full_deck_simulation, a MATLAB code which simulates a process in which a random card is drawn from a deck of 52, and then replaced, continuing until every card has been seen at least once.
A New York artist carried out an equivalent project by wandering the streets and picking up single playing cards that had been thrown away. Once a full, though motley, deck had been collected, it was displayed in a gallery. (Of course, many of the collected cards were duplicates, and thus didn't make the show!)
This is a version of a well-known problem in probability known as "the coupon collector's problem".
The computer code and data files described and made available on this web page are distributed under the MIT license
full_deck_simulation is available in a MATLAB version.
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.
clock_solitaire_simulation, a MATLAB code which simulates the game of clock solitaire. The deck is dealt into 13 piles of 4 cards each. Repeatedly, the top card a pile is removed, and its rank indicates the next pile to consider. Game continues until an empty pile is reached. The game is won if all piles are empty. The quantity of interest is the probability of winning.
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, a MATLAB code which simulates N tosses of M dice, making a histogram of the results.
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 game in which you have one chance to select the highest card from a deck.
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.