## 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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## Concepts 9: Creating A Casino Game

Creating A Casino Game We’ve discussed the process for the creation of a casino game, namely: Calculating possibilities using combinatorial analysis Calculating the expectation Setting the odds Let’s use a simple example – something I saw in a Chinese drama. The game involves using 5 coins and tumbling them in an opaque container.  The container is then placed base up and players are then invited to make their wagers based on the permutations of the coins. Here are the calculations based on some of the possible wager types I can think of: Combinations Permutations Probability Expectation Break-Even Odds Total (5 + 2 -1!) / (5! X 2-1!) = 6 25 = 32 – – – 5 Tails 2! / 2! = 1 5! / 5! = 1 1/32 = 0.03125 0.03125 – (1-0.03125) = -0.9375 0.96875/0.03125 = 31 5 Heads 2! / 2! = 1 5! / 5! = 1 1/32 = 0.03125 0.03125 – (1-0.03125) = -0.9375 0.96875/0.03125 =

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## 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

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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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