Mc Mahon Pairing/ Discussion

Sub-page of McMahonPairing

Old content and discussion below: (7-9-2005)

McMahon Pairing has become the standard in amateur Go tournaments.

McMahon Pairing essentially is Swiss Pairing, but players start on a score that corresponds to their rank rather than all starting on zero. E.g., a 1-kyu player could start at -1, a 1-dan at 0, a 2-dan at 1, etc. In order to make the competition at the top reasonably fair, a McMahon bar is set, above which all players have the same initial McMahonScore. Here are some pointers to further explanations of the system:

It is, of course, possible to do McMahon Pairing by hand, and this was normal practice until the early 1990s. However, it's now usual to use a pairing program. Some of those commonly used are:

According to page 95 of the 1986 Ranka Yearbook (at least as quoted [ext] here), the original McMahon system was invented by Lee McMahon and Bob Ryder of Bell Labs.

BillSpight: Could someone please explain the popularity of McMahon?

1) What's wrong with handicap games?

Niklaus:At almost all the McMahon tournaments I've been to, there were handicaps if there were "gaps" in the ranks of players attending (rather common at smaller tournaments (which, unfortunately, are rather common around here...)) and people with a sizeable difference in McMahon points were paired against each other. They were usually reduced by one or two stones in favour of white though, but I still had to give 9 stones once...

2) What's wrong with flights[1]?
Maybe the top flight could be even games, while the rest would be handicapped.

Historically, I suspect that McMahon arose from adapting chess-style Swiss Tournaments to go. My experience with go tournaments in the early 70s was that they were flighted and handicapped. I have never understood the AGA policy of even game tournaments.

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) where 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.

McMahon is the name of the person who invented the system . See, for example, [ext]

--Tim Hunt

Dear Tim,

Thanks for the historical note. :-)

It appears that players did desire to play even game tournaments, neither handicapped, nor flighted, nor open plus handicapped. And this when there weren't too many players, so that there were probably large ranges of strength among relatively few tournament entrants.

I am still curious why they had such a preference, or why people like the format today. Any suggestions?


-- Bill

[1] Bill, what does flighted mean ? From the context of your complaint I suspect it has to do with making separate groups, but can you provide more detail ?


Dear Dieter,

Let me illustrate with a quote from Olli Lounela's page:

<< Doing the top

It's not all that easy, however. The organizer needs to cut the increasing points somewhere. It is entirely possible that a 4 dan in good form can beat a strong 6 dan, and go on to win the tournament. To counter losing this, one sets up so called top bar, that limits the top group.
The criteria for the top bar is twofold, and very simple after all:

everyone who has realistic chance of winning tournament should be in top group

maximum size of top group becomes surprisingly small
For example, in a tournament with 5 rounds (2^5=32) I'd set up top group of at most 12 players. Why? Because the players in the next group interfere with the top group people in any case. If there are more participants who are considered winning candidates, then one needs to increase the number of rounds. Further, usually one wants also the second place resolved.

If I understand correctly, everyone in the top group gets the same McMahon score. Fine. :-)

What bothers me is the statement that the players in the next group interfere with the top group. Why? Because players with one less McMahon point than the top group who win their first game now have the same number of points as those in the top group who lost their first game, and will typically be paired with them, across the group boundary.

The problem, as I see it, is two-fold. First, among the top group, it is not unlikely that the winner will lose one game. After that loss, he may be getting a relatively easy win by a pairing with someone not from the top group.

{Note: Maybe I should have said, "not too unlikely". I have not done exact calculations. McMahon increases the probability that the winner will have no losses. For instance, after 4 rounds it is quite possible that one player in the top group will have no losses, and will have played everybody with one less point, except the player from the lower group who also has no losses. In that case they will be paired in the last round, with a likely rank difference of 3.}

Second, and more generally, players in the top group will be compared relatively indirectly, depending in part on how well they do against players in the second group. Lounela's choice of the word "interfere" is appropriate.

With flighting, the top flight would simply be restricted to, say, the top 12 players, or 4-dan players and up. They would compete among themselves in the championship flight.

The next group would compete among themselves in the first flight, etc. There would be no pairing across flight boundaries, no "interference".


Herman Hiddema: At the yearly Martini Cup tournament organised by the Groningen Go Club, we use a system without interference. It works as follows:

We organise a 5 round McMahon tournament, with 2 games on saturday and 3 on sunday. With 1 hour main time and 20 second ByoYomi.

We make sure that the top bar is such that there are more than 16 players in the top group.

From this top group, the best rated 16 players are placed in a supergroup (giving them 1 extra McMahon point).

These 16 players play knockout, with players knocked out in the first two rounds entering the normal McMahon tournament group. Games in the knockout group are played with 1h30 main time and 30s ByoYomi

This results in 4 players from the top group left on sunday, the other 12 have lost a game and are now playing the remaining 3 rounds normally.

