Standard deviation of the sum of two cards labelled 0 to 4

There are two identical decks, each consisting of five cards marked $0,1,2,3,4$. One card is drawn at random from each deck and the two values are added. What is the standard deviation of the total?

$2$. Each card is uniform on $\{0,\dots,4\}$ with mean $2$ and variance $\tfrac{0+1+4+9+16}{5}-4=2$. The draws are independent, so the total has variance $4$ and standard deviation $2$.