One-Dimensional Random Walk/Examples/Gambling Game

Example of One-Dimensional Random Walk

Consider the gambling game in which a player with initial capital $k$ wins $1$ unit with probability $p$ and loses $1$ unit with probability $1 - p$.

This is a one-dimensional random walk with absorbing state $k = 0$.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): random walk
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): random walk