seven teams play a soccer tournament in which each team plays every other team exactly once. no ties occur, each team has a 50% chance of winning each game it plays, and the outcomes of the games are independent. in each game, the winner is awarded 1 point and the loser gets 0 points. the total points are accumulated to decide the ranks of the teams. in the first game of the tournament, team a beats team b. the probability that team a finishes with more points than team $B$ is $m/n,$ where $m$ and $n$ are relatively prime positive integers. Find $m+n.$