Animated gambler and money pile
Mood: focused
Money stack (1 coin = 1 unit)
A gambler repeatedly wins or loses one unit of money. Eventually, they are ruined — or reach a target.
Gambler's Ruin is a classic probability model: a player starts with finite capital and repeatedly wins or loses one unit. The game ends when the capital hits one of two absorbing states: ruin at 0 or success at target n.
The process is a finite Markov chain and a bounded random walk. It is memoryless because the next move depends only on the current capital. This makes it ideal for understanding absorption probabilities and expected hitting times.
Historically, it appears in early studies of random games in the 17th-18th centuries and later became a foundational example in modern stochastic processes and Markov chain theory.