The Red and Black Experiment

State Space
Distribution graph

Description

In the red and black experiment, a player starts with an initial fortune $$x_0$$ and bets (at even stakes) on independent trials for which the probability of winning is $$p$$. Play continues until the player is either ruined or reaches a fixed target fortune $$a$$.

Either of two player strategies can be selected from a list box. With timid play, the player bets 1 on each trial. With bold play, the player bets her entire fortune or what is needed to reach the target (whichever is smaller). Random variable $$J$$ indicates the event that the player wins (reaches her target) and variable $$N$$ is the number of trials played. These variables are recorded in the data table. The fortune graph shows the space of fortunes $$\{0, 1, \ldots, a\}$$, with the initial fortune in blue and the current fortune in red. In single step mode, the outcome of each trial is shown; in run mode, only the final outcome is shown. The probability density function of $$J$$ is shown in blue in the distribution graph and recorded in the distribution table. When the experiment runs, the empirical density function of $$J$$ is shown in red in the distribution graph and recorded in the distribution table. The parameters $$x_0$$ and $$p$$ and $$a$$ can be varied with input controls.