McMahon Tournament System: How the Format Works

The McMahon tournament system is a pairing format for individual competitions, most often used in Go, chess variants, and other two-player games. It combines elements of Swiss and knockout systems by giving each player a starting score based on their rating or rank. Players are then paired each round against opponents with similar current scores, and the player with the highest total score at the end is the winner. This guide explains how to organize a McMahon tournament for a group of friends, covering starting scores, pairings, scheduling, and final standings.

What Is the McMahon Tournament System?

The McMahon tournament system is a method of pairing players in a multi-round competition. Each player begins with a starting score determined by their rating or rank. In each round, players are paired against opponents with the same or similar current score. A win typically adds one point to the player's score, a loss adds zero, and draws may add half a point. After a set number of rounds, players are ranked by their total score: starting score plus earned points.

Unlike Swiss tournaments, where all players start at zero and are paired solely on current wins, the McMahon system uses rating groups to give stronger players a head start. This ensures that top players meet later in the tournament, while less experienced players face appropriate opposition throughout. The system is named after Lee McMahon, who developed it for Go tournaments.

How Do Starting Scores Work?

In a McMahon tournament, each player's starting score is derived from their rating or rank. For example, in a Go tournament using a common scale, a player rated 4 kyu might start at 0 points, while a 1 dan starts at 5 points, and a 5 kyu starts at -1 point. The exact assignment depends on the tournament's rating bands. You can define these bands based on your group's skill levels.

A simple approach for friends: assign each player a number based on their experience or a known rating. For instance, a beginner starts at 0, an intermediate at 2, and an advanced player at 4. The exact values are up to you, but the differences should reflect the expected skill gap. If you have enough players, you can create groups of similar strength, each with its own starting score.

How to Set the McMahon Bar and Thresholds

The McMahon bar is a score threshold that determines the pairing bands. Typically, the bar is set just below the starting score of the highest-seeded players, so that top players are in a group by themselves for the first round. The bar can be adjusted between rounds to ensure that players are not paired against the same opponent twice and that the top group remains competitive.

For a casual event, you can simply set the bar as the highest starting score, and then group players who are within a certain range of the bar. For example, if the highest starting score is 4, players with scores 3 and 4 might be in the top band, 1 and 2 in the middle, and 0 and below in the lower band. After each round, players' scores change, and they are re-grouped accordingly.

Step-by-Step: Creating Round Pairings

Pairing players each round is the core of the McMahon system. Follow these steps:

1. Sort players by their current score from highest to lowest. Use tie-breakers such as their rating or previous opponents' scores if needed.
2. Group players with the same score, or within a small score range, into rating groups for pairing. In a small tournament, you might group all players within one point of each other.
3. Within each group, pair the top half against the bottom half. For example, if there are 8 players in a group, Player 1 plays Player 5, Player 2 plays Player 6, and so on.
4. Ensure no two players meet twice. If a pairing would repeat, swap players within the group or with an adjacent group.
5. Assign colors or sides (e.g., black/white in Go) as evenly as possible. Players should alternate colors; if both have had the same color sequence, use a random method or the higher-rated player gets the less desirable color.
6. Publish the pairings clearly before each round.

Example: Suppose after round 1, scores are: Alice 5, Bob 5, Carol 4, Dave 4, Eve 3, Frank 3. Pair Alice vs Bob (both 5), Carol vs Dave (both 4), Eve vs Frank (both 3). If Alice and Bob already played, swap Bob with Carol, so Alice vs Carol (5 vs 4) and Bob vs Dave (5 vs 4), which is acceptable if score difference is small.

Planning a Realistic Schedule

A McMahon tournament requires a fixed number of rounds, usually between 3 and 6, depending on the number of players and available time. Here is a sample schedule for a one-day event with 8 players and 4 rounds:

Adjust round lengths based on the game. For a board game like Go, a casual round might be 45–60 minutes. Always include buffer time for slower games and unforeseen delays.

Communicating Pairings and Scores

Make the next round clear to everyone by using a visible pairing board or a shared digital document. Post the current scores and the pairings after each round. For each game, indicate the table number, player names, and the color or side assignment. Announce the start of each round and remind players of the time control.

A typical pairing format: "Table 1: Alice (5) vs Bob (5). Alice plays Black." Keep a running score sheet where players can see their total points.

Determining Final Standings

After all rounds are complete, rank players by their total score (starting score + earned points). Use tie-breakers in this order if needed:

1. Sum of opponents' scores (stronger opposition gives a higher tie-break).
2. Head-to-head result if only two players are tied.
3. Rating or starting score (higher starting score wins the tie).

Example: Alice and Bob both finish with 7 points. Alice played opponents with total scores 20, Bob's opponents totaled 18. Alice ranks higher.

Announce the final standings clearly, and consider small prizes or certificates for the top finishers and perhaps a "most improved" award.

Handling Breaks and Changes

Unexpected events happen. If a player must drop out or arrive late, adjust the pairings. A late player may be given a zero-point bye for the round they miss, and then re-enter with that score. If an odd number of players remains, the lowest-scoring player receives a bye (typically awarded full point) and helps with pairings or timing.

Keep the group informed of any changes via announcements or a messaging app. Flexibility is key to keeping the event friendly and enjoyable.