You are invited to play the following game. You may repeatedly roll a fair six-sided die unless you roll a one, at which point you must stop, but you may also elect to stop at any point. Your score is the number on the nal roll. Consider the strategy of continuing to roll as long as possible until you roll a k or higher, for k {1, 2, 3, 4, 5, 6}. Which k maximizes the expected score?