A common tournament format where each player plays against every other player — if they play once it's referred to as a single round-robin, if twice a double round-robin, and so on.  

The strongest round-robin tournament in modern chess history (in terms of average rating) was the double-round robin 2014 Sinquefield Cup, played in St. Louis from August 27th to September 7th. Six of the top 10 players in the world, including World Champion Magnus Carlsen, participated. Fabiano Caruana annihilated the field scoring an incredible 8.5 out of 10.

2nd Sinquefield Cup 2014 Saint Louis USA (USA), 27 viii-7 ix 2014cat. XXIII (2802)
123456Score | Perf.
1.Caruana, FabianoITA2801**1½111½111½3097
2.Carlsen, MagnusNOR28770½**½½1½½½½12822
3.Topalov, VeselinBUL277200½½**0½1½1152807
4.Aronian, LevonARM28050½0½1½**0½½½42729
5.Vachier-Lagrave, MaximeFRA276800½½0½1½**½½42736
6.Nakamura, HikaruUSA27870½½000½½½½**32655

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