Battle of Gaugamela: Alexander the Great leads the combined Greek forces to defeat Darius III of Persia. Contemporary accounts put the size of the Greek army at 47,000, which is respectable, but the size of the Persian army is estimated at anywhere between 250,000 and 1,000,000.
It was probably lower simply because of the difficulties involved with managing and feeding such a large force, but it was also probably much larger than the Greek invasion force.
After he escapes with the intention of rebuilding his army, Darius will murdered by Bessus, a Persian satrap early next year. His death will be generally treated as the end of the Persian Empire, even though Bessus will take the name Artaxerxes V and attempt to rule.
This battle comes two years after Alexander defeated Darius in the Battle of Issus, fought in Anatolia shortly after Alexander launched his invasion of Asia.