Tennis Game

What this conditional probability interview question tests

This is an easy probability problem that probes your ability to reason about sequential outcomes and recursive probability. It's a classic warm-up at quant firms because it has a clean setup but requires you to think carefully about state transitions rather than just multiply probabilities together.

To solve problems like this, you identify all paths to a winning outcome from a given game state, account for the possibility of returning to that state, and set up an equation that captures the recursive structure. The key insight is recognizing when a situation repeats and leveraging symmetry or algebra to avoid infinite case enumeration.

• State-based probability and Markov chains
• Recursive equations and back-solving
• Win probability from arbitrary game positions