Computer-aided modeling is a systematic approach to grasp the physics of macromolecules, but it remains essential to know when to trust the results and when not. For a polymer star, we consider three approaches: (i) Molecular Dynamics (MD) simulations and implementing a coarse-grained model, (ii) the self-consistent field approach based on a mean-field approximation and implementing the lattice model due to Scheutjens and Fleer (SF-SCF) and (iii) novel hybrid Monte Carlo self-consistent field (MC-SCF) method, which combines a coarse-grained model driven by a Monte Carlo method and a mean-field representation driven by SF-SCF. We compare the performance of these approaches under a wide range of solvent qualities. The MD approach is formally the most exact but suffers from reasonable convergence. The mean-field approach works similarly in all solvent qualities but is quantitatively least accurate. The MC-SCF hybrid allows us to combine the benefits of the simulation route and the effective performance of SCF. We consider the center-to-end distance Rce, the radius of gyration Rg2 of the star and the polymer density profiles φ(r) of polymer-segments in it. All three methods show a good qualitative agreement one to another. The MC-SCF method is in good agreement with the scaling predictions in the whole range of solvent quality values showing that it grasps the essential physics while remaining computationally in bounds.