Summary: N. D. Mermin [“Bringing home the atomic word: Quantum mysteries for anybody”, Am. J. Phys. 49, 940–943 (1981)] described a simple device to explain A. Einstein, B. Podolsky and N. Rosen (EPR) [“Can quantum-mechanical desription of physical reality be considered complete?” Phys. Rev., II. Ser. 47, 777–780 (1935; Zbl 0012.04201)] correlations. This device was studied by means of a class of probabilistic (Mermin) automata in (*) [C. S. Calude, E. Calude and S. Svozil, “Quantum correlations conundrum: An automaton-theoretic approach”, in: G. Păun, (ed.), Recent Topics in Mathematical and Computational Linguistic, Romanian Academy Publishing Company, Bucharest, 2000 (in press)]. In [C. S. Calude, E. Calude and K. Svozil, “Computational complementarity for probabilistic automata”, in: C. Martín-Vide (ed.) et al., Where mathematics, computer science, linguistics and biology meet. Essays in honour of Gheorghe Păun. Dordrecht: Kluwer Academic Publishers. 99–113 (2001; Zbl 1052.68070)] the authors show that every deterministic automaton simulating with confidence \(1/2\) a probabilistic Mermin automaton features a classical behaviour. Is the above result true when the simulation is done at higher levels of confidence? To answer this question we study the distribution of two computational complementarity principles for two classes of deterministic automata which mimic the behaviour of Mermin’s device with confidence in the intervals \((1/2,11/16]\) and \((11/16,7/8]\). Since the class of automata to be studied is large, it contains \(9^{18}\approx 150\cdot 10^{15}\) elements, we use simulation techniques. We show that, statistically, at any level of confidence \(\alpha\in(1/2,11/6]\), the class of deterministic automata simulating Mermin probabilistic automata displays less correlations than typical deterministic automata with 9 states and 7 outputs, but at higher levels of confidence \(\alpha\in(11/16,7/8]\), when the simulation is more accurate, deterministic automata simulating Mermin probabilistic automata display more correlations than typical deterministic automata with 9 states and 2 outputs, but at this level the difference seems to be less significant. In the last case, EPR correlations established in (*) for Mermin probabilistic automata correspond to computational complementarity of the deterministic automata simulating Mermin probabilistic automata.