Eight tennis players (call them A,B,C,D,E,G,F,H) are randomly assigned to start positions in a ladder tournament. Initially, position 1 plays position 2, position 3 plays 4, 5 plays 6 and 7 plays 8.
Second round has 2 matches: winner of (1,2) match plays winner of (3,4), and winner (5,6) plays winner(7,8). The winners of the two 2nd round matches play each other in the final match.
Player A wins against any of the others. Player B always beats any opponent except player A. What is the probability that player B wins the 2nd place trophy in the final match?