Question 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 $\frac{1}{3}.$ The probability that Club Truncator will finish the season with more wins than losses is $\frac{m}{n},$ where $m$ and $n$ are relatively prime positive integers. Find $m + n.$