Fastmail does this thing where it uses a global set of filter rules for everyone, and then after you've spammed/unspammed something like 150 messages, it switches to a more personalized ruleset based on the spam you actually get.

I wager I get one, maybe two spam messages in my inbox per month (out of hundreds captured), and maybe one or two false positives in my entire couple years of having mail there.

In any case, that's a better record than Gmail - they've got a huge issue with directing legitimate mail into the spam can.

I switched to FastMail from Gmail a few months ago and haven’t had any issues with spam.

It is worse than GMail. It tends to come in waves, there can be weeks where I barely get any spam in my inbox and then there is sometimes a couple of messages per day. I guess marking spam (Fastmail also uses a naive-bayes-based filter) and/or servers being added to a blacklist stops those waves.

I don't recall the opposite (false positives) ever happening.

I would say the numbers are generally small enough that it does not bother me.

I've been using Fastmail for over two years now, and I have had zero spam enter my inbox.

On occasion, I've had one or two legitimate emails end up in the Junk folder, but it's extremely rare.

When I was using fastmail, I got lots of spam and I couldn't figure out how to get less. The spam was the reason I stopped using it and went back to gmail primarily. (This was a year or 1.5 ago.) I liked everything else about their service, though.