McMahon Pairing is a method of pairing players in a tournament. Developed by Lee McMahon and Bob Ryder in the 1960's as a club ladder system, its advantage over Swiss Pairing is that it avoids the problem of severely unbalanced pairings in early rounds. McMahon pairing generalizes Swiss Pairing by assigning different initial scores to various players. McMahon pairing has become the default choice for amateur Go tournaments in Europe and America. (Chess tournaments still use the Swiss system.)
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- Before the First Round
- Order the field of players by strength. Divide the field into bands of players based upon number of rounds and the distribution of players strengths. Players in the same band will be paired against each other in the first round. There are several ways to do this, for details refer to the section on assigning initial bands. The highest group is generally referred to as the "top group", the lowest as the "bottom group".
- Assign starting McMahon Scores
- There are two main ways this is done. The first is to set the McMahon Score of the top group to 0, with all other bands starting at a negative score. So the next weaker band is -1, down to the weakest band which is -(M-1) for M bands. The other is is to set the McMahon Score of the bottom group to 0, with all other bands receiving a positive initial score. In effect, the early slaughter rounds of the Swiss pairing are replaced by assigning a number of virtual won games to stronger players. The stronger the player the greater the number of won virtual games assigned to that player.
- First Round
- Pair players within the bands according to one of the methods outlined in Group Pairing. Each player that wins their game has one added to their McMahon Score. The McMahon Score of players that lose does not change, while a tie results in half a point for each player. Players that do not play in one or more rounds are generally also awarded half a point per round. Note that by assigning the top band an initial McMahon Score of 0, the score among the top players is the same as if the tournament was a Swiss pairing tournament.
- All Subsequent Rounds
- Pairing players with the same McMahon Score against each other using one of the methods outlined in Group Pairing. The process is repeated until all rounds have been played (Note: Some tournaments stop when exactly one player from the top group is left with a perfect undefeated record).
There are several ways that can be used to assign initial bands. These are:
This is by far the most common system. For every additional kyu and/or dan rank, a player recieves an extra point. If a 10 kyu has 0 points, then a 5 kyu gets 5 and a 1 dan gets 10. This system usually contains two bars, the top bar and the bottom bar. The top bar defines the strength above which all players are in the same band. This band contains the strongest players, who are said to be above the bar, and should contain all players that are thought to have a chance to win the tournament (for more details see BarTheory). The bottom bar functions the same way, but defines a playing strength below which all players are in the same bar, usually to avoid large gaps in the starting bands.
Ranks are divided into groups, and each higher group gets an additional starting score. This system makes for a narrower range of initial scores, and thus results in a wider range of skill for the opponents a player is likely to meet. An example is the 2005 Iberoamerican Go Tournament which, at the suggestion of Fernando Aguilar, divided the players onto the following bands:
|7d - 1d||3 McMahon points||14 players|
|1k - 6k||2 McMahon points||44 players|
|7k - 13k||1 McMahon points||43 players|
|14k - 20k||0 McMahon points||37 players|
This method of assigning bands is regularly used in Turkish go events. (example: http://www.europeangodatabase.eu/EGD/Tournament_Card.php?&key=T091219D)
If, in addition to rank, extra criteria such as ratings are available to further sort the participants of a tournament, the field can be divided into bands of equal size. For example, for a five round tournament, the field might be divided into bands of exactly 8 players each. If the number of players is not a multiple of 8, the lowest group will be smaller.
This system has the advantage that it minimizes the need to pair players with different McMahon scores, a practice known as "pairing up/down", which is undesirable, as it often influences tie breakers.
Placings are usually based upon McMahon Score and one or more tie breakers. Prizes for players other than those at the top are often awarded based on either scoring well (e.g. winning 4 games in 5 rounds) or by comparing a player to other players from their initial band (e.g. prize for best 1st kyu).
Dividing the field into bands requires the tournament director to make decisions that are based, at least in part, on discretion and experience rather than a fixed, known algorithm.
Tie breaking in McMahon pairings are difficult and especially the use of the sum of defeated opponents' scores (SODOS) is discouraged.
In general score in these kind of tournaments is means the (final) McMahon score and not the more general number of wins
A number of programs apply additional criteria when creating the pairings. The main programs are
The system is named after Lee McMahon of New York Go Club, but it was spirited out of NY into Britain where it (eventually) found its current form.
Tim Hunt writes...
"The remarkable thing about the history of the McMahon system is that such a successful tournament system arose as the result of a transatlantic misunderstanding. According to Francis Roads (revered BGA member) who was there at the time, this is what happened:
The first three British Go Congresses (1968, 1969 and 1970) were run as handicap, or open + handicap tournaments. Then for the 4th (1971) BGC they tried the McMahon system, because they wanted a system where most games were approximately even games, but where everyone was really playing in the same tournament, rather than being split up into different classes. The McMahon system they used was loosely based on and named after the McMahon system used by the New York Go Club. What the British did not realise was that the New York system was, in fact, a club ladder/grading system, not a tournament system. Anyway, the BGA used it as a tournament system and, apart from one small bug (later) the first time around, it seemed a success. So much so that eventually it spread to Europe and back to America.
The bug: the mistake they made the first time around was to say if you win you move up one, and if you lose you go down one (rather than staying the same). This meant that if your McMahon score was even in the first round then it was odd in the second round and vice-versa and similarly in later rounds. This meant that people who started with an even McMahon score (almost) never played people with an odd McMahon score and so effectively they had two separate tournaments going on side-by-side. Oops! They got it right the second time around."
It is often called MacMahon too, but nobody is quite sure why. The BGA Journal Feb 1978 refers only to MacMahon for example. Although a few years previous to that, McMahon was exclusively mentioned.
Personally I would be interested in finding more information on the original usage in New York Go Club.
- Group Pairing
- Swiss Pairing
- Tournament Directing Software
- McMahon Example
- British Go Association McMahon Tournament Pairing Rules
- AGA tournament standards highly recommended
- Christoph Gerlach's thesis (PDF file, in German)
- Cambridge Go club page on McMahon
- Geoff Kaniuk on McMahon
- Olli Lounela's description of McMahon ( Wayback machine link (2002) to Olli Lounela's page )
- McMahon explained by Christoph Gerlach
- According to page 95 of the 1986 Ranka Yearbook (at least as quoted here), the original McMahon system was invented by Lee McMahon and Bob Ryder of Bell Labs.
- RGG: MacMahon and Swiss Tournaments