We considered the problem how to handle the exploding number of possibilities<br />
to choose atomic sites to be replaced by substituents in the supercell modeling<br />
of alloys, solid solutions, intermetallic compounds and doped materials. The<br />
number sometimes amounts to $\sim$ trillion, as we show in some selected<br />
examples, and hence straightforward manner to write out all the configurations<br />
to be sorted into group-theoretically equivalent clusters becomes not<br />
practically feasible due to the lack of the storage capacity even though there<br />
are several tools available to perform this straightforward method. We have<br />
developed a stochastic framework to avoid the shortage of capacity, implemented<br />
in a package of Python scripts, named as &#039;SHRY&#039;. The package provides several<br />
different methods to estimate the number of the symmetrically equivalent<br />
structures from the statistical estimates obtained in the stochastic<br />
operations. A prominent conclusion derived here is that the statistical<br />
variation of the number of equivalent structures obtained by sorting the<br />
limited number of sampling of substitutions is working as a promising measure<br />
to estimate the total number of equivalent structures for the whole<br />
distribution even without performing the whole sampling. The package also<br />
provides a way to get a set of representative structures of each equivalent set<br />
with much less consumptions of data storage. The package is capable to be used<br />
as a generator to provide structural models to any following ${\it ab\ initio}$<br />
analysis for doped materials like alloys.