Note on efficient correlated Monte-Carlo games

It is demonstrated through a simplified example that when playing a correlated Monte-Carlo game in a reference system (in general different from both the unperturbed and perturbed real systems) the optimum reference system (the one that yields a minimum variance of the correlated score) does not necessarily lie ''between'' the real ones, i.e. one must be careful in selecting the reference system and ''common sense'' may sometimes be misleading. (author)