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