# 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 )
where
• throws is the number of times the dice are thrown.
• dice is the number of dice.

### Languages:

DICE_SIMULATION is available in a MATLAB version.

### Related Data and Programs:

BROWNIAN_MOTION_SIMULATION, a MATLAB program which simulates Brownian motion in an M-dimensional region.

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

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

FAIR_DICE_SIMULATION, a MATLAB program which simulates N tosses of 2 dice, making a histogram of the results.

GAMBLERS_RUIN_SIMULATION, a MATLAB program which simulates the game of gambler's ruin.

HIGH_CARD_SIMULATION, a MATLAB program 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 program 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.

LIFE_OPENGL, a C program which uses OpenGL to display the evolution of John Conway's "Game of Life", by Simon Green.

LORENZ_SIMULATION, a MATLAB program which solves the Lorenz equations and displays the solution, for various starting conditions.

MD1, a FORTRAN90 program which carries out a simple molecular dynamics simulation;

MD2, a FORTRAN90 program which carries out a simple molecular dynamics simulation;

MD3, a FORTRAN90 program which carries out a simple molecular dynamics simulation;

MD3GLUE, a FORTRAN90 program which carries out a simple molecular dynamics simulation;

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

RANDOM_WALK_1D_SIMULATION, a MATLAB program which simulates a random walk in a 1-dimensional region.

RANDOM_WALK_2D_AVOID_SIMULATION, a MATLAB program which simulates a self-avoiding random walk in a 2-dimensional region.

RANDOM_WALK_2D_SIMULATION, a MATLAB program which simulates a random walk in a 2-dimensional region.

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

REACTOR_SIMULATION, a MATLAB program which 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."

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

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

THREE_BODY_SIMULATION, a MATLAB program which simulates the behavior of three planets, constrained to lie in a plane, and moving under the influence of gravity, by Walter Gander and Jiri Hrebicek.

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.

XISING, a C program which models the variations in ferromagnetism in a material, displaying the results using X Windows.

XWAVES, a C program which simulates the behavior of solutions of certain forms of the wave equation, displaying the results using X Windows.

### 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.

### Examples and Tests:

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

Last revised on 14 June 2011.