Using first-principles methods, we study the magnetic and electronic properties of three different spin configurations of the L1 0 phase of FePt and MnPt alloys. It is found that MnPt and FePt may be approximately considered as magnetic antipodes with opposite ferromagnetic ͑FM͒-antiferromagnetic ͑AFM͒ and in-plane/ out-of-plane magnetocrystalline anisotropy ͑MCA͒ relationships. In MnPt, the most stable phase is the AFM configuration with AFM chessboard spin coupling in the ͑001͒ plane, FM spin coupling between ͑001͒ planes, and all spin directions aligned in the ͑001͒ plane. Whereas in FePt, the most stable is the FM configuration with all spin directions aligned perpendicular to ͑001͒ plane. The out-of-plane MCA of MnPt is more than an order of magnitude less ͑ϳ0.1 meV͒ than that of FePt ͑ϳ2.9 meV͒ in their corresponding magnetic ground states. Our calculations indicate that an AFM state can be achieved in FePt by a small variation in tetragonality ratio ͑from 0.98 to 0.94͒. A pseudogap is observed at the Fermi energy for MnPt and just below the Fermi energy for FePt for the chessboard AFM model. This pseudogap may explain the ground-state magnetic configuration of MnPt.