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In some states, this law has resulted in casinos employing electronic table games, such as roulette , blackjack , and craps. 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 possessing sufficient skills to eliminate the inherent long-term disadvantage the house edge or vigorish in a casino game are referred to as advantage players. 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 the roll of one die, 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. The house edge or vigorish is defined as the casino profit expressed as the 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. In American roulette , 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.

Therefore, the house edge is 5. The house edge of casino games varies greatly with the game, with some games having an edge as low as 0. The calculation of the roulette house edge is a trivial exercise; for other games, this is not usually the case. In games that 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.

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 online properties revealing this information and some independent research conducted by Michael Shackleford in the offline sector, this pattern is slowly changing. In games where players are not competing against the house, such as poker , the casino usually earns money via a commission, known as a " rake ". The luck factor in a casino game is quantified using standard deviations SD. Furthermore, if we flat bet at 10 units per round instead of 1 unit, the range of possible outcomes increases 10 fold.

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 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. 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 a 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 they outsource their requirements to experts in the gaming analysis field. Contents move to sidebar hide. Article Talk. Read Edit View history. Tools Tools. Download as PDF Printable version. Types of casino games. Not to be confused with Arcade game or Cassino card game.

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