We study the problem of distinguishing between two independent samples [EQUATION], [EQUATION] of a binomial random graph G(n, p) by first order (FO) sentences. Shelah and Spencer proved that, for a constant α ∈ (0, 1), G(n, n−-α) obeys FO zero-one law if and only if α is irrational. Therefore, for irrational α ∈ (0, 1), any fixed FO sentence does not distinguish between [EQUATION] with asymptotical probability 1 (w.h.p.) as n → ∞. We show that the minimum quantifier depth kα of a FO sentence [EQUATION] distinguishing between [EQUATION] depends on how closely α can be approximated by rationals: