## 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

read more Casino Gaming: Theoretical Win, Expected Value and Standard Deviation

## 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

read more The Logic Of The Losing Shoe

## Sic-Bo and Dice – An Analysis

Sic-Bo is really popular in Asia.  This game involves 3 dice in a tumbler or variant which is tumbled, with varying payments for specific combinations of the dice. There is an amazing way to calculate how many possible outcomes for a particular score from 3 six-sided dice there can be.  This involves the use of polynomial multiplication. Here’s a simple way to look at this… You have 3 dice with numbers from 1 to 6 on each of them. Die 1 1 2 3 4 5 6 Die 2 1 2 3 4 5 6 Die 3 1 2 3 4 5 6 Now, add each number from Die 1 to the first number of Die 2 and then the second and so on like this. Die 1 Die 2 1 2 3 4 5 6 1 2 3 4 5 6 7 2 3 4 5 6 7 8 3 4 5 6 7 8 9 4 5 6

read more Sic-Bo and Dice – An Analysis

## 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

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