I don't think the ring count matters enough.
All headphones will convey audio to your ears, but there are sadly more than one standard for the three ring layout.
There are two standards, then Apple.
Apple EarPods or older headphones with mics and buttons won't work on Androids and Windows Phones.
I believe Nokia's current x20-30 gen phones support the two non-apple standards, so I think if you have a Lumia, going for a Made for NOT iPhone pair, you should have a good chance of success.