DICE_SIMULATION
Simulation of a Dice Game

DICE_SIMULATION is a MATLAB program which simulates N games in which M dice are thrown and summed.

The user specifies the number of games (throws of the dice) and the number of dice. The program plots a histogram or bar chart of the number of times each score was attained, an estimated probability chart (simply normalizing the frequencies), as well as the average and variance of the scores.

Of course, for 1 die, we expect the histogram to be roughly uniform, for 2 dice, it should have a pyramidal shape, and for higher numbers of dice, the frequency plot should suggest the normal curve.

Usage:

dice_simulation ( throws, dice )

• throws is the number of times the dice are thrown.
• dice is the number of dice.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Related Data and Programs:

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Reference:

1. Paul Nahin,
   Digital Dice: Computational Solutions to Practical Probability Problems,
   Princeton University Press, 2008,
   ISBN13: 978-0-691-12698-2,
   LC: QA273.25.N34.
2. Dianne OLeary,
   Scientific Computing with Case Studies,
   SIAM, 2008,
   ISBN13: 978-0-898716-66-5,
   LC: QA401.O44.

Source Code:

• dice_simulation.m, the program.

Examples and Tests:

• dice_freq_100_1.png, a frequency plot of 100 throws of 1 die
• dice_prob_100_1.png, a probability plot of 100 throws of 1 die
• dice_freq_1000_2.png, a frequency plot of 1000 throws of 2 dice
• dice_prob_1000_2.png, a probability plot of 1000 throws of 2 dice
• dice_freq_10000_3.png, a frequency plot of 10000 throws of 3 dice
• dice_prob_10000_3.png, a probability plot of 10000 throws of 3 dice
• dice_freq_100000_4.png, a frequency plot of 100000 throws of 4 dice
• dice_prob_100000_4.png, a probability plot of 100000 throws of 4 dice

You can go up one level to the MATLAB source codes.