Here is a simulation of a gambler's ruin process.
This applet simulates a gambler who repeatedly bets $10, until he either
loses by going broke, or wins by doubling his initial fortune (Init).
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),
which is very small if p < 0.5 and I is large.
[If p = 0.5 then this formula does not apply; in that case
the probability is of course 0.5.]
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 'T' or 'H' or 'G' or 'F' to set the initial fortune to
$10 or $100 or $1000 or $5000, respectively.
- Use 'A' to jump to $10 ahead of bankruptcy,
or 'B' to jump to $10 behind victory.
Applet by Jeffrey S. Rosenthal
(contact me).
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