By ancient, I mean anywhere from Roman to Medieval era armies, prior to the invention and widespread use of firearms. I'm fairly sure that armies rarely fought to the last man, but if that was a more common occurrence than routing, I'll be glad to be proven wrong.
Appreciate any answers I get. Thank you!
The vast majority of casualties in ancient battles came after one side broke and routed, most wouldn't die in actual fighting. There was no set ratio where suddenly people would turn and run, battles are about momentum and morale and an army, or portion of an army, might break and run at any time if it seemed like things weren't going their way, even if their section hadn't seen any fighting yet. Ancient battles were also chaotic affairs and it would have been incredibly difficult for soldiers to perceive exactly who was dying and in what numbers, anyway. Things like the death of a general might also cause a rout even if the numbers of the army were relatively intact.
While there might be a few examples of armies fighting to the last man, this was exceedingly rare and worth special note. For example, the army of one of the tribes Caesar fought, the Nervii, supposedly fought nearly to the last man (according to Plutarch something like 500 of 60,000 survived) but they are described as one of the fiercest and most warlike tribes, and an enemy fighting to the last man without running in open battle doesn't really appear anywhere else in the descriptions of his campaigns.