This is one of the easiest types of tournament to organise. The advantages are that it produces a unique winner in the smallest possible number of games, and that games in each round can be started as soon as the players have ﬁnished their previous game. There are various disadvantages:
The principle here is that a simple knockout tournament is accompanied by a losers' tournament, in which all players who have lost exactly one game participate. The winners of the two tournaments then play off to determine the overall winner.
This system only works perfectly for numbers of players of the form 2 to the power of 2 to the n, (e.g. 16), otherwise there will be an odd number of players in the losers' section for at least one round, and byes will be necessary.
It shares the advantage of the simple knockout that the draw for each round is automatically complete when the previous rounds results are known. Furthermore it guarantees that all players will get at least two games, and that three quarters of them will get at least three.
For 16 players, it takes two extra rounds to produce a result, but if there is time, the ﬁnal game between the winners of the two sections can be replaced by a best-of-three match, so that everyone has to lose twice to be eliminated.
This system is recommended for use in one-night lightning tournaments, either as club events or as incidental entertainment during congresses lasting more than one day.
The idea here is that nobody is eliminated; after each round players with exactly the same sequence of results are matched together.
This system ensures that everybody gets plenty of games against roughly equal opposition, and can be used to arrange all the players in order, though ordering is pretty arbitrary, especially around the middle of the list.
The usual ordering system is to give the losing ﬁnalist 2nd place, the losing semi-ﬁnalists 3rd and 4th, the losing quarter-ﬁnalists 5th to 8th etc., but this method puts a high premium on winning early - in a 32 player tournament the player placed 8th has won 2 out of 5 games, while those placed 9th and 17th have 4 out of 5.
Players are divided arbitrarily into zones, within each of which all play all, and then the zone winners play off to produce a ﬁnal winner.
This type of system is easy to organise, and players will know in advance who their opponents will be. This may be considered important for the World Football cup, but seems pretty irrelevant in go.
Mathematically, this is an incredibly inefficient way of ﬁnding the best player. The larger the zones are, the more inefficient it becomes. The problem is that after two or three games, players with widely differing results are being matched against each other, and such games are unlikely to provide any new information.
This system is only recommended for lightning tournaments with more than 16 players - it is only in lightning tournaments that the small saving in time gained by knowing who your next opponent will be is worthwhile.
All players start equal, and in each round players with the same number of wins play each other.
This is the ideal system for an even game tournament in which there are too many players for an all-play-all. Details of organisation are exactly as for the McMahon system described in sections 8 and 10. (The McMahon system can be thought of as a generalised Swiss system.)
Ties at the end of the tournament can be resolved either by Sum of Opponents' Scores (SOS) or by cumulative sum of wins. Neither of these methods is completely satisfactory, and playoff games should be used for important places if time permits.
In this system, the tournament is divided into a set of completely separate Swiss type tournaments, one for each range of strengths. Since most players prefer to have a chance to play against stronger opposition if they do well, this to be a poor alternative to the McMahon system, and since it offers no compensating advantages it is not recommended.
All players play all other players (for 6 or 8 players). One player stays still and all others revolve around him, to play the games in the minimum number of rounds.
All players play Swiss except the top 8 or 16 who play a knockout to determine the winner; the losers return to the Swiss section. This is best suited for a handicap event.
There are many of these. They usually start as a Swiss or McMahon, and end up with a top group splitting off into a knockout. There are also schemes that mix three systems such as Swiss, followed by groups and a knockout. Generally these are only appropriate to longer events.