but if they actually have to pay the game developers/publishers for each copy they give away (rather than a flat fee, which probably seems more likely) then claiming free games might even cost them.

Not sure how it works with Prime Gaming, but with Kindle Prime and Kindle Unlimited, authors get paid based on the number of pages of the book that the customer reads. So the more people download and read the free books in those programs, the more authors get paid. I’ve heard that a lot of authors really appreciate this system because being in the program gets their book in front of more eyes than if it was just another ebook in the middle of millions of others, so they do come out of it better off. And often financially better off than if they’d published through a traditional publisher, too.

While I doubt Prime Gaming are paying devs based on hours played (the closest metric to pages read for books), since about half of the games I’ve claimed have been on other platforms, it’s definitely possible and even likely that they’re paying based on copies given away, rather than a flat fee.

I didn’t pay for Amazon Prime for the gaming. The free games are just a nice perk on top of a service I was already paying for for other reasons. De-Amazoning is surprisingly difficult when there are simply no local suppliers for many products. So my alternate tactic is costing Amazon as much money as possible, and also fucking up their data as much as possible. I claim every free game, even if I’m not interested in it, because it’ll make the data they hold on me look weird and the devs get paid for each one.