In Risk Theory Beard, Pentikanen and Pesonen (1969) mention a method of assessing number of samples needed for Monte Carlo simulation as
$$ \sigma = \sqrt{\frac{p(1-p)}{s}} \leq \frac{1}{2} \sqrt{ \frac{1}{s}} $$
where $F(x) = p$, i.e. it is a probability of observing some value $x$ and $s$ is a number of samples. This shows us that with 99% confidence value we can expect that values observed in simulation study will lie $\pm 2.576 \sigma$ from $p$'s. This is similar to simulation standard error estimation based on observed variance mentioned by Aksakal. The authors seem to suggest that the formula can be used before the simulation to assess number of samples needed ($s$) to obtain simulated results with some precision of interest.
How good is this approximation?