  Using combined strong coupling and hopping parameter expansions, we derive an
effective three-dimensional theory from thermal lattice QCD with heavy Wilson
quarks. The theory depends on traced Polyakov loops only and correctly reflects
the centre symmetry of the pure gauge sector as well as its breaking by finite
mass quarks. It is valid up to certain orders in the lattice gauge coupling and
hopping parameter, which can be systematically improved. To its current order
it is controlled for lattices up to N_\tau\sim 6 at finite temperature. For
nonzero quark chemical potentials, the effective theory has a fermionic sign
problem which is mild enough to carry out simulations up to large chemical
potentials. Moreover, by going to a flux representation of the partition
function, the sign problem can be solved. As an application, we determine the
deconfinement transition and its critical end point as a function of quark mass
and all chemical potentials.
