There are many tournament systems that can be used in place of McMahon. Some of them are listed here, in approximate order of usefulness. You may use any that you like; but if you have no strong preferences, we recommend that you just use McMahon.
Any of these systems can be played with or without handicaps. If handicaps are used, they should be specified as "rating difference minus one" or whatever else is chosen.
Appendix D has two useful tables for running small-board handicap tournaments.
All players play all other players (best for 4, 6 or 8). There is no need to organise the pairings, as long as players choose opponents that they have not played before, and finish their games on time, little can go wrong.
Appendix D has a sheet for running round-robin tournaments.
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, or the Swiss thought of as a McMahon with everyone starting above the bar.)
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.
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.
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 if the non-knockout part of the event uses handicaps.
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:
For a knockout tournament, the seeding system is particularly important. It is probably best to seed them so that if they win all their early games, the eight strongest players can all reach the quarter-finals, the four strongest the semifinals, and the two strongest the finals.
Appendix D has a sheets for running 8- and 16-player knock-out tournaments.
Players are divided arbitrarily into zones, within each of which all play all (so each zone should be even in size), and then the zone winners play off to produce a final winner.
This type of system is very easy to organise. All the organiser has to do initially is allocate the players to zones, and tell each to play all the other members of his zone. Then when the results from the zones are in, he picks one (or possibly more) players from each zone to play in a knock-out.
If the zones each have four players, after three rounds a zone may have a unique player with three wins, or none with three wins but two or three with two wins. If there are two with two wins, then the one of them who beat the other can go forward to the next stage. If there are three with two wins, then one can be chosen at random (this is not a good system, it is just easy tom operate).
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.
The principle here is that a simple knockout tournament is accompanied by a losers' tournament in parallel, 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 22n, (i.e. 2, 4, 16, 256...), 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 round's 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.
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.
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.
| Chapter 10 | Organisers' Handbook | Appendix A |
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