The term Gambler's Ruin has had many meanings throughout the years. The most commonly used meaning is as follows:
Despite any initial amount of wealth, a gambler will always eventually go broke if he is consistently playing a game with a negative expected value
This is an obvious corollay to the law of large numbers, as a gamblers wealth will on average deviate by the expected value of the game.
Although there are older meanings of the term that are much interesting. The original meaning of gambler's ruin is that a gambler who always raises his bet to a fixed percentage of his wealth when he wins, but does not reduce his wealth when he loses, will always go broke eventually. Another meaning is that a gambler with finite wealth playing a game with 0 expected value, will always go broke eventually when playing against an opponent with infinite wealth.
These latter two meanings are interesting because they can be modeled by something known as a random walk. A random walk is one of the simplest forms of a stochastic process. This project aims to model several stochastic processes through real world examples such as mimicing a gambler's eventual despair.
A stochastic process is any random occurrence usually represented by a collection of random variables with a known probability distribution. It is a mathematical object in the field of probability theory, and has many real-world applications, especially in computer science and finance.
As said before, a random walk is one of the simplest stochastic process. The simplest form of a random walk is a simple symmetric random walk, which can easily be thought of as a fair-coin game.
Suppose you play a game where you win $1 if a fair coin (50-50 odds) lands on heads but have to pay $1 if it lands on tails. It is a fair game since the expected value of the game is $0.
The "walk" part of this model can be represented by a graph with the y-axis representing your wealth, and the x-axis representing the number of games you have played. As you play games, you always "walk" 1 unit right on the x-axis, and either 1 unit up or down depending on if you have won the game or not. The image below shows a simple symmetric random walk.
