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The games available in most casinos are commonly called casino games. In a casino game, players bet money 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 the casino for tertainm purposes such as parties or school competitions, some on machines that simulate gambling.
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There are three general categories of casino games: slots, table games, and random number games. Slot machines, such as slot machines and pachinko, are usually played by one player at a time and do not require casino staff to be involved in the game. Table games such as blackjack or craps involve one or more players competing against the house (the casino itself) rather than against each other. Table games are usually operated by casino employees known as croupiers or dealers. Random number games are based on the selection of random numbers, either from a computer random number generator or from another gaming device. Random number games can be played at a table or through the purchase of paper tickets or cards, such as ko or bingo.
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Some casino games combine more of the above aspects; for example, roulette is a dealer-run table game that involves random numbers. Casinos may also offer other types of games, such as hosting poker games or tournaments where players compete against each other.
In the United States, “table game” is the term used for games of chance such as blackjack, craps, roulette, and baccarat that are played against a casino and operated by one or more live dealers, as opposed to games played on mechanical equipment. like a slot machine or against other players instead of a casino like standard poker.
Table games are commonly played in casinos and involve some form of legal gambling, but are also played privately under various house rules. The term has meaning in that some jurisdictions allow casinos to have only slots and no table games. In some states, this law has led to casinos using electronic table games such as roulette, blackjack and craps.
Casino games usually provide a predictable long-term edge to the casino, or “house”, while also offering players the possibility of short-term profit, which in some cases can be large. Some casino games have an element of skill where players’ decisions affect the outcome. Players who have sufficient skill to eliminate an inherent long-term disadvantage (house advantage or edge) in a casino game are referred to as advantage players.
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The disadvantage to players is the result of the casino not paying winning bets at “true odds”, which are the payouts that would be expected given the odds of the bet winning or losing. For example, if the game is played by betting on the number that would result from the roll of a single die, the actual odds would be 6 times the amount bet, since there is a 1 in 6 chance of any single number coming up, assuming the player gets back the original bet . However, the casino can only pay 4 times the staked amount for a winning bet.
House edge or vigorish is defined as the casino’s profit expressed as a percentage of the player’s original bet. (In games like blackjack or Spanish 21, the final bet can be several times the original bet if the player doubles and splits.)
In American roulette, there are two “zeros” (0.00) and 36 non-zero numbers (18 red and 18 black). This leads to a higher house edge compared to European roulette. A player who bets 1 unit on red has an 18/38 chance of winning and a 20/38 chance of losing 1 unit. The player’s expected value is EV = (18/38 × 1) + (20/38 × (−1)) = 18/38 − 20/38 = −2/38 = −5.26%. So 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 has only one “zero” and therefore the house edge (ignoring the prison rule) is 1/37 = 2.7%.
Casino game limits vary greatly from game to game, with some games having an edge as low as 0.3%. Ko can have a house edge of up to 25%, slots up to 15%.
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Calculating the roulette edge is a trivial exercise; this is usually not the case with other games. Combinatorial analysis and/or computer simulation is necessary to complete the task.
In games that have an element of skill, such as blackjack or Spanish 21, the house edge is defined as the house edge from the optimal play (without the use of advanced techniques such as card counting), on the first side of the shoe (the container that holds the cards). The set of optimal games for all possible combinations is known as the “basic strategy” and is highly dependent on the specific rules and ev. number of packages used.
Traditionally, most casinos have refused to disclose house edge information for their slot games, and due to the unknown number of symbols and weights on the reels, it is much more difficult to calculate the house edge in most cases than in other casinos. games. However, due to some online properties revealing this information and some independent research done by Michael Shackleford in the offline sector, this pattern is slowly changing.
In games where players are not competing against house players, such as poker, the casino usually makes money through a commission, known as “rake”.
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The standard deviation of a simple game such as 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 an outcome of 1 unit for a win and 0 units for a loss, rather than -1 unit for a loss, which doubles the range of possible outcomes. In addition, if we bet on 10 units per round instead of 1 unit, the range of possible outcomes increases 10 times.
SD (roulette, ev-money bet) = 2b √npq , where b = even bet per wheel, n = number of wheels, 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, the standard deviation is a multiple of the size of the expected loss.
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The standard deviation for pai gow poker is the lowest of any common casino game. Many casino games, especially slot games, have extremely high standard deviations. The larger the size of the potential payoffs, the more the standard deviation can increase.
Eventually, as the number of rounds increases, the expected loss will exceed the standard deviation many times over. From the formula, we see that 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 much faster. This is why it is impossible for players to win long term. It is the high ratio of short-term standard deviation to expected loss that tricks players into thinking they can win.
It is important for a casino to know both the edge and the variance for all of their games. The house edge tells them what kind of profit they will make as a percentage of turnover, and the spread tells them how much cash reserves they need. Mathematicians and computer programmers who do this kind of work are called game mathematicians and game analysts. Casinos do not have their own expertise in this area, so outsource your requirements to experts in the field of game analysis. People like different games for different reasons, but the most popular slots are usually those with bonus games.
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