Average longest piece of a stick cut twice

A stick of unit length is broken at two points chosen independently and uniformly along its length, producing three pieces. What is the expected length of the longest piece?

$11/18$. The three lengths are uniform on the simplex, and for $n$ such spacings the expected largest is $\tfrac1n\sum_{k=1}^n\tfrac1k$. With $n=3$ this is $\tfrac13\left(1+\tfrac12+\tfrac13\right)=\tfrac{11}{18}\approx0.611$.