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Games available in most casinos are commonly referred to as casino games. In a casino game, players gamble cash or casino chips on various random outcomes or combinations of outcomes. Casino games are also available in online casinos where permitted by law. Casino games can be played outside the casino, such as at parties or school competitions, some on machines that simulate gambling.
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There are three main categories of casino games: slot machines, 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 the presence of casino staff to play. 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 played 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 buying paper tickets or cards like ko or bingo.
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Some casino games combine several 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 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, which are played against a casino and operated by one or more live croupiers, as opposed to those played on a mechanical device. like a slot machine or against other players instead of a casino like standard poker.
Table games are common in casinos and include some form of legal gambling, but are played privately according to different house rules. The significance of this term is 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 advantage for the casino or “house” while also offering players the opportunity to make short-term gains that can be substantial in some cases. Some casino games have an element of skill where players’ decisions affect the outcome. In a casino game, players who have enough skills to overcome a specific long-term disadvantage (house edge or strength) are called advantage players.
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A player’s disadvantage is the result of the casino not paying out winning bets at the game’s “true odds,” which are the expected payouts given the odds of the bet winning or losing. For example, if a game is played by betting on a number coming from a single die, the actual odds will be 6 times the amount bet because the player has a 1 in 6 chance of a single number coming up. will be equal to will get back the initial bet amount. However, the casino can only pay 4 times the stake for a winning bet.
The house edge or boost is defined as the casino’s profit expressed as a perctage of the player’s original bet. (In games like blackjack or Spanish 21, if a player splits twice, the final bet can be many times the original bet.)
American roulette has two zeros (0, 00) and 36 non-zero numbers (18 red and 18 black). This results in a higher house edge compared to European roulette. A player betting 1 unit on red has an 18/38 chance of winning and a 20/38 chance of losing 1 unit. Player’s Expected Value 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 is 10 × 1 × 5.26% = 0.53 units. European roulette wheels have only one “zero” and therefore the house edge (ignoring the prison rule) is 1/37 = 2.7%.
The house limit of casino games varies greatly by game, with some games as low as 0.3%. The house edge can be up to 25% on poker and 15% on slot machines.
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Calculating the roulette house edge is a trivial exercise; for other games, this is usually not the case. Combinatorial analysis and/or computer simulation is required to complete the task.
In games with an element of skill, such as blackjack or Spanish 21, the house edge is defined as the advantage of the house over the optimal play (without using advanced methods such as card counting) in the first hand (container) of the shoe. holds the cards). The optimal set of games for all possible hands is called “basic strategy” and is highly dependent on the exact rules and the number of decks used.
Traditionally, most casinos have refused to disclose the house edge for their slot games, and due to the unknown number and weights of the wheels, calculating the house edge in most cases is more difficult than in other casinos. . games. However, thanks to some online features that reveal this information and some independent research done by Michael Shackleford in the offline sector, this pattern is slowly changing.
In games where the players do not compete against the house, such as poker, the casino receives money through a commission commonly known as “rake”.
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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 accepts an outcome of 1 unit for a win and 0 unit for a loss, not -1 unit for a loss, which doubles the range of possible outcomes. Also, if we bet 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 = straight bet per turn, n = number of turns, p = 18/38, and q = 20/38.
For example, after 10 rounds of 1 unit per round, the standard deviation would be 2 × 1 × √10 × 18/38 × 20/38 = 3.16 units. Expected loss after 10 rounds is 10 × 1 × 5.26% = 0.53. As you can see, the standard deviation is many times larger than the expected loss.
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The standard deviation for pai gow poker is the lowest of all common casino games. Many casino games, especially slot machines, have very high standard deviations. The larger the payouts in the box, the larger the standard deviation can be.
As the number of rounds increases, eventually the expected loss will exceed the standard deviation by many times. 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 loss increases at a much faster rate. Therefore, it is impossible for the gambler to win in the long run. This high ratio of short-run standard deviation to expected loss makes gamblers think they can win.
It is important for a casino to know the house edge and spread for all games. The house edge tells them what profit they will make as a percentage of turnover, and the variance tells them how much they need in the way of cash reserves. Mathematicians and computer programmers who do such work are called game mathematicians and game analysts. Casinos do not have in-house expertise in this area, so leave their requirements to experts in the field of game analysis.