  A vertex $x$ in a tournament $T$ is called a king if for every vertex $y$ of
$T$ there is a directed path from $x$ to $y$ of length at most 2. It is not
hard to show that every vertex of maximum out-degree in a tournament is a king.
However, tournaments may have kings which are not vertices of maximum
out-degree. A binary inquiry asks for the orientation of the edge between a
pair of vertices and receives the answer. The cost of finding a king in an
unknown tournament is the number of binary inquiries required to detect a king.
For the cost of finding a king in a tournament, in the worst case, Shen, Sheng
and Wu (SIAM J. Comput., 2003) proved a lower and upper bounds of
$\Omega(n^{4/3})$ and $O(n^{3/2})$, respectively. In contrast to their result,
we prove that the cost of finding a vertex of maximum out-degree is ${n \choose
2} -O(n)$ in the worst case.
