Gambler's Ruin Calculator

Amount of money player A starts with

Combined capital of both players (Player B starts with 3)

Probability that Player A wins $1 each round (Player B wins with probability 0.500)

Problem Setup

Two players with initial capitals of $i$ and $m-i$ dollars play a sequence of games. Each game, Player A wins $1 with probability $p$or loses $1 with probability $q = 1-p$. The game ends when one player has all the money.

Key Questions

• What is the probability that Player A goes bankrupt?
• How long will the game last on average?
• Is the game fair or does one player have an advantage?

Applications

• Stock market analysis and portfolio management
• Insurance company reserve modeling
• Casino game analysis and betting strategies
• Population genetics (random drift)

Fair vs Unfair Games

• Fair game (p = 0.5): Ruin probability depends only on initial wealth ratio
• Favorable (p > 0.5): Player A has lower ruin probability
• Unfavorable (p < 0.5): Player A likely to go bankrupt