  Approximate numerical methods are one of the most used strategies to extract
information from many-interacting-agents systems. In particular, numerical
approximations are of extended use to deal with epidemic, ecological and
biological models, since unbiased methods like the Gillespie algorithm can
become unpractical due to high CPU time usage required. However, the use of
approximations has been debated and there is no clear consensus about whether
unbiased methods or biased approach is the best option. In this work, we derive
scaling relations for the errors in approximations based on binomial
extractions. This finding allows us to build rules to compute the optimal
values of both the discretization time and number of realizations needed to
compute averages with the biased method with a target precision and minimum
CPU-time usage. Furthermore, we also present another rule to discern whether
the unbiased method or biased approach is more efficient. Ultimately, we will
show that the choice of the method should depend on the desired precision for
the estimation of averages.
