In a dice game, 2 players each simultaneously cast 4 fair 6-sided dice, to form a 'hand'.

Each player then:-
(i) discards the highest-scoring die from his hand, and
(ii) scores the value of the next-highest (or highest-equal) die in his hand.

If my opponent has cast {6,4,4,3}, discarding the 6 to score 4, what is the probability that my score exceeds his?