dice_simulation

dice_simulation, a Python code 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 code 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 MIT license

Languages:

dice_simulation is available in a MATLAB version and an Octave version and a Python version.

Related Data and codes:

python_simulation, a Python code which uses simulation to study card games, contests, and other processes which have a random element. Usually, the purpose is to try to predict the average behavior of the system over many trials.

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.py, the source code.
• dice_simulation.sh, runs all the tests.
• dice_simulation.txt, the output file.

• 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