## 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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## The Logic Of The Losing Shoe

The Logic of the Losing Shoe For those in the casino industry, especially for us surveillance folks, the words ‘losing shoe’ are all too familiar. A losing shoe is a period of play, normally lasting the length of one shoe of cards (which may be from one to as many decks as the shoe can hold!), which registers a substantial loss. Ever wondered how that loss limit was set? In considering this question, it is useful to once again refer to our central limit theorem.  Here is the graph again. (Source: http://schools-wikipedia.org/) The central limit theorem proposes that up to 99.9% of all occurrences happen between -3 to -1 and 1 to 3 σs from the average or mean.  σ extends into the positive (meaning 1 to 3 σ) and negative (meaning -1 to -3 σ). In order to derive any sort of boundary in a casino game, one has to calculate the following: Probability Of Events Occurring (for more

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## Understand Your Casino: Mean and Standard Deviation in Gaming

Mean and Standard Deviation in Gaming In the previous post, we talked about the long term expectation of games derived from the probabilities of outcomes in casino games. How about measuring results in the short-term such as when the results of shoes or player activity appear inconsistent with the expected values?  Let’s face it, they usually do! For this, it is useful to apply the principles of the central limit theorem, in particular, the concepts of mean and standard deviation. But first… Central Limit Theorem The central limit theorem explains that the outcome of repeated experiments will follow a bell-shaped pattern.  In terms of casino games, we can translate this as meaning that the outcomes of play will follow a certain pattern of winnings and losses. (Source: http://schools-wikipedia.org/) This is a bell-curve, so named due to its shape. The bell-curve’s centre is known as the mean or average (µ). Notice that the bell-curve is divided into 6 parts from -3σ