Problem 3.3 • Roll dice with re-roll option - conditional expectation
1. Roll two dice
2. You may re-roll the lower die (once)
3. Score = sum of both dice
4. Optimal strategy: re-roll if lower die ≤ 3
Optimal strategy: Re-roll if the lower die shows 1, 2, or 3 (since E[die] = 3.5 > any of those).