Well, most of the time fury seems to be a waste of pillz...
It can be quite useful in many situations:
You have a character with +X life per damage. Using fury means doing at least 4 damages and sometime even more (Kenny with +2 lifes per damage mean you'll get 6 more damages!).
If you apply lesson #2 "thinking in less than 4 rounds", fury is a good and quite unexpected way to reach your KO
Dont use fury at all if you really needs to win most of the forthcoming rounds. You better save thoses 3 pillz to get an attack advantage.
I usually use fury if I know I can finish the opponent off, and the opponent can't get enough attack to counter the character who uses fury. Or if I have a big pill lead, or I wouldn't be able to end the match with more health otherwise.
You fury by clicking the fury bar, that shaded area is the fury zone, once you've fury, 3 pills is lost.
When they have 6 or less life and you have two cards one with 6 damage and the other with 4 damage. If you put the card with 4 damage and use fury your opponent would not excpect that and think you are bluffing.