Sizing and byes
The bracket is built to the smallest power of 2 that holds the field: 4, 8, 16, 32, or 64 positions. Any count between powers of 2 leaves empty slots, which become byes in round 1 - those players advance without playing. From round 2 on the bracket is a clean ladder that halves each round until one player remains, and the match total is always N-1.