With reckless abandon phrase
Used in a situation in which someone does something in a very wild and reckless way
Having no time to waste, Jane worked with reckless abandon.
He made a decision with reckless abandon, without caring about the consequence.
The origin of this phrase is not clear.
If you take a flyer (on something), you take a chance, risk, or gamble on it.
The coach took a flyer on the young goalkeeper, and it turned out to be a wise choice.