Numerical solutions for patterns statistics on Markov chains. We propose here a review of the methods available to compute pattern statistics on texts generated by a Markov source. Theoretical, but also numerical aspects are detailed for a wide range of techniques (exact, Gaussian, large deviations, binomial and compound Poisson). The SPatt package (Statistics for Pattern, free software available at implementing all these methods is then used to compare all these approaches in terms of computational time and reliability in the most complete pattern statistics benchmark available at the present time.