GameA game is a structured activity, usually undertaken for enjoyment and sometimes used as an educational tool. Games are distinct from work, which is usually carried out for remuneration, and from art, which is more concerned with the expression of ideas...
s available in most
casinoA casino is a facility that houses and accommodates certain types of gambling activities. Casinos are most commonly built near or combined with hotels, restaurants, retail shopping, cruise ships and other tourist attractions...
s are commonly called
casino games. In a casino game, the players
gambleGambling is the wagering of money or something of material value on an event with an uncertain outcome with the primary intent of winning additional money and/or material goods. Typically, the outcome of the wager is evident within a short period....
casino chipsCasino tokens are small discs used in lieu of currency in casinos. Colored metal or compression molded clay tokens of various denominations are used primarily in table games, as opposed to metal token coins, used primarily in slot machines...
on various possible random outcomes or combinations of outcomes. Casino games are available in
online casinoOnline 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....
s, where permitted by law. Casino games can also be played outside of casinos for entertainment purposes, some on machines that simulate gambling.
Categories of casino games
There are three general categories of casino games: table games, electronic gaming machines, and random number ticket games such as
KenoKeno is a lottery-like or bingo-like gambling game often played at modern casinos, and is also offered as a game in some state lotteries. A traditional live casino keno game uses a circular glass enclosure called a "bubble" containing 80 ping pong-like balls which determine the balldraw result. ...
and simulated racing. Gaming machines, such as
slot machineA slot machine , fruit machine , or poker machine is a casino gambling machine with three or more reels which spin when a button is pushed...
s and
pachinkois a Japanese gaming device used for amusement and gambling. A pachinko machine resembles a vertical pinball machine, but with no flippers and a large number of relatively small balls. The player fires a ball up into the machine, controlling only its initial speed. The ball then cascades down...
, are usually played by one player at a time and do not require the involvement of casino employees to play.
Random numberRandom number may refer to:* A number generated for or part of a set exhibiting statistical randomness.* A random sequence obtained from a stochastic process.* An algorithmically random sequence in algorithmic information theory....
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, such as
RouletteRoulette is a casino and gambling game named after a French diminutive for "little wheel". In the game, players may choose to place bets on either a number, a range of numbers, the colors red or black, or whether the number is odd or even....
, or through the purchase of paper tickets or cards, such as
KenoKeno is a lottery-like or bingo-like gambling game often played at modern casinos, and is also offered as a game in some state lotteries. A traditional live casino keno game uses a circular glass enclosure called a "bubble" containing 80 ping pong-like balls which determine the balldraw result. ...
or Bingo.
Gaming machines
- Pachinko
is a Japanese gaming device used for amusement and gambling. A pachinko machine resembles a vertical pinball machine, but with no flippers and a large number of relatively small balls. The player fires a ball up into the machine, controlling only its initial speed. The ball then cascades down...
- Slot machine
A slot machine , fruit machine , or poker machine is a casino gambling machine with three or more reels which spin when a button is pushed...
- Video Lottery Terminal
A Video Lottery Terminal or VLT is a gaming machine that allows gamblers to bet on the outcome of a video game.A VLT is similar to a slot machine, except that it is connected to a centralized computer system that determines the outcome of each wager using a random number generator...
- Video poker
Video poker is a casino game based on five-card draw poker. It is played on a computerized console similar in size to a slot machine.- History :...
House advantage
Casino games generally provide a predictable long-term advantage to the casino, or "house", while offering the player the possibility of a large short-term payout. Some casino games have a skill element, where the player makes decisions; such games are called "random with a tactical element." While it is possible through skillful play to minimize the house advantage, it is extremely rare that a player has sufficient skill to completely eliminate his inherent long-term disadvantage (the
house edge or house
vigorishVigorish, or simply the vig, also known as juice or the take, is the amount charged by a bookmaker, or bookie, for his services. In the United States it also means the interest on a shark's loan. The term is Yiddish slang originating from the Russian word for winnings, vyigrysh...
) in a casino game. Such a skill set would involve years of training, an extraordinary memory and numeracy, and/or acute visual or even aural observation, as in the case of
wheel clockingThe Eudaemons were a small group headed by graduate physics students J. Doyne Farmer and Norman Packard at the University of California Santa Cruz in the late 1970s. The group's immediate objective was to find a way to beat roulette, but a loftier objective was to use the money made from roulette...
in Roulette.
The player's 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 6 times the amount wagered since there is a 1 in 6 chance of any single number appearing. However, the casino may only pay 5 times the amount wagered for a winning wager.
The house edge (HE) or vigorish is defined as the casino profit expressed as a percentage of the player's original bet. (In games such as
BlackjackBlackjack, also known as Twenty-one, Vingt-et-un , or Pontoon, is the most widely played casino banking game in the world. The basic rules of the game involve adding the value of an initial two card hand in hopes of being dealt a value of twenty-one...
or
Spanish 21Spanish 21 is a variant of blackjack owned by Masque Publishing Inc., a gaming publishing company based in Colorado. Unlicensed, but equivalent, versions may be called Spanish Blackjack...
