players compete against each other.

Common casino games

Notable games that are commonly found at casinos include:

House advantage

Casino games typically provide a predictable long-term advantage to the casino, or "house", while offering the players the possibility of a short-term gain that in some cases can be large. Some casino games have a skill element, where the players' decisions have an impact on the results. Players possessing sufficient skills to eliminate the inherent long-term disadvantage (the house edge or vigorish) in a casino game are referred to as advantage players.

The players' disadvantage is a result of the casino not paying winning wagers according to the game's "true odds", which are the payouts that would be expected considering the odds of a wager either winning or losing. For example, if a game is played by wagering on the number that would result from the roll of one die, true odds would be 5 times the amount wagered since there is a 1 in 6 chance of any single number appearing, assuming that the player gets the original amount wagered back. However, the casino may only pay 4 times the amount wagered for a winning wager.

The house edge or vigorish is defined as the casino profit expressed as the percentage of the player's original bet. (In games such as blackjack or Spanish 21, the final bet may be several times the original bet, if the player double and splits.)

A European roulette ("single zero") wheel Roulette casino.JPG
A European roulette ("single zero") wheel

In American roulette, there are two "zeroes" (0, 00) and 36 non-zero numbers (18 red and 18 black). This leads to a higher house edge compared to European roulette. The chances of a player, who bets 1 unit on red, winning is 18/38 and his chances of losing 1 unit is 20/38. The player's expected value is EV = (18/38 × 1) + (20/38 × (−1)) = 18/38 − 20/38 = −2/38 = −5.26%. Therefore, the house edge is 5.26%. After 10 spins, betting 1 unit per spin, the average house profit will be 10 × 1 × 5.26% = 0.53 units. European roulette wheels have only one "zero" and therefore the house advantage (ignoring the en prison rule) is equal to 1/37 = 2.7%.

The house edge of casino games varies greatly with the game, with some games having an edge as low as 0.3%. Keno can have house edges up to 25%, slot machines having up to 15%.

The calculation of the roulette house edge is a trivial exercise; for other games, this is not usually the case. Combinatorial analysis and/or computer simulation is necessary to complete the task.

In games which have a skill element, such as blackjack or Spanish 21, the house edge is defined as the house advantage from optimal play (without the use of advanced techniques such as card counting), on the first hand of the shoe (the container that holds the cards). The set of the optimal plays for all possible hands is known as "basic strategy" and is highly dependent on the specific rules and even the number of decks used. Good blackjack and Spanish 21 games have house edges below 0.5%.

Traditionally, the majority of casinos have refused to reveal the house edge information for their slots games and due to the unknown number of symbols and weightings of the reels, in most cases it is much more difficult to calculate the house edge than that in other casino games. However, due to some online properties revealing this information and some independent research conducted by Michael Shackleford in the offline sector, this pattern is slowly changing. [1]

In games where players are not competing against the house, such as poker, the casino usually earns money via a commission, known as a "rake".

Standard deviation

The luck factor in a casino game is quantified using standard deviations (SD). [2] The standard deviation of a simple game like roulette can be calculated using the binomial distribution. In the binomial distribution, SD = npq, where n = number of rounds played, p = probability of winning, and q = probability of losing. The binomial distribution assumes a result of 1 unit for a win, and 0 units for a loss, rather than −1 units for a loss, which doubles the range of possible outcomes. Furthermore, if we flat bet at 10 units per round instead of 1 unit, the range of possible outcomes increases 10 fold. [3]

SD (roulette, even-money bet) = 2bnpq, where b = flat bet per round, n = number of rounds, p = 18/38, and q = 20/38.

For example, after 10 rounds at 1 unit per round, the standard deviation will be 2 × 1 × 10 × 18/38 × 20/38 = 3.16 units. After 10 rounds, the expected loss will be 10 × 1 × 5.26% = 0.53. As you can see, standard deviation is many times the magnitude of the expected loss. [4]

The standard deviation for pai gow poker is the lowest out of all common casino games. Many casino games, particularly slot machines, have extremely high standard deviations. The bigger size of the potential payouts, the more the standard deviation may increase.

