Reroll for the sum but pay if it reaches seven

Roll a fair six-sided die. You may stop and collect the number shown in dollars. Or you may roll a second time: if the two rolls total $7$ or more, you must pay out an amount equal to your first roll; if the total is $6$ or less, you collect the total in dollars. With optimal decisions, what is your expected payout?

$47/12$ dollars. Rolling again after a $1$ is worth $\tfrac{19}{6}>1$ and after a $2$ is worth $\tfrac73>2$, but after a $3$ it is worth only $1$, and it gets worse for higher rolls. So reroll only on $1$ or $2$: $\tfrac16\left(\tfrac{19}{6}+\tfrac{7}{3}+3+4+5+6\right)=\tfrac{47}{12}$.