Former US Army Captain Nathan Algren, a bitter alcoholic traumatized by the atrocities he committed during the American Indian Wars, is approached by his former commanding officer Colonel Bagley to train the newly formed Imperial Japanese Army for Japanese businessman Omura, who intends to use the army to suppress a samurai-headed rebellion against Japan's new Emperor. Despite his hatred of Bagley for his role in the Indian Wars, an impoverished Algren takes the job for the money, and is accompanied to Japan by his old friend Sergeant Zebulon Gant and Simon Graham, a British translator knowledgeable about the Samurai.
Algren finds the Imperial soldiers are poorly-trained, conscripted peasants without knowledge of firearms. Before training is completed, the army is ordered to defend a railroad owned by Omura under threat from the samurai. The battle is a disaster; the soldiers panic and are swiftly routed, and Gant is killed. Algren kills several Samurai before he is captured, impressing Samurai leader Katsumoto, who orders that Algren be spared. Algren is taken to the Samurai's village to live among Katsumoto's family. Over time, Algren overcomes his alcoholism and guilt over his past sins, learns the Japanese language and culture, and develops sympathy for the Samurai, who are angry that the spread of modern technology has eroded traditional feudalism and the status and power of the Samurai. Algren becomes close with Taka, Katsumoto's sister and the widow of a Samurai Algren killed.
Omura sends Ninja to assassinate Katsumoto. In the ensuing battle, Algren helps defend Katsumoto's family, earning the Samurai's respect. Katsumoto requests a meeting with Emperor Meiji and is given safe passage to Tokyo, bringing Algren with the intent to release him. Upon arriving in Tokyo, Algren finds the Imperial Army is now a well-trained and equipped fighting force, while Katsumoto, to his dismay, discovers that the Emperor is essentially a puppet of Omura. At a government meeting, Omura orders Katsumoto's arrest for carrying a sword in public and asks him to commit seppuku to redeem his honor. When Algren refuses Omura's offer to lead the new army to crush the rebels, Omura orders him killed as well. Surviving the assassination attempt, Algren and a group of samurai free Katsumoto, whose son Nobutada sacrifices himself to let them escape.
As the Imperial Army marches against the Samurai, a grieving Katsumoto contemplates seppuku, but Algren convinces him to fight until the end, and joins the Samurai in battle. Citing the Battle of Thermopylae, the Samurai use the Imperial Army's overconfidence to lure their soldiers into a trap and deprives them of artillery support. The ensuing mĂŞlĂŠe battle inflicts massive casualties and forces the Imperial soldiers to retreat. Knowing that Imperial reinforcements are coming and defeat is inevitable, Katsumoto orders a suicidal charge on horseback into machine-gun fire. In the chaos, Algren kills Bagley. Moved by the sight of the dying samurai, the Imperial captain, previously trained by Algren, disobeys Omura and orders the Army's guns to cease fire. A mortally-wounded Katsumoto commits seppuku with Algren's help, as the Imperial Army kneels in respect for the dead.
Days later, as trade negotiations conclude, Algren, though injured, arrives and interrupts the proceedings. He presents the Emperor with Katsumoto's sword and asks him to remember the traditions for which Katsumoto died. The Emperor realizes that while Japan must increase in foreign interaction, it also should remember its own culture and history. He rejects the trade offer and confiscates Omura's property to be given to the poor. Algren returns to the village to Taka, Graham concluding that Algren had at last found a measure of peace with his life.

Question: What war did Captain Algren fight in?
Answer: The American Indian Wars