Industrial and Management Systems Engineering



Law of Large Numbers - Dice Rolling Example

Date of this Version



P. Savory (2009), “Law of Large Numbers - Dice Rolling Example”, Mathematica Software Demonstration, The Wolfram Demonstations Project. Available at:


This Mathematica demonstration showcases the law of large numbers, a key theorem in probability theory, that describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed. For this demonstration, consider rolling a die. If each roll is independent of the next (the result of one roll does not change the probabilities of any number of spots appearing)), then average of the rolls should converge to 3.5 (expected value for the roll of a die) as n gets large. This Demonstration simulates a user defined number of rolls of the die. The pie chart shows the distribution of the number of spots that appear and the bottom plot show the average of number of die rolls. As the number of rolls increases, the average will converge to 3.5.