This applet simulates a gambler who repeatedly bets $10, until he either loses by going broke, or wins by doubling his initial fortune.

The applet accepts the following keyboard inputs. (You may need to "click" on the applet first.)

- Use the numbers '0' through '9' to set the animation speed level higher or lower.
- Use 'r' to restart the simulation, or 'z' to zero the Win/Loss counts.
- Use '>' and '<' to increase/decrease the win probability of each bet. (Possible values include 0.492929 [the probability of winning at craps] and 0.473684 [the probability of winning at roulette] plus various other values like 0.333333, 0.4, 0.45, 0.49, 0.495, 0.499, 0.4999, and 0.5.)
- Use '+' and '-' to increase/decrease the initial fortune by $10 (and restart). Or, use 'H' or 'G' or 'F' to set the initial fortune to $100 or $1000 or $5000, respectively.
- Use 'A' to jump to $10 ahead of bankruptcy, or 'B' to jump to $10 behind victory.

The probability of victory in this "gambler's ruin" game is known to be

[((1-p)/p)^(Init/10) - 1] / [((1-p)/p)^(Init/5) - 1](where p is the win probability of each individual bet, and Init is the initial fortune), which is very small if p < 0.5 and Init is large. [If p = 0.5 then this formula does not apply; in that case the probability is of course 0.5.]

Applet by Jeffrey S. Rosenthal (contact me).

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