  The main systematics in cluster cosmology is the uncertainty in the
mass-observable relation. In this paper, we focus on the most direct cluster
observable in optical surveys, i.e. richness, and constrain the intrinsic
mass-richness (MR) relation of clusters in THE THREE HUNDRED hydrodynamic
simulations with two runs: GIZMO-SIMBA and GADGET-X. We find that modeling the
richness at fixed halo mass with a skewed Gaussian distribution yields a
simpler and smaller scatter compared to the commonly used log-normal
distribution. Additionally, we observe that baryon models have a significant
impact on the scatter, while exhibiting no influence on the mass dependence and
a slight effect on the amplitude in the MR relation. We select member galaxies
based on both stellar mass $M_\star$ and absolute magnitude $\mathscr{M}$. We
demonstrate that the MR relation obtained from these two selections can be
converted to each other by using the $M_\star-\mathscr{M}$ relation. Finally,
we provide a 7-parameter fitting result comprehensively capturing the
dependence of the MR relation on both stellar mass cutoff and redshift.
