Abstract:
Gambler’s ruin is a concept in Statistics. That is, regardless of their betting
strategy, a gambler playing a game with negative anticipated value will
eventually go bankrupt. A typical roulette wheel in the U.S. contains a loose
ball and 38 slots: 18 for red numbers, 18 for black numbers, and 2 for green
numbers. Assume we bet $1 that a red number would appear on the next spin
of the wheel. This indicates that if red appears, we earn $1; if black or green
appears, we lose $1. In view of those investigations, we propose a dynamical
system model which gives an idea of probability on eventual win or loss. In
this task we developed a tree diagram to model this situation and obtained a
second order dynamical system in the standard format. We considered the
case in which we arrive at the casino with $n and continue betting $1 on red
until we get a total of $0 or $m, m>n. A simple roulette scenario was studied
and calculated PL(n) which is the probability of leaving the casino with no
money. To find PL(n) we need PL(1) and made trial-and-error guesses for the
correct value of PL(1). This study on a simpler roulette scenario is useful to
study any kind of roulette. Dynamical system gives us an idea of probability
of eventual win from which one can check whether it is possible to go home
in a happy mode!