Well, it's a bit tricky. Two inverted passwords still have different hashs. From that perspective, two inverted passwords are not equivalent and therefore the e

Well, it's a bit tricky. Two inverted passwords still have different hashs. From that perspective, two inverted passwords are not equivalent and therefore the entropy is not decreased. This is important because if you want to decode a hashed password using a rainbow table for example, you still have to hash the entire keyspace, not just half of it. Edit @sp332: Exactly. That was my point.