McMahon Pairings

Is McMahon right for you?

Are you tired of getting slaughtered in so many your tournament games? This is what happens to many players in a Swiss tournament.

Or, perhaps you are in the top 20% of the field and you tired of playing much weaker players for the first two rounds? This is what happens in a Swiss tournament.

If your answer to either of these questions is, "Yes," then the McMahon tournament is for you!

The McMahon system is designed to pair players with opponents of approximately equal strength. Each time you win a game, you are more likely to be paired against a stronger opponent in the next game. Each time you lose a game, you are more likely to be paired against a weaker opponent.

You now have all the information you need to enter a McMahon tournament and to feel comfortable during the rounds. If you want to understand more about how McMahon works, keep on reading.

How does it work?

McMahon pairings are similar to Swiss pairings. As in Swiss pairings, you get a point for every game you win and a half point for every bye. The essential difference is that in Swiss pairings, your initial score is set to zero while in McMahon tournaments, your initial score is derived from your KGS rank.

Players with higher ranks generally get higher initial scores in a McMahon tournament. This is similar to the common method of "seeding" that is used in Swiss tournaments.

Swiss tournaments are sometimes divided into sections according to playing strengths. Players are paired with players in their own section. This results in games where the opponents are more equally matched. Such a tournament is a "Sectioned Swiss."

The McMahon system automatically pairs players with similar playing strengths. This is achieved by matching players with similar scores. As your score increases throughout a McMahon tournament, you are paired with stronger players. In a McMahon tournament, all players with the same score are in the same "bar."

The "bars" in a McMahon tournament are analogous to the "sections" in a Sectioned Swiss.

Think of the Swiss "sections" as a collection of bowls. At the beginning of the tournament you are placed in one of the bowls, and you stay there until the end of the tournament.
Think of the McMahon "bars" as rungs on a ladder. As the tournament progresses, you can move up the ladder, but you never move down the ladder.

In fact, Dr. Lee McMahon introduced the McMahon system for use in the "New York Go Club" ladder in the 1960's.

In the basic McMahon system, there is one bar for each rank spanned by the tournament. For example, in a McMahon tournament spanning the ranks from 18k to 1d, there are nineteen bars corresponding to the 19 ranks from 18k to 1d. The top bar is the 1d bar and the bottom bar is the 18k bar. This does not mean that participation in the tournament is limited to players with a rank in the 18k to 1d range.

At the beginning of a McMahon tournament, players with a rank higher than the top bar are assigned to the top bar, and players with a rank lower than the bottom bar are assigned to the bottom bar. In a tournament spanning 18k to 1d, 6d players are assigned to the 1d bar and 25k players are assigned to the 18k bar.

You advance by one bar every time you are awarded a point until you reach the top bar. If you start the tournament in the top bar, you are essentially playing in a Swiss tournament against the other top bar players.

KGS Pairing Criteria

The basic factors for generating a pairing are:

Avoid pairing the same people multiple times
Avoid high handicaps
Try to pair winners with winners
When a bye is needed, try to give it to somebody in close to last place

Sometimes these rules conflict, at which time the TD software will try to balance things out.

How to read a McMahon tournament announcement

Modern descriptions of the McMahon ladder only mention the bottom bar and the top bar. If a McMahon tournament announcement says, "the bars are 18k and 1d" it means that the bottom bar is 18k and the top bar is 1d. There are usually 19 bars in such a tournament.

For example, the February 2010 KGS Plus tournament was a McMahon tournament that used the basic system. Take a look at its tournament announcement. The phrase "McMahon (bars at 13k and 1k)" specifies that this is a McMahon tournament with 13 bars. All players 13k and below are in the bottom bar and all players 1k and above are in the top bar. It is understood that there are 11 bars between the bottom and top bar, one bar each for the 12k, 11k, 10k, ..., and 2k players. Starting with the bottom bar, the initial scores for the players will be 0, 1, 2, ..., and 12. All players in the top bar will receive a 12 for their initial score.

For another example, if the bars are "1k, 1d" then the players are initially divided into two groups. All the dans are in one group and all the kyu players are in the other group. On the first round all the dans are paired with each other and all the kyu players are paired with each other. Exceptions sometimes occur when either of the groups have an odd number of players.

Glossary

Bar: All players with the same score are in the same "bar".
- At the beginning of the tournament, the strongest players are all in the top bar, and the weakest players are all in the bottom bar.
Sectioned Swiss: Players with similar playing strengths are in the same section.

References

For more information on McMahon pairings, see any of the following pages. This page was written to provide tutorial explanations of the McMahon concepts. This page is a prerequisite for understanding the last two of the three pages listed below.