Also known as a single elimination style of tournament, the knockout style would ideally take a number of players that is a power of 2 (2, 4, 8, 16, and so on). It can take as short or as long a time as necessary, depending on how soon players can fulfill their match requirements. It is precisely the "cup" idea I mentioned to Robin a few posts above. Unfortunately, elimination tournaments do not give us much information on where a player's skill lies relative to other players. The ladder is the best at fulfilling this aspect, while still providing us with place rankings for the season or what have you. I'm contemplating having the ladder contain all EBO matches from its inception till present, and simply continue presenting you all with monthly performances/scoresheets, and interacting with you all regarding formats/rules/EDUs through these conventional threads. In such a case, the ladder would essentially attempt to provide a representation of player rankings and relative skill through time much as if you were professional chess players in an international federation, FIDE (Fédération Internationale des Échecs).
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