gamblers_ruin_simulation, a MATLAB code which simulates the game of gambler's ruin.
In the game of gambler's ruin, two gamblers, A and B, start with $A_STAKES and $B_STAKES, respectively, and play until one of them is bankrupt. They repeatedly flip a coin. On heads, A wins one dollar from B, and on tails, B wins one dollar from A.
The game is easy to simulate, and can also be analyzed. It is worth study in part because the analysis or simulation of the game reveals some surprising features about the chances of winning, the typical length of a game, and the number of times each player will be in the lead.
In particular, most people will be surprised to find that if A starts with $1 and B with $100, the "average" game will take 100 coin tosses.
It is known that, if A and B start the game with $A_STAKES and $B_STAKES,
Note that the game of gambler's ruin can be regarded as a case of a 1D random walk in a finite region, in which the "particle" starts A_STAKES steps from one wall and B_STAKES steps from the other, and in which the walk ends when the particle strikes a wall.
The code GAMBLERS_RUIN_PLOT displays the "score" for player A at each step of the game.
The code GAMBLERS_RUIN_SIMULATION plays the game a number of times, and computes statistics of the number of steps and the probability of winning, as well as histograms of the number of steps and the number of times the lead was reversed.
gamblers_ruin_plot ( a_stakes, b_stakes )where
gamblers_ruin_simulation ( a_stakes, b_stakes, game_num )where
The computer code and data files described and made available on this web page are distributed under the MIT license
gamblers_ruin_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.
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.
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.