Consider a random word $$X^n=(X_1,\ldots ,X_n)$$ in an alphabet consisting of 4 letters, with the letters viewed either as A, U, G and C (i.e., nucleotides RNA sequence) or $$\alpha $$ , $$\bar{\alpha }$$ $$\beta $$\bar{\beta generators free group $$\langle \alpha ,\beta \rangle their inverses). We show that expected fraction $$\rho (n)$$ unpaired bases optimal secondary structure (with only Wa...