The polymerization of amino acids under anhydrous prebiotic conditions was first studied several decades ago. Here we use a stochastic model stressing the relevant role of the polarity of amino acids in the formation of oligopeptides in a prebiotic milieu. Our goal is to outline the predominance of co-polypeptides over homo-polypeptides, resulting not only from the randomness, but also from polarity properties of amino acids. Our results conclude that there was a higher probability of the formation of co-polypeptides than of homo-polymers. Besides, we may hypothesize that the former would have a more ample spectrum of possible chemical functions than homo-polypeptides.