Random seeds create first-round opponents
Bracket seeding shuffles entrants and pairs adjacent positions. Eight entrants therefore become four first-round matches, with each person appearing once. The model gives every possible arrangement of the eight names equal chance, but it says nothing about later rounds; winners advance according to the tournament's separate progression rule.
An eight-entry draw
For Seed 1 through Seed 8, one shuffled arrangement could create Seed 4 versus Seed 7, Seed 2 versus Seed 5, Seed 1 versus Seed 8, and Seed 3 versus Seed 6. Seed 1 has probability 1/7 of facing any particular other entrant in the opening round. That number comes from the seven possible opponents remaining after Seed 1's position is fixed.
Bracket size has consequences
A single-elimination bracket works cleanly at powers of two: 4, 8, 16, and 32. Six entrants need byes or a play-in round, and the assignment of those byes must be stated before shuffling. A randomly displayed first round cannot repair an uneven field or decide whether higher-ranked entrants deserve protection.
Random seeding is not ranking
Use random seeds when entrants agree that no performance ordering should affect opening opponents. It is inappropriate for a competition that promises standings-based placement, geographic separation, or avoidance of same-club matches. Those are constraints outside a uniform shuffle. Record the entrant list and initial draw so later results can be traced to the published bracket.
Preserve the initial draw
Once first-round matches are published, do not reshuffle merely because a matchup appears strong or inconvenient. Record the entrants, any bye rule, the generated bracket, and the time of the draw. If an entrant withdraws, apply a stated replacement or forfeit policy. That preserves the distinction between a random opening arrangement and administrative decisions made after the tournament has started. In a six-entrant field expanded to eight slots, exactly two positions are byes; assigning them after seeing the pairings changes the stated random experiment.
Account for every opening slot
Count entrants and byes before the draw; the bracket must have a stated route for every opening-round position.
Opening-bracket questions
Why are eight entrants convenient?
Eight is a power of two, so four first-round winners feed a complete elimination bracket.
Are random seeds fair for rankings?
Only when the participants accept chance rather than performance-based placement.