4. In a square with side length 3, randomly select $n$ points, among which, the points with a distance less than 1 from the vertices of the square are $m$. Then the experimental value of $\pi$ obtained by random simulation is $\qquad$ .
4. $\frac{9 m}{n}$.

According to the formula for calculating geometric probability, we get
$$
\frac{4 \times \frac{\pi}{4}}{3^{2}}=\frac{m}{n} \Rightarrow \pi=\frac{9 m}{n} .
$$