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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 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.
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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 or , the final bet may be several times the original bet, if the player doubles and splits.)
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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%. can have house edges of up to 25%, slot machines having up to 15%.
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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 possessing sufficient skills to eliminate the inherent long-term disadvantage (the or ) in a casino game are referred to as .
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.
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Traditionally, many casinos were reluctant to disclose the house edge of their slot games, making it difficult for players to assess the true pay out potential. However, this practice is slowly changing, as more online casinos are beginning to provide this information, and independent research, such as that conducted by , has also shed light on these figures. In the UK, the Gambling Commission (GC) now requires that all RTP (Return to Player) values be clearly displayed for both online and land-based casino games. This regulation ensures greater transparency, giving players the information they need to make more informed choices about the games they play.
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Table games are popularly played in and involve some form of , 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 , , and .
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The luck factor in a casino game is quantified using (SD). The standard deviation of a simple game like roulette can be calculated using the . In the binomial distribution, SD = , where = number of rounds played, = probability of winning, and = 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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The standard deviation for 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.