Average number of closed groups from a name draw

At a party, each of $50$ guests drops their name into a hat, and then each guest in turn draws one name. Each guest is linked to the person whose name they drew, so the guests split into closed loops (someone who draws their own name forms a group of one; if A draws B, B draws C and C draws A, then A, B, C form one group). What is the expected number of groups? Give your answer to one decimal place.

About $4.5$. The draw is a uniformly random permutation of $50$ people and groups are its cycles. The expected number of cycles of a random permutation of size $n$ is the harmonic number $H_n$, and $H_{50}\approx4.499$.