  We consider generalizations of the classical secretary problem, also known as
the problem of optimal choice, to posets where the only information we have is
the size of the poset and the number of maximal elements. We show that, given
this information, there is an algorithm that is successful with probability at
least $\frac{1}{e}$. We conjecture that if there are $k$ maximal elements and
$k \geq 2$ then this can be improved to $\sqrt[k-1]{\frac{1}{k}}$, and prove
this conjecture for posets of width $k$. We also show that no better bound is
possible.
