Vlad is playing a dice game with Ulga. Vlad will roll $2$ six-sided dice, and if the sum of the dice is divisible by $3$, he will win $\$6$. If the sum is not divisible by $3$, he will lose $\$3$. **What is Vlad’s expected value of playing this game?** Round your answer to the nearest cent. $\$$ [[☃ input-number 1]]