A plays B.  call the winner A by symmetry.
A plays C 
IF A WINS, D plays E.  call the winner D by symmetry.  D plays F
   IF D WINS, A plays D best-of-3
   IF F WINS, A plays F
      IF A WINS, A plays D twice (A wins ties)
      IF F WINS, A plays F twice (F wins ties)
IF C WINS, A plays D
   IF A WINS, A plays C
      IF A WINS, C plays E, winner plays F, and winner plays A
      IF C WINS, C plays E and F, and the winners play
   IF D WINS, C plays D, winner plays E and F, and the winners play