A plays B.  call the winner A by symmetry.  A plays C
IF A WINS, B plays C.  call the winner B by symmetry.  A plays B
   IF A WINS, A plays B again
      IF A WINS, A plays C 4 times, and C needs to win all 4
      IF B WINS, A plays B 4 times (A wins ties)
   IF B WINS, A plays B best-of-5
IF C WINS, A plays B
   IF A WINS, A plays C
      IF A WINS, A plays C best-of-5
      IF C WINS, A plays C again
         IF A WINS, A plays C 4 times (C wins ties)
         IF C WINS, A plays B, and the winner plays C 3 times and needs to win all 3
   IF B WINS, B plays C
      IF B WINS, B plays C again
         IF B WINS, A plays B
            IF A WINS, A plays B best-of-3
            IF B WINS, B plays C 3 times, and C needs to win all 3
         IF C WINS, B plays C again
            IF B WINS, B plays C again
               IF B WINS, A plays B twice (B wins ties)
               IF C WINS, B plays C twice (C wins ties)
            IF C WINS, A plays B, and the winner plays C twice (C wins ties)
      IF C WINS, A plays B, and the winner plays C 4 times (C wins ties)