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McMahon
    Keywords: Tournament

Christoph Gerlach: This page is not very informative and not well structured. I will master-wiki-edit this page and explain more about the system when I will find time (might take until the end of October 2004).


McMahon has become the standard pairing system? in amateur Go Tournaments.

A McMahon tournament is essentially a Swiss Tournament in which each player starts on a score that corresponds to their rank, rather than starting on 0. E.g., a n-kyu player could start at -n, 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 pairings 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] http://britgo.org/history/bgahist.html.

--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?

Thanks,

-- 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 ?

--Dieter


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".

--Bill


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.



This is a copy of the living page "McMahon" at Sensei's Library.
(OC) 2004 the Authors, published under the OpenContent License V1.0.