  The strong coupling limit ($\beta_{gauge}=0$) of lattice QCD with staggered
fermions enjoys the same non-perturbative properties as continuum QCD, namely
confinement and chiral symmetry breaking. In contrast to the situation at weak
coupling, the sign problem which appears at finite density can be brought under
control for a determination of the full (mu,T) phase diagram by Monte Carlo
simulations. Further difficulties with efficiency and ergodicity of the
simulations, especially at the strongly first-order, low-T, finite-mu
transition, are addressed respectively with a worm algorithm and multicanonical
sampling. Our simulations reveal sizeable corrections to the old results of
Karsch and Muetter. Comparison with analytic mean-field determinations of the
phase diagram shows discrepancies of O(10) in the location of the QCD critical
point.
