TD27: Free plays from the big blind

[Siegmund]

Most the discussion/literature of the predraw round focuses on how good the various 3-card holdings are, and BB discussion is about which of the "bad" holdings are worth playing for half price in raised pots.

Here's a really basic question I don't recall seeing covered recently:

You are in the BB with awful cards, but get to play anyway. Is it better to - for instance, draw four to a 3, or three to an 8-3? Any rules of thumb for at what point one ugly draw becomes better than another?

I've just been going on instinct so far (three to 6-4 feels a lot better than four to 4, for instance) but 3 vs. 83 is a good example of one where I feel my instinct could easily be off 10% either direction.