Casino game
Encyclopedia
Game
s available in most casino
s are commonly called casino games. In a casino game, the players gamble
casino chips
on various possible random outcomes or combinations of outcomes. Casino games are available in online casino
s, where permitted by law. Casino games can also be played outside of casinos for entertainment purposes, some on machines that simulate gambling.
and simulated racing. Gaming machines, such as slot machine
s and pachinko
, are usually played by one player at a time and do not require the involvement of casino employees to play. 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, such as roulette
, or through the purchase of paper tickets or cards, such as keno
or bingo.
) 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 clocking
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 5 times the amount wagered since there is a 1 in 6 chance of any single number appearing, assuming that you get 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 a 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.)
Example: In American Roulette
, there are two zeroes and 36 non-zero numbers (18 red and 18 black). If a player bets 1 unit on red, his chance of winning 1 unit is therefore 18/38 and his chance of losing 1 unit (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 unit per round.
The house edge of casino games vary greatly with the game. Keno
can have house edges up to 25%, slot machines can have up to 15%, while most Australian Pontoon
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 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%.
SD (Roulette, even-money bet) = 2b 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 unit per round, the standard deviation will be 2 x 1 x sqrt(10 x 18/38 x 20/38) = 3.16 units. 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 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 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, such as Mike Shackleford
, the "Wizard of Odds".
Game
A game is structured playing, 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 often an expression of aesthetic or ideological elements...
s available in most casino
Casino
In modern English, a casino is a facility which houses and accommodates certain types of gambling activities. Casinos are most commonly built near or combined with hotels, restaurants, retail shopping, cruise ships or other tourist attractions...
s are commonly called casino games. In a casino game, the players gamble
Gambling
Gambling 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...
casino chips
Casino token
Casino tokens are small discs used in lieu of currency in casinos. Colored metal, injection molded plastic 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 casino
Online casino
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....
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
Keno is a lottery or bingo 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 balls which determine the ball draw result. Each ball is imprinted...
and simulated racing. Gaming machines, such as slot machine
Slot machine
A slot machine , informally fruit machine , the slots , poker machine or "pokies" or simply slot is a casino gambling machine with three or more reels which spin when a button is pushed...
s and pachinko
Pachinko
is a type of game originating in Japan, and used as both a form of recreational arcade game and much more frequently as a gambling device, filling a niche in gambling in Japan comparable to that of the slot machine in Western gambling. A pachinko machine resembles a vertical pinball machine, but...
, are usually played by one player at a time and do not require the involvement of casino employees to play. Random number
Random number
Random 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 roulette
Roulette
Roulette is a casino game named after a French diminutive for little wheel. In the game, players may choose to place bets on either a single number or 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 keno
Keno
Keno is a lottery or bingo 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 balls which determine the ball draw result. Each ball is imprinted...
or bingo.
Gaming machines
- PachinkoPachinkois a type of game originating in Japan, and used as both a form of recreational arcade game and much more frequently as a gambling device, filling a niche in gambling in Japan comparable to that of the slot machine in Western gambling. A pachinko machine resembles a vertical pinball machine, but...
- Slot machineSlot machineA slot machine , informally fruit machine , the slots , poker machine or "pokies" or simply slot is a casino gambling machine with three or more reels which spin when a button is pushed...
- Video Lottery TerminalVideo Lottery TerminalA 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, in that each terminal is a stand-alone device containing a random-number generator...
- Video pokerVideo pokerVideo 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 (HE) or house vigorishVigorish
Vigorish, 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, выигрыш 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 clocking
Eudaemons
The 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 5 times the amount wagered since there is a 1 in 6 chance of any single number appearing, assuming that you get 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 a percentage of the player's original bet. (In games such as Blackjack
Blackjack
Blackjack, also known as Twenty-one or Vingt-et-un , is the most widely played casino banking game in the world...
or Spanish 21
Spanish 21
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...
, the final bet may be several times the original bet, if the player double and splits.)
Example: In American Roulette
Roulette
Roulette is a casino game named after a French diminutive for little wheel. In the game, players may choose to place bets on either a single number or 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 unit on red, his chance of winning 1 unit is therefore 18/38 and his chance of losing 1 unit (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 unit per round.
The house edge of casino games vary greatly with the game. Keno
Keno
Keno is a lottery or bingo 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 balls which determine the ball draw result. Each ball is imprinted...
can have house edges up to 25%, slot machines can have up to 15%, while most Australian Pontoon
Pontoon (card game)
Pontoon is an unlicensed variant of the American game Spanish 21 that is played in Australian, Malaysian and Singaporean casinos, in Treasury Casino, Brisbane, it is known as Treasury 21...
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 Blackjack
Blackjack
Blackjack, also known as Twenty-one or Vingt-et-un , is the most widely played casino banking game in the world...
or Spanish 21
Spanish 21
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...
, the house edge is defined as the house advantage from optimal play (without the use of advanced techniques such as card counting
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, also known as advantage players, attempt to decrease the inherent casino house...
), 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
Blackjack
Blackjack, also known as Twenty-one or Vingt-et-un , is the most widely played casino banking game in the world...
and Spanish 21
Spanish 21
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...
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 distribution. 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.SD (Roulette, even-money bet) = 2b 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 unit per round, the standard deviation will be 2 x 1 x sqrt(10 x 18/38 x 20/38) = 3.16 units. 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 standard deviation for Pai Gow poker
Pai gow poker
Pai Gow poker is an Americanized version of Pai Gow . The games of Pai Gow poker and Super Pan-9 were created by Sam Torosian and Fred Wolf.The game is played with a standard 52-card deck, plus a single joker...
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 mathematicians
Gaming mathematics
Gaming 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 Shackleford
Michael Shackleford
Michael "The Wizard of Odds" Shackleford a trained actuary , now makes his living analyzing casino games...
, the "Wizard of Odds".