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

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Maximise the Profitability of Your Casino by understanding Probability and Expectation in Gaming

Probability The basis of all games of chance is the concept of probability. What is probability?  Probability refers to the chance that an event will occur.  Probability is a value that ranges from 1, for an event that will definitely occur, to 0, for an event that will never occur. We get the probability of an event occurring by dividing the number of possible ways an event can occur by the total possible number of outcomes for all events.  Let’s illustrate: For a 6-sided die, we know that the total number of sides and numbers is 6.  So, for any single roll of the die, we could have any one of 6 possible outcomes.  6 is then the total possible number of outcomes for all events. Thus, the chance of rolling any number from 1 – 6 on a roll of the die is 1/6, assuming that the die isn’t loaded (we hope!). A variation of this, is the chance

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