RM202 Case Study 1 - Dice Throw Exercise [PDF]

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Potential Loss Quantification

Case Study #1: Dice Throw Simulation

This exercise is to allow users to repeatedly simulate the counting of sum of each dice throw. Each dice represents a risk occurrence, which has a range of possible outcomes (in this case, 1-6). The number of dice will be varied to strengthen the idea of a variety of risk outcomes. This takes the standard classroom example of dice throwing and offers the ability to understand the distributions of dice throws via Monte Carlo simulation, and explore how it can be used to model risk. We will construct the experiment first with 2 dice, followed by 10 dice and 20 dice. Assumptions made: 

Dice are not flawed (same probability of hitting 1,2,3,4,5,6)



Tracked forecast: Sum of each Dice Throw

Referring to the steps below, it is your task to apply Crystal Ball software to create the model and report your analysis.

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Potential Loss Quantification

Dice throw simulation 1.

We will be using 2 cells to model the throwing of 2 Dice. First, select the first cell, C12, and select the Crystal Ball tab and click on Define Assumption. A number of different distributions will appear. We will use the Discrete Uniform distribution to model a dice throw. Set the value in Minimum to 1, and Maximum value to 6. Click OK to apply. Apply the same steps above to the cell C13.

2.

Once your 2 cells with assumptions have been set, conduct a few simulations. Click on Step under the Crystal Ball tab.

3.

Insert a forecast to track the sum of dice per throw. Select Cell C33, and sum the 2 dice assumption cells C12 and C13 by inputting the following formula: [=sum(C12:C13)] Next select Cell C33 and select Define Forecast (Crystal Ball tab). Name the Forecast “2 Dice Forecast”. Click OK.

4.

Next, we will run a few 2 Dice simulations, followed by numerous simulation times. In the Crystal Ball “Run” tab, input 10 simulations. Now run a simulation by clicking Start. View the Forecast by clicking View Charts > Forecast Charts. Select the 2 Dice Forecast and click OK. Next, repeat steps using 10,000 simulations. View Forecast Chart.

5.

Next we will set up and run the simulation model for both 10 Dice and 20 Dice. 10 Dice: As the Dice simulations have the same probability and values, we can apply the Crystal Ball Assumptions in Cell C12 to Cells D12-D21 by using Crystal Ball’s Copy and Paste function (in Define tab). 20 Dice: Apply the same step above to Cells E12-E32. Create Forecast for 10 Dice and 20 Dice in Cells D33 and E33 respectively, and name the forecasts accordingly. Run 10,000 Simulations. View all Forecast Charts.

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Potential Loss Quantification

Simulation & Analysis 1.

Run the 3 scenarios simulations (2, 10 & 20 Dice) using 10,000 trials. Set maximum number of trials to 10,000. Start simulation. After simulations are done, click View Charts and open all Forecast Charts.

2.

Identify the following statistics for the respective simulations: 2 Dice Throw

10 Dice Throw

20 Dice Throw

Min Value Maximum Value Mean (Average value of dataset) Median (Middle point value of dataset) Standard Deviation (A measure of a data set’s dispersion from its mean)

Tip: From the individual 2 Dice, 10 Dice, 20 Dice forecasts, click on View and select Statistics and also Split View.

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