  Effective Polyakov loop theories are a useful tool for an investigation of
pure Yang-Mills theory and full QCD. A systematic derivation of the effective
action can be done in a spatial strong coupling expansion. Quite accurate
predictions for the deconfinement phase transition of Yang-Mills theory have
been obtained in this approach. Besides the critical couplings, further
observables can be measured in the effective theory. These provide additional
tests for the reliability of the strong coupling approach and the truncation of
the effective action. In this contribution we will present recent results for
the free energy of the static quark-antiquark pair and the equation of state.
