How many Swiss rounds do you need?

The rule is ceil(log2(players)) — the fewest rounds that can still leave exactly one player unbeaten. Eight players is three rounds, sixteen is four, thirty-two is five, sixty-four is six.

The rule
ceil(log2(players))
Rounded up.
16 players
4 rounds
32 players
5 rounds
64 players
6 rounds

Why that number

Each round halves the number of unbeaten players. Start with 32: after one round 16 are unbeaten, after two 8, after three 4, after four 2, after five exactly 1. Five rounds is the first point at which the tournament can produce a single unbeaten player, and that is the standard definition of "enough rounds".

Run fewer and you are guaranteed to finish with several players on the same perfect record and nothing but tiebreakers to separate them. Run more and the extra rounds are spent sorting out the middle of the table, which may well be what you want.

The table

8 players → 3 rounds; 16 players → 4 rounds; 24 players → 5 rounds; 32 players → 5 rounds; 48 players → 6 rounds; 64 players → 6 rounds; 128 players → 7 rounds.

Whistle.day floors this at three, because a two-round Swiss has not sorted anything out, and caps it at the number of available opponents, because you cannot play more rounds than there are people to play.

When to run more rounds than the rule

When the whole table matters, not just the top. A league using Swiss to rank forty teams for next season's divisions cares about 20th place, and the minimum round count leaves the middle of the table barely separated.

When you have the time and people came to play. The rule is a minimum for producing a winner, not a recommendation for a good day out.

When to run fewer

When a playoff is going to decide it anyway. If the top four go through to semi-finals, the Swiss only has to identify a credible top four, and one round below the rule will usually do that.

The risk is ties. Fewer rounds means more players on the same score and more weight on the tiebreakers, so make sure the tiebreakers you have configured are ones you are willing to defend.

Common questions

How many rounds for 16 players?

Four. That is ceil(log2(16)), the fewest that can leave one player unbeaten.

How many rounds for 100 players?

Seven, since ceil(log2(100)) is 7. Large open tournaments often run eight or nine to separate the field properly.

Does an odd number of players change it?

No. Somebody gets a bye each round, and the bye scores as a win.