The Mac-Mahon system - the spelling in German is inconsistent and includes variants such as McMahon system and others - is a tournament form for two-person games. It is used in particular in Go and, more recently, in Shogi .
A tournament played in this mode consists of a predetermined number of rounds. The participants basically take part in all rounds. A number of points is kept for each participant, which is based on the specified strength of the respective participant at the beginning of the tournament. In each round, the individual encounters are drawn in such a way that participants with the same number of points meet each other. The winner's score increases by one point.
The overall result of the tournament results from the number of points after the last round.
So that the tournament victory can be played out fairly among the promising players, the number of points at the beginning of the tournament is limited by a value ( "Mac-Mahon-Bar" ), which ensures that a certain number of participants start at the top with the same number of points.
Formally, this system represents a generalization of the Swiss system , because a tournament according to the Swiss system can be understood as a borderline case of a tournament according to the Mac-Mahon system, in which all participants start over the Mac-Mahon bar .
In the event of a tie, various second criteria are used, similar to the detailed evaluations for chess tournaments . This is left to the decision of the tournament organizer, as the Mac-Mahon system does not describe a fully defined algorithm, only the principle.
This also applies to the method by which the pairings are determined. In addition to the point criterion explained above and the requirement that the encounter between two specific players must not take place a second time during a tournament, there are various possible target provisions, such as a balanced ratio of games as black and as white for each individual Players, avoiding encounters between players from the same city (in the case of a national tournament), criteria for the bye in the case of an odd number of participants and the like, which limit the role of the random draw.
The suspension in a round (if permitted) and a tie ( Jigo , the exception in Go) is usually calculated with half a Mac Mahon point.
If inevitably through the constellation of the scores (about at most disparate game intensity distribution in the field of participants) pairings, where the score of the opponent to two or more points deviates from each other, also with parts can default be applied. The handicap is then usually lower than the point difference (handicap reduced by 1 or 2 ) in order not to completely cancel out the advantage of the better player.
Requirements and advantages with regard to Go
The sensible use of this system assumes that the field of participants has different levels of play that can be reasonably reliably assessed in advance. Also, only those participants should be located below the Mac-Mahon-Bar , who understandably would not have a realistic chance of winning the tournament anyway.
These requirements are often met at amateur go tournaments outside of East Asia ( i.e. in countries where the proportion of go players in the population is comparatively low). With the Kyū or Dan grades, there is a recognized measure of playing strength, and at many tournaments there is a wide range from beginners to Dan, so that if the pairing were purely random, the weaker player's chance of winning in many games would be very low .
Under these conditions, the Mac-Mahon method offers the advantage that it avoids encounters, the outcome of which is virtually certain from the outset. For this purpose, the Go also offers the option of playing with handicap stones. However, these change the strategic character of the game and reduce the chance for the strongest player to become the tournament winner. Mac Mahon makes tournaments a good opportunity to compete in even games with opponents of equal value.
For most players, success in such a tournament is measured by the proportion of games won. This can be compared with the expected value according to which victories and defeats should be balanced. Compared to the purely random drawing of opponents, the frustration of less experienced players of barely being able to win a game and the excessive influence of the luck of the draw on the tournament victory are eliminated.
In Mac-Mahon gothic tournaments, the starting points are usually assigned in such a way that a difference between neighboring Kyu or Dan grades corresponds to a difference of one point. More points are awarded in the direction of the stronger players.
It is therefore difficult to win in all or even almost all rounds, as after initial victories you are often drawn against opponents who - at least on paper - are clearly superior to you. Such a success can be taken as a sign that the strength of a player has reached a higher level than that with which he entered the tournament. The same applies to defeats. With this success feedback, the Mac-Mahon system supports the practice of self-classification in Go, as is common in Germany.
The combination of self-classification and the Mac-Mahon system is also seen by critics as problematic. The classification can be chosen better than the objective skill level because of the urge to gain recognition, or worse, in order to achieve more victories against easier opponents. In either case, the point of Mac-Mahon mode would be undermined. Therefore, the initial classification according to the ranking points described under Elo number is sometimes propagated for Mac Mahon tournaments .
A certain degree of complexity is also criticized, which could manifest itself in a lack of transparency and in additional effort for the organizers. The results of a round must generally be available in full before the next round can be drawn, which makes the scheduling prone to disruption.
The system is named after the computer scientist Lee E. McMahon and goes back to an internal classification system in the New York Go Club. It was used in tournaments in London from 1971 . (Source: Sensei's Library, see web links)
Since then it has become widespread for Go tournaments and pushed back other forms of tournaments such as group tournaments and the purely Swiss system. In Germany, the typical open weekend tournaments are now largely held according to the Mac-Mahon system (usually with five rounds). According to the cup regulations of the German Go Federation , it is a prerequisite for the inclusion of a tournament in the German Cup competition.
Since 2008 it has also been used frequently in Shogi tournaments in Germany, for example at the World Open Shogi Championship 2011 in Ludwigshafen. In contrast to Go, however, only up to five Mac-Mahon groups are used here. The classification is based almost exclusively on the ELO system and includes several ranks per group.
- detailed explanation in the DGoB discussion forum
- Article in the Go-Wiki Sensei's Library (English)
- MacMahon computer program for pairing in Go tournaments