McMahon Tournament Pairing: How to Set Up and Pair Each Round

What is McMahon tournament pairing?

McMahon tournament pairing is a method of matching opponents in a tournament for games like Go, where players have known ranks. Unlike Swiss pairing, which treats all players as equal at the start, McMahon gives players initial scores based on their ranks. This spreads the field and reduces mismatches in early rounds. Each round, players are paired with opponents who have the same or similar current scores, and wins add to a player's score. The system is named after Lee McMahon, who adapted it for Go tournaments.

How do McMahon tournament starting scores work?

McMahon tournament starting scores are assigned before the first round. The top-ranked player (or a chosen reference rank) gets a baseline score, often 0, and each rank below adds points. A common set-up is: top rank gets 0, next rank gets 1, then 2, and so on. For example, in a tournament with ranks from 5-dan to 20-kyu, the 5-dan might start with 0, 4-dan with 1, down to 20-kyu with 15. Some tournaments add a fixed bonus, like 0 or 2, to avoid negative scores. In each game, a win adds 1 point to the winner's score; a loss adds 0. Some events use tie-breakers like SOS (sum of opponents' scores) to rank players with equal wins.

How to set up a McMahon tournament step by step

1. Collect player ranks

Ask each participant for their rank in the game (e.g., Go rank: 3-dan, 1-kyu, etc.). Convert ranks to a numeric scale for easier calculation. In Go, dan ranks are positive (higher is stronger), kyu ranks are negative. For McMahon, a simple approach is to define a starting score formula: starting score = (top rank number) - (player's rank number). For instance, if the top player is 5-dan, that rank is 5; a 1-dan has starting score 5 - 1 = 4, a 5-kyu (rank -5) has 5 - (-5) = 10.

2. Determine the McMahon bar

The McMahon bar is a score threshold that separates the top group. Players with starting scores at or above the bar are considered 'above the bar' and will be paired only among themselves for the first rounds, unless the field is small. A typical bar is set so that the top 25-50% of players are above it. For example, with 16 players and starting scores 0 to 8, the bar might be at score 4, meaning players with scores 0-3 are above the bar. This reduces early mismatches.

3. Create initial score groups

Group players by their starting scores. Players with the same score form a score group. In the first round, players within each group are paired against each other. If a group has an odd number, one player may be paired with a player from the adjacent group (the next higher or lower score), or receive a bye. Pairing within a group is usually done by random draw or by ranking within the group (e.g., top half vs bottom half).

4. Pair each round using McMahon pairing rules

After each round, update scores: winner +1, loser +0. For the next round, again form score groups based on current scores. Within each group, pair players who have not played each other before. If a player cannot be paired within their group without a repeat, they may be paired with someone from an adjacent group. Key rules: avoid repeat opponents, minimize score differences, and balance colors (in games like Go, alternating black and white).

5. Handle byes and odd numbers

If there is an odd number of players, one player gets a bye each round. The bye usually counts as a win (adds 1 point). Give byes to the lowest-scoring players first, and avoid giving the same player multiple byes. In some tournaments, a bye gives 0.5 points.

How to make the next round clear to everyone

After each round, publish the pairings for the next round promptly. Use a tournament board or software. List each pairing with player names, ranks, current scores, and board numbers. Announce the time for the next round clearly. Provide a printed or digital bracket showing the progression of scores. Avoid last-minute changes and explain any pairing anomalies (like floaters) to the affected players.

Planning a realistic schedule

For a one-day event, 3-4 rounds are common. For a weekend, 5-6 rounds. Each game duration depends on the game and time limits. In Go, a typical game with 30 minutes per player plus byo-yomi lasts about 1.5-2 hours. Add 15-30 minutes between rounds for pairing and breaks. Example schedule for 4 rounds: Round 1 10:00-12:00, break, Round 2 13:00-15:00, break, Round 3 15:30-17:30, Round 4 18:00-20:00. Adjust based on player fatigue and venue.

Comparison of McMahon vs Swiss pairing

Examples of McMahon pairing in practice

Suppose 8 players with starting scores: A:0, B:1, C:2, D:2, E:3, F:3, G:4, H:4. Bar at 3 (so A,B,C,D,E are above bar). Round 1 pairings: A vs B (scores 0 and 1), C vs D (both 2), E vs F (both 3), G vs H (both 4). After round 1, winners gain 1 point. If A beats B, C beats D, F beats E, G beats H, new scores: A:1, B:1, C:3, D:2, E:3, F:4, G:5, H:4. Round 2 groups: score 1: A,B; score 2: D; score 3: C,E; score 4: F,H; score 5: G. Pair within groups where possible: A vs B (again? If they already played, avoid repeat; pair A with D and B with a bye or float), C vs E, F vs H, G vs a floater. This illustrates how the system adapts.