In the red and black experiment, a player starts with an initial fortune and bets (at even stakes) on independent trials for which the probability of winning is . Play continues until the player is either ruined or reaches a fixed target fortune .
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 indicates the event that the player wins (reaches her target) and variable is the number of trials played. These variables are recorded on each update in the data table. The first graph shows the initial and target fortunes and the final outcome. The probability density function of is shown in blue in the distribution graph and recorded in the distribution table. On each update, the empirical density function of is shown in red in the distribution graph and recorded in the distribution table. The mean of is shown in blue in the last graph and is recorded in the moment table for . On each update, the empirical mean of is shown in red in the last graph and recorded in the moment table. The parameters and can be varied with scroll bars, and the target fortune can be chosen from a list box.