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The games available in most casinos are generally called casino games. In a casino game, 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 the casino, such as at parties or school competitions, on some machines that simulate gambling.

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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 personnel to play. Table games, such as blackjack or craps, involve one or more players competing against the house (the casino itself) instead of each other. Table games are usually handled by casino employees known as croupiers or dealers. Random number games are based on the selection of random numbers from a computerized random number generator or other gaming equipment. Random number games can be played at a table or by purchasing paper tickets or cards, such as ko or bingo.

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Some casino games combine multiple of the above aspects; For example, roulette is a dealer-run table game involving random numbers. Casinos may also offer other types of gaming, 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 in front of a casino and operated by one or more live croupiers, played on a mechanical device. Like a slot machine or against other players instead of a casino, like standard poker.

Table games are popularly played in casinos and include some form of legal gambling, but are also played privately by different house rules. The significance of this term is that some jurisdictions permit casinos to have only slots and no table games. In some states, this law has resulted in casinos employing electronic table games, such as roulette, blackjack, and craps.

Casino games generally provide predictable long-term profits for the casino or “house”, while offering players the possibility of short-term profits that can be large in some cases. Some casino games have a skill element, where players’ decisions affect the outcome. Players who have enough skill to overcome a long-term disadvantage (house edge or bullish) in a casino game are known as advantage players.

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The disadvantage to players is the result of the casino not paying out winning bets according to the game’s “true odds”, which are the payouts expected given the odds of winning or losing. For example, if a game is played with a bet on a number that will result from the roll of a die, the true odds will be 6 times the amount bet because there is a 1 in 6 chance of any one number appearing, assuming the player returns the original bet. Get. However, the casino can only pay 4 times the amount for a winning bet.

The 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, if the player doubles and splits, the final bet may be many times the original bet.)

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 a 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%. Therefore, the house edge is 5.26%. After 10 spins, bet 1 unit per spin, the average house profit would be 10 × 1 × 5.26% = 0.53 units. European roulette wheels have only one “zero” and so the house advantage (ignoring the prison rule) is 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%. House edge in Ko can be up to 25%, slot machines can have an edge of up to 15%.

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Calculating the house edge in roulette is a trivial exercise; For other sports, this is usually not the case. Combinatorial analysis and/or computer simulation are required to complete the task.

In games with skill elements such as blackjack or Spanish 21, the house edge is defined as the house advantage from the best play (without using advanced techniques such as card counting), on the first hand (container) of the shoe. which holds the card). The set of best plays for all possible hands is known as “basic strategy” and is highly dependent on the specific rules and number of decks used.

Traditionally, most casinos have refused to disclose the house edge information for their slots games and due to the unknown number of symbols and weights on the reels, in most cases, the house edge is more difficult to calculate compared to other casinos. Games However, thanks to some online properties disclosing this information and some incredible research conducted by Michael Shackelford in the offline sector, this pattern is slowly changing.

In games like poker where the players are not competing against the house, the casino usually makes money through commissions, known as “rakes”.

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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 an outcome of 1 unit for a win and 0 unit for a loss instead of −1 unit for a loss, which doubles the range of possible outcomes. Furthermore, if we place a flat 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 = 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 would 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 many times the expected loss magnitude.

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The standard deviation for Pi Go Poker is the lowest of all common casino games. Many casino games, especially slot machines, have extremely high standard deviations. The larger the size of the potential payout, the larger the standard deviation.

As the number of rounds increases, the expected loss will increase by several times the standard deviation. From the formula, we can 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 damage increases at a much faster rate. This is why gambling is impossible to win in the long run. It is the high ratio of expected loss to short-term standard deviation that fools gamblers into thinking they can win.

It is important for casinos to know both the house edge and the spread for all their games. House Edge tells them what kind of profit they’ll make as a percentage of turnover, and the difference tells them how much they need in the way of cash reserves. Mathematicians and computer programmers who do this kind of work are called gaming mathematicians and gaming analysts. Casinos do not have in-house expertise in this area, so outsource their needs to experts in the field of gaming analysis. People choose different games for different reasons but the most popular slots are usually bonus games.

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