Card value or a fixed 3.50 dollars

Ten face-down cards carry the values $1$ to $10$. You turn over one card chosen at random and then decide whether to be paid its face value in dollars or a guaranteed $\text{\char36}3.50$. What is this game worth?

$\text{\char36}5.95$. Take the $\text{\char36}3.50$ for cards $1$–$3$ and the face value for $4$–$10$. The value is $\tfrac{3\times3.5+(4+5+\dots+10)}{10}=\tfrac{10.5+49}{10}=5.95$.