MediumStochastic Processes

Gambler’s Ruin

Jane StreetSIG / Susquehanna

You start with $30 and bet$ 1 on a fair coin each round, stopping when you reach $0 or$ 100. What is the probability you reach $100 before going broke?

Approach

Your wealth is a martingale.

For a fair game the hitting probability is linear in your starting wealth.