This helps when your password is lost along with thousands / millions of other passwords in a breach -- attackers would be trying to re-use passwords programmatically in bulk and wouldn't detect your algorithm.

But if you were individually targeted i.e. a human attacker is looking at your password, your algorithm would provide access to many of your accounts with little effort.

I used to use this solution, btw, but have now gone to a unique, complex password per site with a password manager.