Expected longest piece after two random cuts

Two points are chosen independently and uniformly on a stick of length $1$, and the stick is cut at both, giving three pieces. Find the expected length of the largest piece.

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