Swiss Pairing

    Keywords: Tournament

Swiss Pairing is a TournamentFormat, i.e. a method of pairing players in a tournament. First used in Switzerland in 1895, Swiss pairing based tournaments are primarily associated with chess, they have also been used for a number of amateur go tournaments, notably the World Amateur Go Championship. The Swiss Paring method addresses significant problems of round robin and single elimination tournaments.

  • Round robin tournaments require as many rounds as the number of players minus 1. Many tournaments are limited to a single weekend which limits play to about 5-6 rounds provided reasonable time limits (one hour per player with some byo-yomi). The field is then limited to six players. Swiss pairing limits the number of rounds required to log base 2 of the number of players.
  • Single elimination tournaments leave half the field with nothing to do after the first round. Each successive round half the field is eliminated leaving these players with nothing to do. Swiss pairing is one way to provide pairings for all players in all rounds.

Swiss Pairing Method Details

  • First Round: The Swiss pairing method does not mandate how players are paired for the first round, any of the Group Pairing methods may be used. In chess, fold pairing or slide pairing (see Group Pairing) is typically used. After the first round, players that won their game or received a bye are awarded one point[1] and therefore have a score of 1. Players that lost, do not receive a point and so have a score of 0. Players that tied, if the komi allows it, receive half a point, as do those that did not play (e.g. because they were late). Roughly half of the players now have a score of 1, and roughly half the players have a score of 0.
  • Second Round: Players with the same score are paired against each other using any of the Group Pairing methods. In chess, fold or slide pairing is typically used. Again, players that won their game are awarded one point and therefore have a score of 1. Players that lost, do not receive a point and so have a score of 0. There are (assuming no ties) three groups of players: those with a score of 2 (one quarter of the field), those with a score of 1 (half the field), and those with a score of 0 (one quarter of the field).
  • All Subsequent Rounds: Players with the same score are paired against each other using any of the Group Pairing methods. The process is repeated till only one player has a perfect undefeated record provided there is a sufficient number of rounds.

Tournament Placings

First place is the tournament winner. Placings are ususally based upon number of wins and one or more tie breakers.

Problems with Swiss Pairing

  • In order to have the highest rated players meet each other in the final rounds of the tournament either fold pairing or slaughter pairing is often used. These pairings make the first rounds of the tournament quite boring as the players have significantly different strengths. McMahon Pairing addresses this problem.
  • If there are N participants in the tournament, Swiss pairing requires log base 2 of N rounds. For large tournaments, such as the 2008 North American Toyota Denso Oza Championship with 200 players, eight rounds are required. The tournament provided for only six rounds. For Swiss paired tournaments that have less than the required number of rounds, there will be more than one player with a record of all wins. In that case, the final ranking is usually based upon the following criteria:
    1. number of wins (called "score", but not to be confused with the scores of the games)
    2. additional tie breakers
  • Unless N is a power of two, the number of players with the same score will be odd for one or more rounds. An odd number of players cannot be paired. At least one player must be paired against someone with a different score. This may result in a different group of players with the same score having an odd number of unpaired players. The problem may thereby ripple across the score groups.
  • In order to make the pairings as fair as possible, the pairing rules can become quite complicated (see, for example, the [ext] FIDE Swiss Rules). This problem is particular to chess due to the significant advantage of having the white pieces (first to play) combined with the lack of komi in chess. Due to these complications for chess pairings, the pairings are usually done by computer. Many programs are available to do this, in particular any program that can handle McMahon Pairing should be able to handle Swiss Pairing - since the Swiss Pairing is identical to McMahon Pairing with all players' starting McMahon Score set to zero.

Historical Information

The Swiss system is so called because it originated in Switzerland: the first person to suggest the system appears to have been a Swiss citizen named Dr Julius Müller (not to be confused with the German theologian of the same name), and the first chess tournament run under this system took place in Zürich in 1895.

Number of rounds and validity of places.

Swiss is in general good to decide who ends up at the top spot. (The one player who wins all her games), unfortunedly it is not always clear who should get the 2nd and third place prize. there are many different tiebreakers for doing this

An old rule to approximately decide on the number of rounds, number of players and number of validated places was invented by Mr. Model. His formula was:

  • R = (P + 7 x Q) /5

in which

  • R is the number of rounds,
  • P is the number of participants, and
  • Q is the number of qualified places

xela: The above was added by an anonymous IP address, based on a source that's paywalled, and gives ridiculous results for large tournaments (more than about 30 players). I don't think "Mr. Model" is a real person, and I wonder if this is a practical joke. Scroll down to "another approximation" for something more practical.

This formula can be applied in several ways:

  • Example 1: Suppose there are 20 participants and 3 will receive a prize. In this case the number of rounds is (20 + 7 x 3) : 5 -> (20 + 21) : 5 = 8.
  • Example 2: There is time to play 9 rounds, there are 4 prizes. How many participants should take part? 9 = (P + 7 x 4) : 5 -> 45 = P + 28 -> P = 17
  • Example 3: There are 16 participants and there is time for 12 rounds. How many places at the top are more or less reliable? 12 = (16 + 7 x Q) : 5 -> 60 = 16 + 7 x Q → 44 = 7 x Q -> Q = 6.

(this is from [ext]

Using this rules gives the following table

Rounds   players  number of places validated
  6         26          1
  6         19          2
  6         12          3
  7         17          3
  8         24          3
  9         31          3

Another approximation is:

The number of rounds for a Knock out plus 2 rounds per validated place

(From the Chess Organisers Handbook)

See Also

[1] It is also possible to choose 0.5 points for a Bye. This is generally avoided in Go as the probability of a draw is rather low.

Swiss Pairing last edited by xela on March 20, 2024 - 11:49
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