Swiss System in Chess: How Pairings and Rounds Work

The Swiss system is a tournament format in which no player is eliminated and not everyone plays everyone. Players with similar scores are paired against each other, no two players meet twice, and the pairings for each round are made only after the previous round has finished. The method suits events with too many entrants for a round robin, where nobody wants to be knocked out early.

History

The system was first used at a chess tournament in Zurich in 1895 and is credited to Julius Müller, which is where the Swiss name comes from.

How a round is paired

In the first round pairings are random or follow a pattern, often with the top half of the field paired against the bottom half. In later rounds players are sorted by cumulative score and paired within each score group. The number of rounds is fixed in advance. To produce a clear winner it takes about as many rounds as a knockout bracket, which is the binary logarithm of the number of players rounded up. With sixteen players, for example, four rounds do the job in principle.

If the number of players is odd, one player sits out each round and normally receives the points for a win, never a second time.

Pairing methods and tiebreaks

FIDE’s default for chess is the Dutch system, in which players are grouped by score and the top half of each group is paired with the bottom half. The Monrad system orders players by score and starting number and gives each the next suitable opponent, and it is common in Denmark and Norway. The Burstein system resembles the Dutch one but orders players within a score group by rating and tiebreaks. Accelerated pairings meet the strongest players sooner.

Players who finish on equal scores are separated by a tiebreak, of which the Buchholz system, the sum of the opponents’ scores, is the best known.

Strengths and weaknesses

Everyone stays in the event and the whole field is ranked. The drawbacks are a possible dull final round when a leader has already clinched first place, and the need to finish each round before pairing the next.

Number of rounds in practice

The rule of thumb is simple: three rounds can separate up to 8 players, four rounds up to 16, five rounds up to 32. The count only guarantees a single player with a perfect score if every game is decisive, which draws make unlikely, so organisers often add a round or accept shared first place and settle it by tiebreak. The natural ceiling is half the number of entrants, rounded up.

A worked example with eight players

Take eight players seeded 1 to 8 in a three-round event. In a Dutch pairing the first round puts the top half against the bottom half: 1 against 5, 2 against 6, 3 against 7 and 4 against 8. If the higher seeds win, four players are on 1 point and four on 0. Round two pairs inside those groups, so the four winners play each other and the four losers play each other. After it, two players have 2 points, four have 1 and two have none. The two leaders meet in round three, and the rest are paired within their own score groups. Nobody has been eliminated, and every player has played three games.

Pairings also have to avoid rematches while keeping colours roughly even, and in chess the aim is that nobody plays the same colour three times in a row.

Byes

A field with an odd number of players cannot be paired completely, so one player receives a bye in each round. The bye counts as a win, worth a full point in chess, and no player is given a second one.

Tiebreaks in more detail

Several players usually finish on the same score, so the order is settled by tiebreaks. Buchholz, the sum of the opponents’ final scores, rests on the idea that a player who met strong opponents earned the same points under harder conditions. It was developed by Bruno Buchholz, who died in 1958, and the first recorded use is probably the Bitterfeld tournament of 1932. Two variants are common. Buchholz Cut-1 leaves out the single lowest opponent score, and median Buchholz drops both the highest and the lowest, which reduces the distortion caused by one unusually weak or strong opponent, especially in early rounds. The Buchholz tiebreak is equivalent to the older Solkoff system.

Accelerated pairings

In an open Swiss with a wide rating range, the first rounds are often dull for the strongest players, who meet far weaker opponents. Accelerated pairings give the top half of the field an extra point for pairing purposes in the first two rounds. Without acceleration about one quarter of the players have a perfect score after two rounds. With it the figure falls to about one eighth, so the leaders meet sooner, although the result is not guaranteed in any single event.

Other games and other formats

The Swiss system is used in bridge, chess, Go and other games. The first United States national event run under it was held in Corpus Christi, Texas, in 1945, and the first Chess Olympiad paired this way took place in Haifa in 1976. Go tournaments in Europe and America mostly use the McMahon system, a Swiss variant in which players start with points set by their strength, which avoids lopsided early games. In bridge the Danish system lets the final rounds repeat pairings between leading teams. At Scrabble events the Gibson rule can pair a player who has already clinched first place against someone who cannot win a prize, leaving the others to compete for the remaining places. Esports qualifiers use a Swiss in which teams advance or are removed on reaching preset win or loss counts.

Where it appears

Scoring rules and tiebreaks matter most in events of this kind, and the article on BAP scoring compares several systems. Tournaments of other games are covered in the piece on the World Xiangqi Championship, and the chess history page gives the wider background.

Questions