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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). Multiplayer machines are where a player’s decision may affect others at the same game, such as when to press the button to roll dice in craps. The term has significance in that some jurisdictions permit casinos to have only slots and no table games.

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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.

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