  We derive three-dimensional, Z(N)-symmetric effective actions in terms of
Polyakov loops by means of strong coupling expansions, starting from thermal
SU(N) Yang-Mills theory in four dimensions on the lattice. An earlier action in
the literature, corresponding to the (spatial) strong coupling limit, is thus
extended by several higher orders, as well as by additional interaction terms.
We provide analytic mappings between the couplings of the effective theory and
the parameters $N_\tau,\beta$ of the original thermal lattice theory, which can
be systematically improved. We then investigate the deconfinement transition
for the cases SU(2) and SU(3) by means of Monte Carlo simulations of the
effective theory. Our effective models correctly reproduce second order 3d
Ising and first order phase transitions, respectively. Furthermore, we
calculate the critical couplings $\beta_c(N_\tau)$ and find agreement with
results from simulations of the 4d theory at the few percent level for
$N_\tau=4-16$.
