## 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