Heavy ion collision experiments reveal that, at temperatures of the order of 200 MeV, hadronic matter turns into a nearly inviscid, strongly coupled plasma. While perturbative QCD calculations are not reliable in this regime, it is expected that some thermodynamic properties of the plasma can be worked out using techniques based on the conjectured duality between gauge and string theories. In particular, these computations undergo dramatic simplifications when the rank of the gauge group is taken to infinity. In turn, the relevance of this limit for the physical case of QCD with N=3 colors can be investigated via computer simulations based on the lattice formulation of QCD. In this talk, I shall present some lattice results for equilibrium thermodynamic observables in SU(N) gauge theories with different numbers of colors: the results reveal a very mild dependence on N, and are compared with predictions derived from holographic models developed in string theory.