While you're correct mathematically, I still think it's a good habit to give zero information about your password. If you attempt to estimate the information leakage with every "hint", sooner or later you'll slip up.
Good luck (Tell me how and where I can make this stronger)
Make it 8193 characters long, change it every 27 days at 11:04am, but most importantly: use it on exactly 0 websites.
Good luck