As the number of rounds increases, eventually, the expected loss will exceed the standard deviation, many times over. From the formula, we can see the standard deviation is proportional to the square root of the number of rounds played, while the expected loss is proportional to the number of rounds played. As the number of rounds increases, the expected loss increases at a much faster rate. This is why it is impossible for a gambler to win in the long term. It is the high ratio of short-term standard deviation to expected loss that fools gamblers into thinking that they can win.

It is important for a casino to know both the house edge and variance for all of their games. The house edge tells them what kind of profit they will make as percentage of turnover, and the variance tells them how much they need in the way of cash reserves. The mathematicians and computer programmers that do this kind of work are called gaming mathematicians and gaming analysts. Casinos do not have in-house expertise in this field, so outsource their requirements to experts in the gaming analysis field.

See also

Related Research Articles

Blackjack Gambling card game

Blackjack, formerly also Black Jack and Vingt-Un, is the American member of a global family of banking games known as Twenty-One, whose relatives include the British game of Pontoon and the European game, Vingt-et-Un. It is a comparing card game between one or more players and a dealer, where each player in turn competes against the dealer. Players do not compete against each other. It is played with one or more decks of 52 cards, and is the most widely played casino banking game in the world.

Craps Dice game

Craps is a dice game in which the players make wagers on the outcome of the roll, or a series of rolls, of a pair of dice. Players may wager money against each other or a bank. Because it requires little equipment, "street craps" can be played in informal settings. While shooting craps, players may use slang terminology to place bets and actions.

Chuck-a-luck

Chuck-a-luck, also known as birdcage, is a game of chance played with three dice. It is derived from grand hazard and both can be considered a variant of sic bo, which is a popular casino game, although chuck-a-luck is more of a carnival game than a true casino game. The game is sometimes used as a fundraiser for charity.

Gambling Wagering of money on a game of chance or event with an uncertain outcome

Gambling is the wagering of money or something of value on an event with an uncertain outcome, with the primary intent of winning money or material goods. Gambling thus requires three elements to be present: consideration, risk (chance), and a prize. The outcome of the wager is often immediate, such as a single roll of dice, a spin of a roulette wheel, or a horse crossing the finish line, but longer time frames are also common, allowing wagers on the outcome of a future sports contest or even an entire sports season.

Roulette Game of chance

Roulette is a casino game named after the French word meaning little wheel. In the game, players may choose to place bets on either a single number, various groupings of numbers, the colors red or black, whether the number is odd or even, or if the numbers are high (19–36) or low (1–18).

Baccarat (card game)

Baccarat or baccara is a card game played at casinos. It is a comparing card game played between two hands, the "player" and the "banker". Each baccarat coup has three possible outcomes: "player", "banker", and "tie". There are three popular variants of the game: punto banco, baccarat chemin de fer, and baccarat banque. In punto banco, each player's moves are forced by the cards the player is dealt. In baccarat chemin de fer and baccarat banque, by contrast, both players can make choices. The winning odds are in favour of the bank, with a house edge no lower than around 1 percent.

Spread betting is any of various types of wagering on the outcome of an event where the pay-off is based on the accuracy of the wager, rather than a simple "win or lose" outcome, such as fixed-odds betting or parimutuel betting.

A martingale is any of a class of betting strategies that originated from and were popular in 18th-century France. The simplest of these strategies was designed for a game in which the gambler wins the stake if a coin comes up heads and loses it if the coin comes up tails. The strategy had the gambler double the bet after every loss, so that the first win would recover all previous losses plus win a profit equal to the original stake. The martingale strategy has been applied to roulette as well, as the probability of hitting either red or black is close to 50%.

Card counting

Card counting is a casino card game strategy used primarily in the blackjack family of casino games to determine whether the next hand is likely to give a probable advantage to the player or to the dealer. Card counters are a class of advantage players, who attempt to reverse the inherent casino house edge by keeping a running tally of all high and low valued cards seen by the player. Card counting allows players to bet more when the count gives an advantage as well as minimize losses during an unfavorable count. Card counting also provides the ability to alter playing decisions based on the composition of remaining cards.

