The question asks for a strategy ...... That, I think, is the strategy.

Let's say you roll the first time and get a 2. My strategy says roll again. When you do, the probabability of each number is obviously still equal to 1/6. Let's say you get a 3. My strategy is to roll again. On the third roll, the probabability of each number is still obviously equal to 1/6. Let's say you get a 5. My strategy is to stop.

Obviously there's always a chance of getting a 1, in which case you're

But it's all about having a strategy to maximise your expected score .....

I haven't worked out exactly what that expected score will be, but it's seems clear (a dangerous statement) that it'll be greater than 3.5