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585:= 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.
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Traditionally, the majority of casinos have refused to reveal the house edge information for their slots games, and due to the unknown number of symbols and weightings of the reels, in most cases, it is much more difficult to calculate the house edge than in other casino games. However, due to some
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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, betting 1 unit per spin, the average house profit will be 10 × 1 × 5.26% = 0.53 units. European roulette wheels have only one "zero" and therefore the house advantage (ignoring
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The players' 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
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As the number of rounds increases, eventually, the expected loss will exceed the standard deviation, many times over. 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
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Casino games typically provide a predictable long-term advantage to the casino, or "house", while offering the players the possibility of a short-term gain that in some cases can be large. Some casino games have a skill element, where the players' decisions have an impact on the results. Players
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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.
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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 a percentage of turnover, and the variance tells them how much they need in the way of cash reserves. The mathematicians and computer
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the roll of one die, the true odds would be 6 times the amount wagered since there is a 1 in 6 chance of any single number appearing, assuming that the player gets the original amount wagered back. However, the casino may only pay 4 times the amount wagered for a winning wager.
368:, there are two "zeroes" (0, 00) and 36 non-zero numbers (18 red and 18 black). This leads to a higher house edge compared to European roulette. The chances of a player, who bets 1 unit on red, winning are 18/38 and his chances of losing 1 unit are 20/38. The player's
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208:, but they are also played privately under varying house rules. The term has significance in 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
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is the lowest out of all common casino games. Many casino games, particularly slot machines, have extremely high standard deviations. The bigger size of the potential payouts, the more the standard deviation may increase.
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The calculation of the roulette house edge is a trivial exercise; for other games, this is not usually the case. Combinatorial analysis and/or computer simulation is necessary to complete the task.
86:, where permitted by law. Casino games can also be played outside of casinos for entertainment purposes, like in parties or in school competitions, on machines that simulate gambling.
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118:, involve one or more players who are competing against the house (the casino itself) rather than each other. Table games are usually conducted by casino employees known as
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571:
694:= 3.16 units. After 10 rounds, the expected loss will be 10 × 1 × 5.26% = 0.53. As you can see, standard deviation is many times the magnitude of the expected loss.
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and gaming analysts. Casinos do not have in-house expertise in this field, so they outsource their requirements to experts in the gaming analysis field.
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or from other gaming equipment. Random number games may be played at a table or through the purchase of paper tickets or cards, such as
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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
402:), on the first hand of the shoe (the container that holds the cards). The set of optimal plays for all possible hands is known as "
102:
There are three general categories of casino games: gaming machines, table games, and random number games. Gaming machines, such as
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is a table game conducted by a dealer, that involves random numbers. Casinos may also offer other types of gaming, such as hosting
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Gao, J.Z.; Fong, D.; Liu, X. (April 2011). "Mathematical analyses of casino rebate systems for VIP gambling".
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The house edge of casino games varies greatly with the game, with some games having an edge as low as 0.3%.
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or dealers. Random number games are based on the selection of random numbers, either from a computerized
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Games commonly found at casinos include table games, gaming machines and random number games.
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For example, after 10 rounds at 1 unit per round, the standard deviation will be 2 × 1 ×
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539:(SD). The standard deviation of a simple game like roulette can be calculated using the
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online properties revealing this information and some independent research conducted by
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possessing sufficient skills to eliminate the inherent long-term disadvantage (the
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Overhead view of a casino floor with table games (bottom) and slot machines
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891:(1st ed.). London: European Lawyer Reference Series/Thomson Reuters.
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outcomes or combinations of outcomes. Casino games are also available in
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can have house edges of up to 25%, slot machines having up to 15%.
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Some casino games combine multiple of the above aspects; for example,
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Casino Gamble Talk: The
Language Of Gambling And The New Casino Game
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In games where players are not competing against the house, such as
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that are played against the casino and operated by one or more live
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or against other players instead of the casino, such as standard
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games or tournaments where players compete against each other.
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in the offline sector, this pattern is slowly changing.
41:"Casino games" redirects here. For the video game, see
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Hagan, general editor, Julian Harris, Harris (2012).
744:"UNLV Center for Gaming Research: Casino Mathematics"
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The luck factor in a casino game is quantified using
807:. Kensington Publishing Corporation. pp. 135–.
463:. Unsourced material may be challenged and removed.
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710:programmers that do this kind of work are called
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311:Random numbers games found in casinos include:
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889:Gaming law : jurisdictional comparisons
390:In games that have a skill element, such as
856:"Michael Shackleford is the wizard of odds"
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281:Gaming machines found in casinos include:
924:CS1 maint: multiple names: authors list (
523:Learn how and when to remove this message
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804:Powerful Profits from Casino Table Games
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687:{\displaystyle {\sqrt {10*18/38*20/38}}}
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543:. In the binomial distribution, SD =
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868:from the original on 18 October 2015
461:adding citations to reliable sources
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200:Table games are popularly played in
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828:Victor H. Royer (26 August 2014).
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589:SD (roulette, even-money bet) = 2
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70:. In a casino game, the players
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448:needs additional citations for
377:rule) is equal to 1/37 = 2.7%.
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941:International Gambling Studies
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834:. Lyle Stuart. pp. 134–.
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581:= probability of winning, and
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977:Practical Business Statistics
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615:{\displaystyle {\sqrt {npq}}}
566:{\displaystyle {\sqrt {npq}}}
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