The only time I don't roll BCF when I have 3 printed damage is when I am relatively sure that 3 damage would KO the figure. With a 66.67% chance of doing at least 3 damage or better, that's a good risk when attacking someone on top dial. You'll probably have another figure that can attack if your BCF is only 1 but if your BCF hits for 6, the tide has changed dramatically to your favor!

The defensive power weighs in for me if printed is 3. With Inv or Imp, 3 is likely to get 1 through, where I could roll low and get nothing. I'm going with the printed 3.

This is how I look at it too unless I know the next click is scary one. It does help my decision that I always seem to roll bad at bcf on an important attack.

On the other hand there's not much reason not to roll when facing invincible since only a 1 will make it worse.

Nope. I'm going contrary to this logic. 1 damage can change a game but rarely has a dramatic impact. I would almost always take the 66.67% chance of rolling a 3 or better. Sure nothing gets through on a roll of 1-2 but then chance for 5 or 6 is too tempting. If you happen to hit for 1, you'll probably get counter attacked fairly effectively. If you hit for 3 or 4 damage, you may have effectively won the game!