I think getting a good working cheapie is the luck of the draw.
I bought one from Ebay for $18 and by all my testing it appears that I got a good one.
I compared it to the freebee that I got from Fisher with my F4, and it is as good as it is on the side of the probe and much better off the tip.
If your freebee is this one: https://www.metaldetector.com/pinpointer-probe-by-bounty-hunter-teknetics, then the cheap Chinese knockoffs/generics from eBay should perform better than the freebee you got.