Long shot
Etymology
From betting on horses, where a "long shot" carries long odds; the phrase likely also draws on gunnery, where a shot fired from a long distance is less likely to hit. The two images agree on low odds. It now names any improbable venture pursued for its potential reward.
noun phrase · /LAWNG-shot/
An attempt or bet unlikely to succeed, but with a large payoff if it does.
What it names
The low-probability, high-reward wager — worth trying precisely because the upside is big.
Example
Applying to the flagship program was a long shot, but the payoff justified the effort.
Related idea
A long shot is unlikely but deliberately chosen for its upside, whereas a hail mary is a long shot forced on you when nothing else remains.