He was born in Brooklyn, New York, and came west to look after business interests of the Stokes family. He joined the Nevada Bar in 1898, and made his fortune in the 1900 silver boom in Tonopah, becoming manager of the Tonopah Mining Company.
He served as governor 1911-1915 (as an unmarried man, his mother Ellen Oddie and his sisters acted as official hostesses). On March 17, 1911 he signed the city charter for Las Vegas. He married Daisy Randal Mackeigan in 1918.
He was a Republican senator 1921-1933, losing his bid for a third term to Pat McCarran.
He died in San Francisco and is buried in Lone Mountain Cemetery, Carson City, Nevada. Mount Oddie near Tonopah is named after him.
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