We have estimated the potential curves of the Mg(3s3p pi). He[(3)Pi], Mg(3p pi 3p pi). He[(3)Sigma(-)], Mg+(3s). He[(2)Sigma(+)], Mg+(3p pi). He[(2)Pi], and Mg+2(2p(6)). He[(1)Sigma(+)] van der Waals states by means of ab initio calculations. Similar to the analogous doubly excited states of MgNe, MgAr, and MgKr, the Mg(3p pi 3p pi). He[(3)Sigma(-)] state is found to be unusually strongly bound, D-e=2386 cm(-1), a bond strength which is an astounding 165 times that of the singly excited Mg(3s3p pi). He[(3)Pi] state and 35 times that of the Mg+(3s). He ion. The strong bonding is attributed primarily to the lack of a Mg(3s) electron, so that all the attractive forces can extend to smaller internuclear distances because there is no Mg(3s sigma)/He(1s sigma) repulsion. In fact, the Mg(3p pi 3p pi). He[(3)Sigma(-)], Mg+(3p pi). He[(2)Pi], and Mg+2(2p(6)). He[(1)Sigma(+)] states have quite similar bond energies and bond lengths, indicating that for RG=He, the primary attractive force in all these states is the ion/induced-dipole interaction of the "Mg+2/He" core. This is consistent with the fact that the bond energy of the Mg(3p pi 3p pi). He[(3)Sigma(-)] state is more than four times greater than that of the Mg(3p pi 3p pi). Ne[(3)Sigma(-)] state, where there is substantial Mg(3p pi)/Ne(2p pi) repulsion not present in the Mg(3p pi 3p pi). He[(3)Sigma(-)] state.