Expected cards turned until an ace shows

A standard $52$-card deck is shuffled and you turn cards face up one at a time from the top. What is the expected number of cards you turn over up to and including the first ace?

$53/5 = 10.6$. The four aces split the $48$ other cards into five gaps that are equally large on average, so the gap before the first ace has mean $48/5$. Adding the ace itself gives $48/5+1=10.6$.