The remaining 4 players play only 2 rounds, first semi-finals and then a final and a game for 3rd/4th place.

The players competing in the MacMahon tournament are considered to have come in 5th and further.

To resolve issues with SOS for the players from the knockout group, the 4 players playing semi-finals are given a virtual BYE in the 4th round. This puts the final and 3rd/4th place in the 5th round where the McMahon system is concerned.

So far, this system has been received enthousiastically by the players. Any input is very welcome!

How about fractional McMahon scores? Say you are playing a 6-round tournament with 50 players from 4d to 27k. give the 4d 6 - 1 = 5 McMahon points and the 27k 0 McMahon points. Each rank gets 5/30=.167 McMahon points, and in the unlikely event that the 27k wins all his/her games and the 4d loses all his/her games, the 27k will rank higher :-) More significantly, a 3k would get 4 McMahon points, so winnning all games (s)he is quite likely to win the tournament. - Migeru

Niklaus: Doesn't seem like such a good idea to me, unless one gets .167 points for a win, which still doesn't make much sense since it just complicates the math :)... The idea behind McMahon is that you play against equally strong players as much as possible. With your proposed system, if one wins the first round, one doesn't possibly get paired against a player one rank stronger who lost his first game, but somebody six ranks stronger... The "problem" you are adressing, namely low ranking players playing very good and still having no chance of winning the tournament, is more or less solved by awarding prizes for winning a large number of games in addition to awarding being on top of the table at the end of the tournament.

Migeru: The 2005 Iberoamerican Go Tournament is being run (on KGS) by dividing the participants into 4 groups initially:

  7d- 1d -- 3 McMahon points  -- 14 players
  1k- 6k -- 2 McMahon points  -- 44 players
  7k-13k -- 1 McMahon point   -- 43 players
 14k-20k -- 0 McMahon points  -- 37 players

This was actually on the suggestion of Fernando Aguilar who thought this addressed a number of concerns that players had been expressing over the years, and the results of trying out different variations of the Swiss/McMahon system. The tournament will last 8 rounds.

What was the general opinion as to the success of this format?

Phelan: I can't be sure now, but from what I remember it was favorable. The biggest problem was higher level players not playing some rounds. Some lower level players were ranked below them, despite playing all games in the tournament. Results at [ext]

Avio?: This system will produce highly unbalanced pairings. Not many but there will be some. I may have no complaints for an easy win on internet, but when I spend a lot (time and money) to come to your several hundreds km away 5 rounds tournament and you pair me to play even against 6-10 ranks lower ranked players, I will not be very happy :) It happened to me. I also experienced a pair championship where, after the first 3 rounds, in the evening, they tried a pairing for the next day. There was a mess: a 4 dan pair (the 4th rated but on three losses) was paired with a 19 kyu pair (the 20th and some rated but with 3 wins against 20 and 19 kyu pairs). Another 1 dan against 16 kyu, and few more. I remember very well the few german players spending a couple of hours to solve the problem. The final decision: reseting the whole tournament on "one rank - one point of Starting McMahon Score".

jwaytogo: I have a question about McMahon Pairing. Olli wrote "However, the primary criteria for prizes and good success should never be the current McMahon Score, but the number of wins, just as in Swiss system. In effect, McMahon points are just a tool for being able to do a meaningful pairing." Does this make sense? It is my understanding that the winner of most McMahon Tournaments is determined by the McMahon Score, and not by number of wins? I am trying to understand the McMahon system. Hope someone can help.

Andrew Grant: At the top of a McMahon tournament there is a group of players who all start on the same McMahon Score. All players gain one McMahon point per win. Therefore the player who ends with the highest McMahon Score in this group - the tournament winner - will also be the player with the most wins in this group. It makes no difference.

jwaytogo: Is it possible for a player in the second group to have the highest McMahon Score? Will he/she be declared winner? Or will only top group members be allowed to win?

Phelan: Yes, it's possible. He/she would be declared the winner. But this usually doesn't happen for two reasons: The top group is usually composed of the best ranked players; and he/she would have to play against them at some point, at which point he/she would (probably) lose. I think the purpose of the top group is to make sure the top players have challenging games, mostly amongst themselves and other good players.

Andrew Grant: The main reason for the top group is to prevent the strongest player having an unbeatable advantage. Consider, for example, a three round tournament with one 6 dan and nobody else stronger than 2 dan. Without the top group, the 2 dans would start on a McMahon Score of +1, and could not end higher than +4. The 6 dan would start on +5 and would therefore win the tournament even if he resigned all three games at move one. With the top group all starting on the same McMahon Score, the 6 dan will presumably still win but will at least have to play his games to do so.

Mc Mahon Pairing/ Discussion last edited by on May 4, 2011 - 18:40
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