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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). In American roulette, there are two “zeroes” (0, 00) and 36 non-zero numbers (18 red and 18 black).
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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. 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 calculation of the roulette house edge is a trivial exercise; for other games, this is not usually the case.
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