TL;DR
Gambler's Ruin: A canonical quantitative trading interview question at intermediate difficulty. Commonly asked at Jane Street, Two Sigma, Citadel, SIG.
By Valenke Exam Prep Team·Last updated 2026-06-01
intermediateMarkov Chains & Random Walks
Gambler's Ruin
Asked at: Jane Street, Two Sigma, Citadel, SIG
Problem
A gambler starts with dollars and plays a fair coin-flipping game: heads wins \$1, tails loses \$1. The gambler plays until going broke (reaching \$0) or reaching \$N.
What is the probability of ruin (reaching \$0 before \$N)?
What if the coin is biased with ?
Related concepts
Ready to practice for the Valenke Finance Exam?
Adaptive practice powered by Item Response Theory targets your weak areas. Start with 3 free sessions.
Start free practice →