You have a six sided dice. You roll the dice and decide if you want to stop and keep the current value as your result. If not you try again. You can at most throw the dice n times. If you throw it n times you have to keep the last result.
What is the optimal strategy to get the highest expected result? How to proof that this is the optimal strategy?
Example (n=3): Strategy is "Stop if you have a 5 or better". Applying this strategy you would throw 3 5 and have a result of 5. Or throw 4 1 2 and have a result of 2 as no more throws are available.
