Which battle is considered the biggest Native American victory against the American military?

The Battle of the Wabash or St. Clair's Defeat took place on November 4, 1791 during the battle for the Old Northwest in what is now Ohio. It pitted the US Army against the Western Confederacy of American Indians. The opposing forces were roughly equal, 920 Americans against 1,000 Native Americans. Only 24 Americans escaped unharmed. One quarter of the then current US Army had been wiped out. The American casualty rate was 97.4%, with 632 killed outright and 264 wounded. Many of the wounded were executed by being burned alive over the next few days. Nearly all of the 200 camp followers had also been slaughtered. Native casualties have been estimated at 61, with 21 killed. It was the largest victory won by the Native American Indians and has been called the "most decisive defeat in the history of the American military."

The Battle of Little Big Horn (1876) saw the destruction of a portion of General Custer's command with 268 killed and 49 wounded. An estimated 41 Native Americans were killed and around 160 wounded.

The Battle of White Bird Canyon (1877) took place during the Nez Perce War. Americans suffered 34 killed and 4 wounded. The Nez Perce suffered 3 wounded.

The Fettreman Fight or Massacre took place during Red Cloud's War (1866-1868). 81 American soldiers were wiped out during the battle. The Northern Arapaho, Northern Cheyenne, and Sioux force consisted of over 1,000 warriors. It's estimated that 13 to 60 were killed. An indeterminate amount were wounded.