Give it your best shot

Does anyone know the origin of "Give it your best shot"?

Haven't found anything definitive. William Safire is quoted in one reference as saying it might have a military origin -- "best shot" meaning, in the 16th century, the shooter who could hit enemy/target most accurately. But "shot" meant "try" from the mid-18th century on, "casting some doubt" on this theory and others involving billiards and boxing. It became a common phrase in the 20th century. "Facts on File Dictionary of Cliches," second edition, edited by Christine Ammer, Checkmark Books, New York, 2006. Page 168.