  The study of fluctuations of particle multiplicities in relativistic
heavy-ion reactions has drawn much attention in recent years, because they have
been proposed as a probe for underlying dynamics and possible formation of
quark-gluon plasma. Thus, it is of uttermost importance to describe the
baseline of statistical fluctuations in the hadron gas phase in a correct way.
We have performed a comprehensive study of multiplicity distributions in the
full ideal hadron-resonance gas in different ensembles, namely grand-canonical,
canonical and microcanonical, using two different methods: asymptotic
expansions and full Monte Carlo simulations. The method based on asymptotic
expansion allows a quick numerical calculation of dispersions in the hadron gas
with three conserved charges at primary hadron level, while the Monte-Carlo
simulation is suitable to study the effect of resonance decays. Even though
mean multiplicities converge to the same values, major differences in
fluctuations for these ensembles persist in the thermodynamic limit, as pointed
out in recent studies. We observe that this difference is ultimately related to
the non-additivity of the variances in the ensembles with exact conservation of
extensive quantities.
