The ridge signal, which is long-ranged in rapidity, in di-hadron correlations in high-multiplicity p-p and p-A collisions opened up a whole new research area in high-energy QCD. Although the ridge had been observed in A-A collisions and interpreted as a result of the radial flow of quark-gluon plasma, it had not appeared until recently in the data of small collision systems such as p p and p A, nor had it been predicted theoretically or seen in event generators. There are two competing approaches that attempt to explain the systematics of the di-hadron ridge signal: hydrodynamics and gluon saturation physics (color glass condensate/glasma). In this work, we present predictions for the transverse momentum and rapidity dependence of the three-particle correlation function within gluon saturation physics. Tri-hadron correlations can be measured, and the data can possibly rule out one of the two alternative approaches.