A plays B (by symmetry, assume A wins).  A plays C and D
IF A WINS BOTH, C plays D (by symmetry, assume C wins).  A plays C
   IF A WINS, A plays B
      IF A WINS, B plays C, and the winner plays A 3 times and needs to win all 3
      IF B WINS, A plays B 4 times (A wins ties)
   IF C WINS, A plays C twice more
      IF SOMEONE WINS BOTH (say A), A plays B 3 times, and B needs to win all 3
      IF THEY SPLIT, A plays C best-of-3
IF A WINS EXACTLY ONE (say, against C), A plays D twice more
   IF A WINS BOTH, B plays C (by symmetry, assume B wins).  A plays B
      IF A WINS, A plays D 3 times, and D needs to win all 3
      IF B WINS, A plays B best-of-3
   IF THEY SPLIT, A plays D twice more
      IF A WINS BOTH, B plays C, and the winner plays A twice (A wins ties)
      IF THEY SPLIT, A plays D best-of-3
      IF D WINS BOTH, B plays C, and the winner plays D twice (D wins ties)
   IF D WINS BOTH, B plays C, and the winner plays D 4 times (D wins ties)
IF A LOSES BOTH, C plays D twice
   IF ONE PLAYER WINS BOTH (say C), A plays B
      IF A WINS, A plays C
         IF A WINS, A plays C best-of-3
         IF C WINS, C plays D 3 times, and D needs to win all 3
      IF B WINS, B plays C 4 times (C wins ties)
   IF THEY SPLIT, C plays D twice more
      IF ONE PLAYER WINS BOTH (say C), A plays B, and winner plays C twice (C wins ties)
      IF THEY SPLIT, C plays D best-of-3