Here we present the results of our experimental and computational studies on RbBi2 and CsBi2, concentrated on the effects of strong SOC on superconducting properties. We show that in both compounds superconductivity emerges from the Bi4 2-pyrochlore lattice and that the relativistic effects play a complex role in stability and properties of the two phases. We found that strong SOC is crucial for the stability of charged Bi pyrochlore network and discuss the implications of this fact for the search for new heavy element-bearing superconducting materials. Figure . Crystal structure of the cubic Laves phases ABi2 (A = K, Rb, Cs). Bi atoms (drawn in purple) form a vertex-sharing tetrahedral (pyrochlore) lattice with voids filled with alkali atoms (green).