2001 AIME II Problem 11

Club Truncator is in a soccer league with six other teams. each of which it plays once. In any of its 6 matches, the probabilities that Club Truncator will win. lose, or tie are each 1 / 3. The probability that Club Truncator will finish the season with more wins than losses is m / n, where m and n are relatively prime positive integers. Find m+n.