We present a Monte-Carlo calculation of the microcanonical ensemble of the of the ideal hadron-resonance gas including all known states up to a mass of about 1.8 GeV and full quantum statistics. The microcanonical average multiplicities of the various hadron species are found to converge to the canonical ones for moderately low values of the total energy, around 8 GeV, thus bearing out previous analyses of hadronic multiplicities in the canonical ensemble. The main numerical computing method is an importance sampling Monte-Carlo algorithm using the product of Poisson distributions to generate multi-hadronic channels. It is shown that the use of this multi-Poisson distribution allows an efficient and fast computation of averages, which can be further improved in the limit of very large clusters. We have also studied the fitness of a previously proposed computing method, based on the Metropolis Monte-Carlo algorithm, for event generation in the statistical hadronization model. We find that the use of the multi-Poisson distribution as proposal matrix dramatically improves the computation performance. However, due to the correlation of subsequent samples, this method proves to be generally less robust and effective than the importance sampling method.

23 pages, 21 figures, style files attached. Published version, minor corrections