Average card value when hearts count double

Give each card in a standard 52-card deck its rank as a value (ace $=1$, numbers at face value, jack $=11$, queen $=12$, king $=13$), except that every heart is worth twice its rank (so the ace of hearts is worth $2$). If one card is drawn uniformly at random, what is its expected value?

$\tfrac{35}{4}$. Each suit's ranks sum to $91$, and hearts count twice, so the deck totals $5\times 91=455$. Dividing by $52$ cards gives $8.75$.