Have you verified whether that is actually the case for DoC, or have you only read up about base BtS? Because DoC uses the Advanced Combat Odds component from BUG. While I have not reviewed it and cannot vouch for its mathematical correctness, it is at least capable of printing output that lists the probabilities of winning a battle with specific numbers of hitpoints left. To me that suggests that ACO does at least not just do the naive approximation. If you want to look into the code I would be very happy about that of course.