I was recently asked this question in an interview. I was able to solve it for two rolls but could not solve it for three or more rolls.
You toss a die and after seeing the outcome, and you are told that you could toss it one more time if you want, with your aim beings to maximize the expected outcome. Under what circumstances would you throw the die a second time? Similarly, what if you are given three trials? If you get 1000 such trials, what would it be?
Just to be clear if you choose to throw the second die then the number on the first die will be discarded and the number on the second die would be taken into account. So when we solve for two die then it comes out that wee should roll the second die only when the number on the first die was 1,2 or 3