  We provide completely effective error estimates for Stirling numbers of the
first and second kind, denoted by $s(n,m)$ and $S(n,m)$, respectively. These
bounds are useful for values of $m \geq n - O(\sqrt{n})$. An application of our
Theorem 5 yields, for example, \[ s(10^{12},\ 10^{12}-2\times
10^6)/10^{35664464} \in [ 1.87669, 1.876982 ], \] \[ S(10^{12},\
10^{12}-2\times 10^6)/10^{35664463} \in [ 1.30121, 1.306975 ]. \] The bounds
are obtained via Chen-Stein Poisson approximation, using an interpretation of
Stirling numbers as the number of ways of placing non-attacking rooks on a
chess board.
  As a corollary to Theorem 5, summarized in Proposition 1, we obtain two
simple and explicit asymptotic formulas, one for each of $s(n,m)$ and $S(n,m)$,
for the parametrization $m = n - t\, n^a$, $0 \leq a \leq \frac{1}{2}.$ These
asymptotic formulas agree with the ones originally observed by Moser and Wyman
in the range $0<a<\frac{1}{2}$, and they connect with a recent asymptotic
expansion by Louchard for $\frac{1}{2}<a < 1$, hence filling the gap at $a =
\frac{1}{2}$.
  We also provide a generalization applicable to rook and file numbers.
