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

The answer is 0.3. Approach: Your wealth is a martingale.

MediumStochastic ProcessesAcceptance 72%

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.

Answer

Show the final answer

The answer is 0.3. Sign in free for the full worked solution and to check your own answer.