# 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?