, the final bet may be several times the original bet, if the player double and splits.)
Example: In American
RouletteRoulette is a casino and gambling game named after a French diminutive for "little wheel". In the game, players may choose to place bets on either a number, a range of numbers, the colors red or black, or whether the number is odd or even....
, there are two zeroes and 36 non-zero numbers (18 red and 18 black). If a player bets $1 on red, his chance of winning $1 is therefore 18/38 and his chance of losing $1 (or winning -$1) is 20/38.
The player's expected value, EV = (18/38 x 1) + (20/38 x -1) = 18/38 - 20/38 = -2/38 = -5.26%. Therefore, the house edge is 5.26%. After 10 rounds, play $1 per round, the average house profit will be 10 x $1 x 5.26% = $0.53.
Of course, it is not possible for the casino to win exactly 53 cents; this figure is the average casino profit from each player if it had millions of players each betting 10 rounds at $1 per round.
The house edge of casino games vary greatly with the game.
KenoKeno is a lottery-like or bingo-like gambling game often played at modern casinos, and is also offered as a game in some state lotteries. A traditional live casino keno game uses a circular glass enclosure called a "bubble" containing 80 ping pong-like balls which determine the balldraw result. ...
can have house edges up to 25%, slot machines can have up to 15%, while most
Australian PontoonPontoon is an unlicensed variant of the American game Spanish 21 that is played in Australian and Malaysian casinos. In Treasury Casino, Brisbane, it is known as Treasury 21, in Jupiters Casino, Gold Coast, it is known as Jupiters 21, in The Reef Casino, Cairns, it is known as Paradise Pontoon, and...
games have house edges between 0.3% and 0.4%.
The calculation of the Roulette house edge was 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
BlackjackBlackjack, also known as Twenty-one, Vingt-et-un , or Pontoon, is the most widely played casino banking game in the world. The basic rules of the game involve adding the value of an initial two card hand in hopes of being dealt a value of twenty-one...
or
Spanish 21Spanish 21 is a variant of blackjack owned by Masque Publishing Inc., a gaming publishing company based in Colorado. Unlicensed, but equivalent, versions may be called Spanish Blackjack...
, the house edge is defined as the house advantage from optimal play (without the use of advanced techniques such as
card countingCard counting is a card game strategy used to determine when a player has a probability advantage. The term is used almost exclusively to refer to the tracking of the ratio of high cards to low cards in blackjack and its derivatives such as Spanish 21, although it is sometimes used to refer to...
), 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
BlackjackBlackjack, also known as Twenty-one, Vingt-et-un , or Pontoon, is the most widely played casino banking game in the world. The basic rules of the game involve adding the value of an initial two card hand in hopes of being dealt a value of twenty-one...
and
Spanish 21Spanish 21 is a variant of blackjack owned by Masque Publishing Inc., a gaming publishing company based in Colorado. Unlicensed, but equivalent, versions may be called Spanish Blackjack...
games have house edges below 0.5%.
Standard deviation
The luck factor in a casino game is quantified using standard deviations (SD). The standard deviation of a simple game like Roulette can be calculated using the
binomial distributionIn probability theory and statistics, the binomial distribution is the discrete probability distribution of the number of successes in a sequence of n independent yes/no experiments, each of which yields success with probability p. Such a success/failure experiment is also called a Bernoulli...
. In the binomial distribution, SD = sqrt (
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. Therefore,
SD (Roulette, even-money bet) = 2
b sqrt(
npq ), where
b = flat bet per round,
n = number of rounds,
p = 18/38, and
q = 20/38.
For example, after 10 rounds at $1 per round, the standard deviation will be 2 x 1 x sqrt(10 x 18/38 x 20/38) = $3.16. After 10 rounds, the expected loss will be 10 x $1 x 5.26% = $0.53. As you can see, standard deviation is many times the magnitude of the expected loss.
The range is six times the standard deviation: three above the mean, and three below. Therefore, after 10 rounds betting $1 per round, your result will be somewhere between -$0.53 - 3 x $3.16 and -$0.53 + 3 x $3.16, i.e., between -$10.01 and $8.95. (There is still a 0.1% chance that your result will exceed a $8.95 profit, and a 0.1% chance that you will lose more than $10.01.) This demonstrates how luck can be quantified; we know that if we walk into a casino and bet $5 per round for a whole night, we are not going to walk out with $500.
The standard deviation for Pai Gow poker is the lowest out of all common casinos . Many , particularly slots, have extremely high standard deviations. As the size of the potential payouts increase, so does the standard deviation.
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 mathematiciansGaming mathematics, also referred to as the mathematics of gambling, is a collection of probability applications encountered in games of chance and can be included in applied mathematics...
and gaming analysts. Casinos do not have in-house expertise in this field, so outsource their requirements to experts in the gaming analysis field, such as
Mike ShacklefordMichael "The Wizard of Odds" Shackleford is one of the world's foremost experts on the math behind casino games...
, the "Wizard of Odds".