McMahon vs Swiss pairing: which to use for a 40-player club

Roberto Delgado · 9 September 2026

A club tournament on a Saturday rarely looks like an open. You do not have 128 unknown players and a weekend to “discover” the field. You have about forty regulars, ranks from 15 kyu to 3 dan, five rounds, and a room that has to be empty by 7 pm.

Swiss pairing and McMahon pairing both keep everyone in the tournament. Nobody is knocked out after a loss. The difference is the starting score — and for a mixed club, that one number decides whether round 1 is a real game or a massacre.

The problem Swiss is built to solve

Classic Swiss pairing starts every player at 0. After round 1, winners sit on 1, losers on 0. Round 2 pairs people with the same (or nearest) score, avoids rematches, and hands a bye to someone if the field is odd. Repeat until you run out of rounds. The player with the most wins is first.

That is the right tool when you do not already know who is strong. A chess open, a card-game event, an esports LAN where ratings are missing or untrusted: Swiss lets the results invent a ranking. The cost is time. The field only sorts itself after enough rounds for the strong players to climb and the weak ones to fall.

A rough floor is log₂(N) rounds if you want a unique leader in a pure knockout sense: 5 rounds for 32 players, 6 for 64. Forty players sit between those. Five rounds often leave two or three people on the same score at the top; the title is then a tie-break (Buchholz, Sonneborn-Berger, head-to-head), not a game. Six rounds is kinder. A one-day club almost never has six.

What McMahon changes

McMahon is Swiss with a head start. Each player begins with a number taken from rank — dan players high, kyu players lower — so round 1 already pairs similar strength. A 3 dan does not need three rounds of beating 12 kyus before they meet another dan. A 15 kyu is not thrown onto a board against 2 dan in the first pairing just because both have 0 points.

If every seed is equal, McMahon collapses into ordinary Swiss. The extra machinery only earns its keep when the ranks are real and spread out.

Two club-specific knobs matter more than the slogan:

Bottom bar (floor). Without a floor, a beginner who loses the first two games can sit on a large negative McMahon score and spend the rest of the day in games that teach nothing. A floor (often 0) keeps them in a competitive band.
McMahon bar. The bar sits on the top group and typically rises one point per round. Games inside that group are treated as even (no handicap stones in the usual EGF-style reading). Below the bar, pairing still follows score, but you are no longer pretending the top of the club and the teaching ladder are the same tournament.

A concrete field: 40 players, 15 kyu to 3 dan, 5 rounds

Suppose the club list looks like this: four players 1 dan and above, eight in 1–4 kyu, twelve in 5–9 kyu, ten in 10–15 kyu, six complete beginners. You have five rounds. Here is a simple band table a director can put on the wall before round 1. The start scores are an example, not a federated law — what matters is that the gaps are published and stable.

Band	Rank range	Players	Start score
Top	1 dan and above	4	4
Upper	1–4 kyu	8	3
Mid	5–9 kyu	12	2
Lower	10–15 kyu	10	1
Floor	Beginners / unranked	6	0

Round 1 under Swiss: everyone is on 0, so the pairing algorithm has no rank to respect. You will get some even games by luck and some 3 dan vs 12 kyu boards that are over in 40 minutes. Round 1 under this McMahon table: the four dans start on 4 and are almost forced to play each other (or the top kyus). The beginners start on 0 and meet other 0s. After five rounds the dans have played a short round-robin among peers; the teaching group has also played five real games. The wall list at the end is a club ranking, not a list of who got lucky with pairings.

Swiss can reach a similar sort — if you had eight or nine rounds. You do not.

Handicap stones are a different lever

Directors mix these up constantly. McMahon start score changes who you sit against. Handicap stones change the rules on that board (extra stones for the weaker player, usually as Black).

You can run McMahon with even games only (typical of many opens above the bar). You can run McMahon plus handicap below the bar so a 5 kyu vs 10 kyu is still a game. You can run Swiss with handicap if you insist. Do not treat “we use McMahon” as a substitute for deciding stones. Publish both: the band table, and whether stones are on or off.

When Swiss is still the better choice

Ranks are missing, stale, or political. If half the field “is 5 kyu because they said so”, McMahon just encodes the lie. Swiss ignores the lie and listens to the games.
The field is already even. A dan-only evening, a school year-group, a chess open with ratings in a narrow band: the head start is noise. Swiss (or a round-robin) is cleaner.
You have enough rounds. A two-day event with 7–9 rounds can afford to start everyone at 0. McMahon still works; it is no longer required.
The sport has no shared rank scale. Padel, football, most esports: there is no kyu/dan. Swiss, groups, or knockout — not McMahon.

McMahon is a Go (and similar rank-band) tool. Using it in a football five-a-side because the software offers the format is how you get a nonsense table.

A short decision rule

If you already know the ranks, the spread is wide, and you have few rounds → McMahon, with a published floor and bar.
If you do not trust the ranks, or everyone is close → Swiss, and budget log₂(N) rounds or accept a tie-break finish.
If N is small (8–12) and you have the afternoon → a round-robin is still the fairest pairing. Neither Swiss nor McMahon beats “everyone plays everyone” when the calendar allows it.

For the 40-player Saturday in the table above, that rule says McMahon. Five Swiss rounds would still be a pleasant day of Go. It would not be a ranking of the club.

Pairings after you have chosen

Once the format is picked, the pairing job is the same: no rematches, odd player gets a bye that counts as a win, floating (playing up or down a score group) should be shared rather than dumped on the same two people, and colours (Black/White) should not all pile onto one player. That machinery is independent of the start score. McMahon does not excuse a sloppy round 3 pairing.

If you want the product walkthrough for running these formats in a browser — generating a round, recording results, exporting a wall list — those live separately: the Go / McMahon guide and the Swiss generator guide. This page is only the choice of format.