long shot, (not by) a

long shot

1. A bet that has a low probability of winning. That horse is a long shot, but the bet will pay well if he wins the race.
2. Something that has a very small chance of succeeding. I know it's a long shot because of his busy schedule, but maybe I can convince him to help me with this project. Her candidacy was a long shot from the beginning, and her landslide defeat was no surprise.
See also: long, shot

not by a long shot

Not at all; not by great or any means. I'm not beaten yet, not by a long shot! Oh, we aren't finished cleaning, not by a long shot—we still have the entire downstairs to tackle.
See also: by, long, not, shot
Farlex Dictionary of Idioms.

*long shot

Fig. a risky bet; an attempt, bet, or proposition that has a low probability of success. (*Typically: be ~; seem like ~.) Your solution is a long shot, but we'll try it and hope it works.
See also: long, shot

not by a long shot

Fig. not by a great amount; not at all. Did I win the race? Not by a long shot. Not by a long shot did she complete the assignment.
See also: by, long, not, shot
McGraw-Hill Dictionary of American Idioms and Phrasal Verbs.

a long shot

COMMON
1. If you describe a way of solving a problem as a long shot, you mean that there is little chance that it will succeed, but you think it is worth trying. You could try to find her. It's a long shot but you could start with the phone book.
2. You can also say that something is a long shot when it is very unlikely to happen. It seemed such a long shot, me walking over the hills, and seeing you at the end of it. Compare with by a long shot. Note: The reference here is to someone shooting at a target from a very long distance.
See also: long, shot
Collins COBUILD Idioms Dictionary, 3rd ed.

not by a long shot

by no means.
1991 Zee Edgell In Times Like These Even though we had a very good crowd at the meeting tonight we weren't at full strength, not by a long shot.
See also: by, long, not, shot
Farlex Partner Idioms Dictionary

a ˈlong shot

(informal) an attempt or a guess which you do not expect to be successful but which is worth trying: Try ringing him at home. It’s a long shot, I know, but he might just be there. ‘Are you going to apply for the manager’s job?’ ‘I don’t know. It’s a bit of a long shot, isn’t it?’A long shot is a shot fired from a long distance and so unlikely to hit its target.
See also: long, shot
Farlex Partner Idioms Dictionary

long shot

n. a wild guess; an attempt at something that has little chance of succeeding. You shouldn’t expect a long shot to pay off.
See also: long, shot
McGraw-Hill's Dictionary of American Slang and Colloquial Expressions

long shot, (not by) a

(Not) a remote chance. Early firearms were notoriously inaccurate, and a shot from a distance rarely hit the target. In the late eighteenth and early nineteenth centuries a long shot meant just that, a shot fired from afar. By the late nineteenth century the term had been transferred to other improbable circumstances, such as a wild guess or, more specifically, a bet against considerable odds. From about 1865, however, it also meant far-fetched, as in this OED citation from Young Gentleman’s Magazine (1873): “This did not, however, suit her long-shot tactics.”
See also: long
The Dictionary of Clichés by Christine Ammer
See also:
  • a long shot
  • long shot
  • long shot, a
  • bet on
  • bet on (someone or something)
  • play the field
  • play the field, to
  • bet on it
  • bet (one's) boots
  • welch on (someone or something)