Roll or Hold

You are presented with the following game: You repeatedly roll a fair $n-$sided with the values $0,1,\dots, n-1$ on the sides. After each roll, assuming it's non-zero, you have the option to end the game and receive a payout equal to the face showing on your die or to roll again. If you ever roll a $0$, the game ends and you receive no payout. Find the optimal strategy for this game. Report your expected payout under this strategy when $n = 8$.