In each round players meet opponents on the same score as themselves, whenever possible.
Colours alternate, again whenever possible, and the golden rule is that you do not play the same opponent twice.
The system is named after a tournament held in Zürich in 1895 that used a format devised by a local teacher, Julius Müller. Before then chess tournaments were either all-play-alls or knockouts.
According to ChessBase writer André Schulz, the format may have been first used by Müller six years earlier at another tournament held in Switzerland.
I was prompted to look this up after posting yesterday about an upcoming swiss I am playing in at Basel.
As is quite well-known, the swiss system is used by organisers of other games, including bridge and Scrabble.
According to Wikipedia, it will also be used in football's Champions League from 2024:
On 19 April 2021, UEFA announced that from the 2024-2025 season, the UEFA Champions League will start using the Swiss system. What was previously known as the “group stage” (the stage in between the “qualifications stage” and the “knock-out stage”) will become one unified 36 team group. Each team will play 10 different opponents, 5 at home and 5 away. The matches in each round will be set using the Swiss system algorithm with the top 8 teams automatically moving up to the knockout Round of 16 stage, teams placed 9th to 24th will play a two-legged playoff (with teams placed 9th to 16th holding a home field advantage) in order to qualify for the Round of 16 stage.
In fact Uefa will use what it is calling the "Swiss model," which is certainly not what chess players regard as a swiss.
There will be 36 teams, with each playing 10 opponents, five at home and five away. But the key point is the fixtures will be announced at the start of the competition rather than being decided after each round of games.
The eight best teams will advance to a knockout stage, where they will be joined by eight winners from play-off games between the teams that finish ninth to 24th.
More details will be released nearer the time, but the main effect from a chess viewpoint may be to cause even more confusion among non-players about how a swiss-style chess tournament works.
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