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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. The house edge of casino games varies greatly with the game, with some games having an edge as low as 0.3%. 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.
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.
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Games commonly found at casinos include table games, gambling machines and random number games. Table games are usually conducted by casino employees known as croupiers or dealers.
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(In games such as blackjack or Spanish 21, the final bet may be several times the original bet, if the player doubles and splits.) The house edge, or vigorish, is defined as the casino profit expressed as a percentage of the player’s original bet. However, the casino may only pay 4 times the amount wagered for a winning wager. There are also hybrid games, as in craps, where the player bets on a terminal at the table but the game is managed by a dealer, although with fewer dealers than the non-hybrid version, this saves costs.