Die game that continues on high rolls

In a casino game you roll a fair six-sided die and bank the number shown. If the roll is $4$, $5$ or $6$ you roll again and keep adding; the first time you roll $1$, $2$ or $3$, that value is added too and the game ends, paying your total. What is the fair price of the game?

$7$. Let $x$ be the value. Half the time you roll a low number (average $2$) and stop; half the time you bank a high number (average $5$) and face the same game again. So $x=\tfrac12\cdot2+\tfrac12(5+x)$, giving $x=7$.