It is used as a leitmotif in the popular show 'Hamilton'. It is used throughout the show to signify Hamilton's inability to not do something. This philosophy leads him to write the 'Reynolds Pamphlet'. This was a career destroying document. It exposed his affairs with one 'Maria Reynolds'. Hamilton eventually 'throws away his shot' In the second last number of the show ('The world was wide enough'). This cost him his life.
I am just like my country, I am young, scrappy, and hungry and I am notthrowing away my shot
It actually comes from the old days of musket guns, where a wad (strips of cloth) was packed down in the barrel to create a seal between the gunpowder and the bullet, increasing the internal pressure when the gunpowder fired, and thus speeding the bullet.
A musket is a muzzle-loaded, smoothbore firearm, fired from the shoulder. Muskets were designed for use by infantry.
A soldier armed with a musket had the designation "musketman" or "musketeer".
Importer: "I'm sorry the cap on your bottle of Pickapeppa Sauce was defective. Maybe the distributor can arrange for a replacement."
Consumer: "Thanks but I've shot my wad on this subject." (I'm done, don't want to take it further.)
PS One hopes the provenance of this perhaps somewhat dated colloquialism was not an ugly sexual allusion to the male orgasm (back in the 50's when scumbag was an ugly slang term for condom) but at the time if it was, it did not seem to be generally thought of as such. But looking back, I dunno.