This is a simulation of simple random walk, including the Gambler's
(If you have trouble running the applet,
see these notes.)
This applet simulates a gambler who repeatedly bets $1, either forever
(for random walk), or until he either
loses by going broke or wins by doubling his initial fortune (for
The probability of victory in the Gambler's Ruin game is known to be
[((1-p)/p)^(Init) - 1] /
[((1-p)/p)^(Target) - 1]
(where p is the win probability of each individual bet, Init is the
initial fortune, and Target is the target fortune).
This 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 simply Init/Target.]
The applet accepts the following keyboard inputs. (You may need to
"click" on the applet first.)
(This applet is a combination of my previous applets
Use the numbers '0' through '9' to set the animation speed level higher
Use 'r' to restart the simulation, or 'z' to zero the Win/Loss counts.
- Use 'g' to toggle between gambler's ruin mode, and full random
walk mode (starting at zero).
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, 0.5,
0.51, and 0.6.)
Use '+' and '-' to increase/decrease Init by $1 (and restart).
Or, use 'T' or 'H' or 'G' or 'F' to set Init to
$1 or $10 or $100 or $500, respectively, with Target equal to twice Init.
- Use 'A' to jump to $1 ahead of bankruptcy,
or 'B' to jump to $1 behind victory.
Applet by Jeffrey S. Rosenthal
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