## Casino Gaming: Theoretical Win, Expected Value and Standard Deviation

Theoretical win and the standard deviations of expected value have been widely covered in numerous articles.  Unfortunately for me, the discussion on the topic has seldom been comprehensive enough to be understood by the layperson (meaning me). This post attempts to explain the issue in the simplest possible way. Why is this important? Theoretical win is derived from the probabilities built into any casino game.  As all casino games are designed (in theory) to guarantee a return to the casino, the theoretical win (winnings for the player) is always negative while the expected value, also known as expectation (winnings for the casino) is always positive. However, like with all probabilities, an element of randomness exists.  The standard deviation of theoretical win thus provides a threshold for casino managers to decide if play has passed the limit where it becomes suspect. Theoretical Win and Expected Value The average of results is determined by the theoretical win formula.  Hence, 50% of all

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