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:

DUEL_SIMULATION a MATLAB program which simulates N repetitions of a duel between two players, each of whom has a known firing accuracy.

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RANDOM_WALK_3D_SIMULATION, a MATLAB program which simulates a random walk in a 3-dimensional region.

REACTOR_SIMULATION is a FORTRAN90 program which is a simple Monte Carlo simulation of the shielding effect of a slab of a certain thickness in front of a neutron source. This program was provided as an example with the book "Numerical Methods and Software."

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TRAFFIC_SIMULATION, a MATLAB program which simulates the cars waiting to get through a traffic light.

TRUEL_SIMULATION a MATLAB program which simulates N repetitions of a duel between three players, each of whom has a known firing accuracy.

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Reference:

1. 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.