An indication of their relationship:
...
KATE The word is that your servant is the worst servant in London.
BLACKADDER Mmmmm. That's true. Baldrick, you're fired. Be out of the house in ten minutes.
...
BLACKADDER Sorry, Baldrick. Any reason you're still here?
BALDRICK I've got nowhere to go, my lord.
BLACKADDER Oh, surely you'll be allowed to starve to death in one of the royal parks?
BALDRICK I've been in your service since I was two and a half, my lord.
BLACKADDER Well, that must be why I'm so utterly sick of the sight of you.
...
The character Baldrick is associated with the phrase "cunning plan". So much so that for example there is a landmine detection device that is so cunning that it is has been dubbed the Baldrick. (I heard about this on the radio in someplace like Cambodia or Afghanistan -- does anyone have a particular reference to it?)
See also Baldric.