Solve a Three-Roll Optimal Stopping Game
Company: Worldquant
Role: Data Scientist
Category: Statistics & Math
Difficulty: medium
Interview Round: Technical Screen
# Solve a Three-Roll Optimal Stopping Game
A fair six-sided die may be rolled at most three times. After each of the first two rolls, stop and receive that face value or continue and forfeit it; after the third, accept it. Find the fair entry price.
### Constraints & Assumptions
- Entry is paid once and does not affect later stopping choices.
### Clarifying Questions to Ask
- Is the objective expected value?
- Must the next result be accepted after continuing from the last choice?
### What a Strong Answer Covers
- Backward induction, thresholds with two and three opportunities, and the exact expectation.
### Follow-up Questions
- How does the policy change for a biased die?
- What is the recurrence for `r` rolls?
Overview: A fair six-sided die may be rolled at most three times. Explain the assumptions and derivation clearly, check edge cases, and show how the result changes when those assumptions no longer hold.
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