8-Sided Dice

Lewis is playing a game with a fair $8-$sided die. If Lewis rolls any value from $1 - 7$, he adds that value to his total and can choose to roll again. If he rolls an $8$, he loses all of his money and the game ends. If Lewis plays optimally then there is a value $v$ such that once he has a total of at least $v$ he should stop rolling. What is $v$?