Online casinos, also known as virtual casinos or Internet casinos, are online versions of traditional casinos. Online casinos enable gamblers to play and wager on casino games through the Internet. It is a prolific form of online gambling.

A betting strategy is a structured approach to gambling, in the attempt to produce a profit. To be successful, the system must change the house edge into a player advantage — which is impossible for pure games of probability with fixed odds, akin to a perpetual motion machine. Betting systems are often predicated on statistical analysis.

Spanish 21 is a blackjack variant owned by Masque Publishing Inc., a gaming publishing company based in Colorado. Unlicensed, but equivalent, versions may be called Spanish blackjack. In Australia and Malaysia, an unlicensed version of the game, with no dealer hole card and significant rule differences, is played in casinos under the name "Pontoon". It was first introduced about 1995.

A progressive jackpot is a jackpot which increases each time the game is played but the jackpot is not won. When the progressive jackpot is won, the jackpot for the next play is reset to a predetermined value, and resumes increasing under the same rule.

Casino War

Casino War is a proprietary casino table game based on the game of War. It is distributed by Shuffle Master, a division of Scientific Games. The game is one of the most easily understood casino card games.

Fixed odds betting terminal

A fixed odds betting terminal is a type of electronic slot machine normally found in betting shops in the United Kingdom and introduced in 2001. The terminals allow players to bet on the outcome of various games and events which have fixed odds, with the theoretical percentage return to player (RTP) displayed on the machine by law. Like all casino games, the "house" has a built-in advantage. Typically, slot machine FOBTs have an RTP of 90% to 94% depending on the chosen stake, and standard roulette FOBTs have a long-term average RTP of 97%.

Even money is a wagering proposition with even odds - the bettor stands to lose or win the same amount of money. Beyond gambling, even money can mean an event whose occurrence is about as likely to occur as not. Even money is also known as 50–50.

The mathematics of gambling are a collection of probability applications encountered in games of chance and can be included in game theory. From a mathematical point of view, the games of chance are experiments generating various types of aleatory events, the probability of which can be calculated by using the properties of probability on a finite space of events.

Advantage gambling, or advantage play, refers to legal methods, in contrast to cheating in casinos, used to gain an advantage while gambling. The term usually refers to house-banked games, but can also refer to games played against other players, such as poker. Someone who practises advantage gambling is often referred to as an advantage player, or AP. Unlike cheating, which is by definition illegal, advantage play exploits innate characteristics of a particular game to give the player an advantage relative to the house or other players. While not illegal, advantage play is often discouraged and some advantage players may be banned by certain casinos.

In the context of casinos, comps are complimentary items and services given out by casinos to encourage players to gamble. The amount and quality of comps that a player is given usually depends on a combination of factors: what game(s) they play, how much they bet, and how long they play.

Aces and eights (blackjack)

Splitting aces and eights is part of blackjack basic strategy. Rules vary across gambling establishments regarding resplitting, doubling, multiple card draws, and the payout for blackjack, and there are conditional strategic responses that depend upon the number of decks used, the frequency of shuffling and dealer's cards. However, regardless of the various situations, the common strategic wisdom in the blackjack community is to "Always split aces and eights" when dealt either pair as initial cards. This is generally the first rule of any splitting strategy.

References

  1. "Michael Shackleford is the wizard of odds". Observer . Retrieved 13 October 2015.
  2. Hagan, general editor, Julian Harris, Harris (2012). Gaming law : jurisdictional comparisons (1st ed.). London: European Lawyer Reference Series/Thomson Reuters. ISBN   978-0414024861.
  3. Gao, J.Z.; Fong, D.; Liu, X. (April 2011). "Mathematical analyses of casino rebate systems for VIP gambling". International Gambling Studies. 11 (1): 93–106. doi:10.1080/14459795.2011.552575. S2CID   144540412.
  4. Andrew, Siegel (2011). Practical Business Statistics. Academic Press. ISBN   978-0123877178 . Retrieved 13 October 2015.