This paper tries to quantify the inequalities that are produced when you select a group of people by means of a draw in witch a pair of letters at random is obtained and the posts are assigned in alphabetical order. The distribution of the firsts letters of surnames is nonuniform, hence this scheme does not guarantee that all participants have the same probability of being selected. This is a well known fact but, as far as we know, those probabilities have not being computed and this kind of draws are still used.
To compute each probability of being selected we simulate many draws of this kind. We analyze the error of the results and we check that those differences arise and the inequalities are significant.
Finally we propose an alternative fair scheme in which all participants have the same probability of being selected.