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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. It is important for a casino to know both the house edge and variance for all of their games. 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. The bigger size of the potential payouts, the more the standard deviation may increase. 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. The luck factor in a casino game is quantified using standard deviations (SD).
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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. Some casino games have a skill element, where the players’ decisions have an impact on the results. 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. Casinos may also offer other types of gambling, such as hosting poker games or tournaments where players compete against each other.
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As the number of rounds increases, eventually, the expected loss will exceed the standard deviation, many times over. Many casino games, particularly slot machines, have extremely high standard deviations. The standard deviation for pai gow poker is the lowest out of all common casino games. As you can see, standard deviation is many times the magnitude of the expected loss. The standard deviation of a simple game like roulette can be calculated using the binomial distribution.
