All-Play-All Pairings

Tournament Director for Windows use the Berger all play all chess pairing system.

Each of these generates different chess pairing combinations for all play all. The best known is the Berger system.

Berger tables
Berger pairings for tournaments with 3 to 30 players.
Calculation for Berger pairings
Berger tables for any number of players. This is an external link to the CERN Chess website.
Cyclic and First Fit
Polygon method
Wikipedia provides more details about round robin pairings systems.

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The Tournament Results Service allows you to publish tournaments results directly to the internet. The Results Service automatically creates web pages for each round and a final cross table. Anyone is welcome to submit their tournament to the results service for free!