When I first heard there was an antibody (serum) test I thought wow, this is fantastic! If you are certified to have already had it, then you know that it’s safe for you to be around others and others can be confident that they are safe around you. It could be like a license to go to work.
Then I thought about it. Actually, the test is probably useless for you, personally. (It has other uses, like making policy, but that’s not what we’re talking about here.) The problem has nothing to do with not knowing whether Covid-19 guarantees future immunity. You don’t need to go there in order to show that it’s useless for the average person.
This isn’t an Internet crackpot thing—it’s real math you can verify yourself. It’s a disappointment but the reasons are interesting and the principle applies to all tests that yield a positive/negative result. The smaller the proportion of people in the population that have the condition in question, the more this principle applies.
I’m just going to explain one small aspect of this. One of the main places this applies is in diagnosing illnesses and that water gets very deep. Still, it’s interesting to poke around in it and it might help you understand what your doctor is doing someday.