dice_simulation


dice_simulation, a MATLAB 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 )
where

Licensing:

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

Languages:

dice_simulation is available in a MATLAB version.

Related Data and codes:

brownian_motion_simulation, a MATLAB code which simulates Brownian motion in an M-dimensional region.

chuckaluck_simulation, a MATLAB code which simulates the Chuck-a-Luck gambling game.

coin_simulation, a MATLAB code which looks at ways of simulating or visualizing the results of many tosses of a fair or biased coin.

dice_simulation_test

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

fair_dice_simulation, a MATLAB code which simulates N tosses of 2 dice, making a histogram of the results.

fire_simulation, a MATLAB code which simulates a forest fire over a rectangular array of trees, starting at a single random location.

gamblers_ruin_simulation, a MATLAB code which simulates the game of gambler's ruin.

high_card_simulation, a MATLAB code which simulates a situation in which you see the cards in a deck one by one, and must select the one you think is the highest and stop.

ising_2d_simulation, a MATLAB code which carries out a Monte Carlo simulation of an Ising model, a 2D array of positive and negative charges, each of which is likely to "flip" to be in agreement with neighbors.

jai_alai_simulation, a MATLAB code which simulates matches of jai alai.

poisson_simulation, a MATLAB code which simulates a Poisson process in which events randomly occur with an average waiting time of Lambda.

random_walk_1d_simulation, a MATLAB code which simulates a random walk in a 1-dimensional region.

random_walk_2d_avoid_simulation, a MATLAB code which simulates a self-avoiding random walk in a 2-dimensional region.

random_walk_2d_simulation, a MATLAB code which simulates a random walk in a 2-dimensional region.

random_walk_3d_simulation, a MATLAB code which simulates a random walk in a 3-dimensional region.

reactor_simulation, a MATLAB code which a simple Monte Carlo simulation of the shielding effect of a slab of a certain thickness in front of a neutron source. This code was provided as an example with the book "Numerical Methods and Software."

roulette_simulation, a MATLAB code which simulates the spinning of a roulette wheel and the evaluation of certain common roulette bets.

sir_simulation, a MATLAB code which simulates the spread of a disease through a hospital room of M by N beds, using the SIR (Susceptible/Infected/Recovered) model.

traffic_simulation, a MATLAB code which simulates the cars waiting to get through a traffic light.

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

urn_simulation a MATLAB code which simulates an experiment in which k colored marbles are drawn from an urn containing a total of n marbles. The quantity of interest is the number of marbles of each color.

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:


Last revised on 07 January 2019.