The Drunk Trader's Ruin

What this gambler's ruin probability question tests

This is a medium-difficulty probability question testing your ability to set up and solve a recurrence relation for a classic random walk problem. It appears frequently in quant interviews because it combines foundational probability reasoning with a touch of algebra, and the closed-form answer is elegant and surprising to many candidates.

The core skill being tested is whether you can translate a sequential decision process (coin flips, running balance, stopping conditions) into a recursive probability equation, then solve it systematically. Strong candidates recognize the symmetry of a fair coin and use boundary conditions to pin down the solution. The problem also rewards intuition: understanding why the answer depends only on the ratio of starting position to target, not on the individual dollar amounts.

• Recurrence relations in probability
• Boundary conditions and base cases
• Fair games and martingale intuition
• Difference equations over state spaces