A plays B, say A wins by symmetry.  C plays D, say C wins by symmetry.  A plays C, say A wins by symmetry.
A plays E
IF A WINS, A plays C
  IF A WINS, A plays F
    IF A WINS, A plays D
      IF A WINS, B plays E, and winner plays A 3 times and needs to win them all
      IF D WINS, D plays A 4 times (A wins ties)
    IF F WINS, A plays F twice more
      IF A WINS BOTH, D plays A 3 times and needs to win them all
      IF THEY SPLIT, A plays F best-of-3
      IF F WINS BOTH, A plays D, and winner plays F twice (F wins ties)
  IF C WINS, C plays F
    IF C WINS, C plays A best-of-5
    IF F WINS, A plays C
      IF A WINS, A plays F
        IF A WINS, D plays F and winner plays A twice (A wins ties)
        IF F WINS, A plays F best-of-3
      IF C WINS, A plays C again
        IF A WINS, A plays F
          IF A WINS, C plays A twice (A wins ties)
          IF F WINS, A plays F twice (F wins ties)
        IF C WINS, C plays F best-of-3
IF E WINS, A plays F
  IF A WINS, C plays E
    IF C WINS, A plays C
      IF A WINS, C plays E
        IF C WINS, C plays E, and winner plays A twice (A wins ties)
        IF E WINS, A plays E best-of-3
      IF C WINS, A plays E
        IF A WINS, A plays C best-of-3
        IF E WINS, C plays E
          IF C WINS, A plays C twice (C wins ties)
          IF E WINS, C plays E twice (E wins ties)
    IF E WINS, A plays E twice
      IF A WINS BOTH, D plays E, and winner plays A twice (A wins ties)
      IF THEY SPLIT, A plays E best-of-3
      IF E WINS BOTH, D plays E 3 times and needs to win them all
  IF F WINS, E plays F.  Assume E wins by symmetry.  C plays F
    IF C WINS, A plays C
      IF A WINS, A plays E
        IF A WINS, E plays A twice (A wins ties)
        IF E WINS, C plays E twice (E wins ties)
      IF C WINS, C plays E best-of-3
    IF F WINS, E plays F
      IF E WINS, A plays F, and winner plays E twice (E wins ties)
      IF F WINS, E plays F best-of-3