We study the asymptotic property of simple estimator of the parameter of a Skew Brownian motion when one observes its positions on a fixed grid — or equivalently of a simple random walk with a bias at 0. This estimator, nothing more than the Maximum Likelihood Estimator, is based only on the number of passages of the random walk at 0. It is very simple to set up, is consistent and satisfies the local asymptotic mixed normality. We believe that this simplified framework is helpful to understand the asymptotic behavior of the maximum likelihood of the SBM observed at discrete time which is studied in a companion paper.