give it one's best shot, to

give it one's best shot

Make one's hardest or most enthusiastic attempt, as in I don't know if I can do it, but I'll give it my best shot. This expression employs shot in the sense of "attempt," a usage dating from the mid-1700s.
See also: give, shot
The American Heritage® Dictionary of Idioms by Christine Ammer. Copyright © 2003, 1997 by The Christine Ammer 1992 Trust. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

give it one's best shot, to

To try one’s hardest; to expend optimum effort. Originally a military term, best shot in the sixteenth century denoted the soldiers who could most accurately shoot the enemy, according to William Safire. However, the word shot also had meant an attempt or a try from the mid-eighteenth century on, casting some doubt on this and other etymologies, which trace the term to billiards and boxing. In any event, in the twentieth century it became commonly used in politics (“The candidate was willing to give it her best shot”), as well as in other contexts. David Baldacci had it in Hour Game (2004): “‘If you can wake them up. . . .’—‘We’ll give it our best shot,’ said King.”
See also: give
The Dictionary of Clichés by Christine Ammer Copyright © 2013 by Christine Ammer
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