I think this is it. Suppose there are C CooperateBots, D DefectBots, and X players who Cooperate with probability p. The expected utility of the probabilistic strategy is (proportional to) (p(C + pX) + 4(1-p)(C + pX))/(C + 4D + pX + 4(1-p)X). Then (he said, consulting his computer algebra system) if C/X < 1/3 then p = 1 (Cooperate), if C/X > 3 then p = 0 (Defect), and p assumes intermediate values if 1/3 < C/X < 3 (including 0.7239 if C/X = 1, as you mention).