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