A little game with rolling a fair dice

Let's say that $k$ points is the place where rolling again and stopping have the same expected value. That means that $$k=\frac16(0)+\frac16(k+2)+\frac16(k+3)+\frac16(k+4)+\frac16(k+5)+\frac16(k+6)\\k=\frac56k+\frac{20}6\\\frac16k=\frac{20}6\\k=20$$

So you are correct.