INSTRUCTIONS:

  • Select the number of dice (1, 2 or 3) to use by clicking on the appropriate checkbox.
  • Set the number of rolls the simulation should run by clicking on the up/down triangles.
  • Click on 'RUN' to start the simulation.
  • The red bars on the graph will track the relative frequencies of each possible dice total.
  • A normal curve will be overlayed onto the bar chart if you are using 2 or 3 dice.
  • Click on the question mark in the lower-left corner for more help with the controls.

ABOUT MONTE CARLO:

Monte Carlo was one of our first NIM (Networked Interactive Multimedia) educational simulations. Using it, students could conduct probability experiments by setting certain parameters of the simulation (such as the number of dice to roll, the number of rolls per round, etc. ), and then analyzing a display of the frequencies of the various dice totals. In conjunction with an instructional module, Monte Carlo provided an avenue for active exploration of the Normal Distribution, perhaps the most important distribution in all of statistics. Developing a solid understanding of its properties is crucial as it forms the foundation for many more complex concepts

Monte Carlo's raison d'etre was stated in the promotional literature which accompanied it

'There are literally thousands of textbooks on statistics. Many of these textbooks are very good. However, just as in many other subjects, developing a solid comprehension of statistical concepts requires activity. You can only read so much about something before it becomes crucial to apply (and experiment with) your new knowledge. The problem with statistics is that, generally speaking, the only way to 'play' with its fundamental ideas is to do alot of equations over and over again. For people who don't particularly find this an intrinsically amusing activity, we present an alternative: Monte Carlo.'

SAMPLE EXPERIMENT:

Step 1:

Click on the Reset button. This will reset the simulation to rolling 1 die per round, and it will also pause after every round.

Step 2:

Click on the Run button. This will 'roll' the die. You can see the result of the die roll in the middle window, and a red bar will appear on the graph corresponding to this result.

Step 3:

Click on Run a few more times. Notice that the Total window is keeping track of how many rounds of the simulation you have run, and that the graph is keeping track of the result of each roll by increasing the height of the corresponding red bars.

If you need some assistance with the different displays and controls, activate the help function by clicking on the question mark in the lower-left hand corner of the Monte Carlo screen.

Step 4:

Now it's time to increase the number of rolls before the simulation pauses. This will let you see how the graph evolves over a high number of rolls without having to spend all day rolling one die at a time. Click on the triangle pointing up in the window marked Rolls. Hold down the mouse button until the number of rolls per round (that is, the number of rolls before the simulation pauses) is around 50. If you overshoot the number you want, use the down triangle.

Step 5:

This time, when you click Run, the simulation will go through the number of rounds you specified (you can see what round number it is currently on by watching the Roll window) before pausing. If you want to see individual dice rolls, you'll have to slow the simulation down by moving the Speed slider to the left.

Keep rolling the dice (by clicking Run), and then take a look at the shape of the graph after approximately 500 rounds. Is it roughly flat (that is, are all the bars about the same height)? If all the bars are approximately the same height, what does that reveal about the 500 dice you have just rolled?

Step 6:

Try it again. Click on the New button, which will reset the graph and the round totals to zero. Set the number of rolls per round to 500, and make sure the Speed slider is at the furthest point to the right (fastest speed). Now, when you run the simulation, it will roll 500 dice before pausing.

When it pauses, is the graph roughly flat again?



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