Discrete Gaussian sampling on lattices is a fundamental problem in lattice-based cryptography . In this paper, we revisit the Markov chain Monte Carlo (MCMC)-based Metropolis-Hastings-Klein (MHK) algorithm proposed by Wang and Ling and study its complexity under the Geometric Series Assumption (GSA) when the given basis is BKZ-reduced . We give experimental evidence that the GSA is accurate in this context, and we give a very simple approximate formula for the complexity of the sampler that is accurate over a large range of parameters and easily computable. We apply our results to the dual attack on LWE of [24] and significantly improve the complexity estimates of the attack. Finally, we provide some results of independent interest on the Gaussian mass of a random q-ary lattices.