The Gambler's Ruin
A Simulated Gambling
|Bernoulli Trials on the
"A customer of the Neptune
Palace Casino is betting at a Roulette table. He is following a gambling
strategy that is often used by prudent gamblers. He has dedicated a capital
of $200 to this session with the plan of not winning more than $20. He
invariably bets $1 on RED at each spin and plans to do continue playing
until one of the following three events occurs E1: He loses all of the
$200, E2: He is ahead by $20, E3: He has placed 2000 successive bets.
Problem: What is the probability that E2 takes place before E1 or E3?
A more general version of this
problem can be described as follows. The customer has a total capital
of H dollars at the start of the session and he proceeds as if at the Neptune
Palace Casino, hereafter referred to as the ``House'' has a total capital
of C dollars. He may also set the upper limit N for the number of times
he should bet. The event that he looses all of its initial capital is usually
referred to as the Gambler's ruin, the event that his capital grows
to C+H will be referred to as Breaking the Bank and we may call Saved
by the bell the event that he has placed N successive bets before loosing
his capital or winning the desired dollars.
The following Applet allows
you to experience the fate of this Gambler by simulating the whole gambling
session in a matter of seconds and plotting for you the successive rises
and falls of your capital during the whole duration of the game. It also
displays the maximum and minimum values attained by your capital during
the session and allows you to get precise information (by clicking at a
point of the histogram) of the amount of capital you had after that particular
bet. If the histogram extends beyond the window you may click and drag
in the field of view any portion you wish to explore.
Experiment with it by entering,
in the appropriate boxes, your choices for C and H , then click on |
and watch it fly!
Repeat this experiment as
often as you wish to gain an idea how you can maximize your chances of
Breaking the Bank by changing your betting strategy. Keep in mind
that given a fixed choice of C and H you may explore what happens if you bet
x dollars each time rather than just one dollar by entering C/x and
H/x in the C and H boxes.
For a view of the
exact probabilities of the Gambler Ruin CLICK