This paper proposes a new fingerprinting decoder based on the Markov Chain Monte Carlo (MCMC) method. A Gibbs sampler generates groups of users according to the poste- rior probability that these users could have forged the sequence extracted from the pirated content. The marginal probability that a given user pertains to the collusion is then estimated by a Monte Carlo method. The users having the biggest empirical marginal probabilities are accused. This MCMC method can decode any type of fingerprinting codes. This paper is in the spirit of the 'Learn and Match' decoding strategy: it assumes that the collusion attack belongs to a family of models. The Expectation-Maximization algorithm estimates the parameters of the collusion model from the extracted se- quence. This part of the algorithm is described for the binary Tardos code and with the exploitation of the soft outputs of the watermarking decoder. The experimental body considers some extreme setups where the fingerprinting code lengths are very small. It reveals that the weak link of our approach is the estimation part. This is a clear warning to the 'Learn and Match' decoding strategy.