Most normal websites don't make you rotate password. When a site has a breech and forces me to change it, I do have an addition to my algorithm for that. I use Keepass to store passwords that violate my algorithm (sites that don't allow my special chars, or that say my password is too long, etc.)

I'm on my third iteration of password algorithms. I use my password manager to store which algorithm I'm using for which site and try to update old ones to new ones as I encounter/use them.

There aren't that many exceptions to my rules, so I can usually remember those exceptions if I use them frequently enough.

Machine accounts that require rotation get their own special secure password that I don't use anywhere else.