If I recall correctly, most of the losses by Indians were when the Bluecoats destoryed their camps. The soldiers had no problem killing old men, women and children. In fact I will stick my head in the noose and say that was the major factor that contributed to the Indians surrendering to the soldiers.
As I think about it I cannot name one man to man battle the Indians lost.
Opinion based on Dee Brown's book "How the west was lost"
GP