# Swiss pairing parameters

I realize that there are various types of Swiss pairing systems. What would be a minimum set of parameters that needs to be specified in order to avoid ambiguity in pairings? I am thinking of parameters like "initial order", "fold/slide/adjacent pairing", ...

Does such deterministic system actually exist or will there always be some pairings that have to be decided by an arbiter or by flipping a coin?

Trying to clarify with an example: As far as I understand for any major tournament there should be rules (either set by FIDE or the organizers) regarding the way the pairings are done. These rules should specify all kinds of things like for instance, how do you pair players with the same number of points? Do you pair the strongest with the second strongest or you split the group in two and pair the first from the first group (i.e. the strongest) with the first from the second group (i.e. the one of medium strength).

Now if all of these rules/parameters have been set, is there still any ambiguity left? Or conversely, is it possible to satisfy all rules or would some get precedence in case they contradict each other?

For instance FIDE specifies that no player should play three games in a row with the same color. But if there are only two players (who both have played the last two rounds with the black pieces) with 7 points left who are therefore going to be paired. What is going to happen then? Is the FIDE rule of three same-color games going to be violated or are they going to be paired with other players first?

Basically what I am asking is, whether in practice the rules are stated and followed completely (meaning that all kinds of exceptions need to be stated) or whether pairing rules are only laid out roughly and if necessary the organizer is entitled to change some pairings?

• It's not clear what you are asking. Perhaps if you read what FIDE have to say about Swiss pairing rules here - fide.com/fide/handbook.html?id=18&view=category you will be able to make yourself clear in the case that that does not already answer your questions. Feb 4, 2017 at 13:40
• @BrianTowers: I read the FIDE rules and am still confused. That's why I asked here. I tried to clarify what I am asking in the question. Feb 4, 2017 at 17:18

## 4 Answers

What would be a minimum set of parameters that needs to be specified in order to avoid ambiguity in pairings?

The minimum would be to have just one rule. Do your first round pairings by sorting players according to their ID number... and then, in the second round, do it again. If you don't have any rules about repeating colors, scores, or meeting the same player twice, there's no ambiguity possible. If you don't want to flip a coin to see who gets White, just declare that the highest-rated player gets White.

This would, of course, be ridiculous and unfair. But it would be unambiguous and minimal!

Now if all of these rules/parameters have been set, is there still any ambiguity left? Or conversely, is it possible to satisfy all rules or would some get precedence in case they contradict each other?

Assuming you have sane rules (not like the one I described above), there are pretty much going to be rules which have precedence over other rules. If White wins more often than Black, there's no way you can have a color preference rule and a same-scores rule without one taking priority. Under FIDE Dutch rules, there is a minimum set of "absolute" rules, and many more "quality" rules with specified precedence.

For instance FIDE specifies that no player should play three games in a row with the same color. But if there are only two players (who both have played the last two rounds with the black pieces) with 7 points left who are therefore going to be paired. What is going to happen then? Is the FIDE rule of three same-color games going to be violated or are they going to be paired with other players first?

The following is considered an "absolute" rule:

non-topscorers with the same absolute colour preference shall not meet

Assuming that 7 points is a "topscorer" (has over half the maximum possible points), then pairing the people with the same absolute color preference would not violate the absolute criteria. And then, "minimize the Pairing Score Difference" has a higher priority than "minimize the number of topscorers or topscorers' opponents who get a colour difference higher than +2 or lower than -2" and "minimize the number of topscorers or topscorers' opponents who get the same colour three times in a row." So the answer is usually going to be that the rule of three same-colored games will be violated, so as to comply with the higher-priority rule that the pairing score differences be minimized. (It's possible that the various absolute rules would require another resolution, of course. For example, if the two players with 7 points had already played each other, they wouldn't be able to play each other again.)

Under the FIDE Dutch rules, with the exception of the coin flip at the beginning to determine colors, the pairings are very deterministic. They have rules like:

All the possible transpositions are sorted depending on the lexicographic value of their first N1 BSN(s), where N1 is the number of BSN(s) in S1

which means the organizers can't ordinarily decide things like which possible transposition to take. There's not any wiggle room.

The exception is if it's somehow impossible to comply with the absolute rules:

If it is impossible to complete a round-pairing, the arbiter shall decide what to do.

The only scenarios I could think of where this might happen is an extremely low turnout, or a mass walkout. (If you have 8 rounds and 8 players, you can't avoid playing the same opponent twice. Or, if everyone who played White quit before playing, after the first round everyone would ineligible for the bye because they'd already had a forfeit win, and after two rounds you'd also have non-top scorers that all had the same absolute color preference.)

• what do you mean by ambiguity? all you need is round number, players name/number, color assigned, table location, but there are other factors for fair pairing. Feb 8, 2020 at 21:39
• @edwinaoliver Ambiguity in generating the pairings, not in the pairings themselves.
– D M
Feb 8, 2020 at 21:47
• There is no ambiguity in generating pairings that I can see. Unless you foolishly pair two people to the same opponent. Then the name/number would have prevented that as noted above. Feb 8, 2020 at 22:34

As actually worded the answer to the OP is two.

As apparently intended, no number is sufficient in some cases.

Generally you only need a very few to do fair pairings. Or as fair as is possible in a particular case.

I used to be a TD before computers and all you need is cards with names/ratings and results so far, and a pencil. With a little bit of planning ahead, and common sense to pair from the extremes to the middle not the middle out or top to bottom. EG round one you alternate w/b given to players in order of round 1 pairings.

Is this question prompted by Hou Yifan's unfortunate experience at Gibchess this year?

The point for her was she was expecting to be paired with less women and 7 out of 9 pairings was rather high.

However the pairing rules made no provision for her gender and have a small but finite probability that this would happen.

How can you make pairings gender agnostic by ignoring gender which they did.

• Welcome to Chess SE! While what you're saying makes sense, it doesn't answer the question at hand. It should be maybe a comment. Stack Exchange is a Q&A site, which is different from a discussion forum. Feb 4, 2017 at 15:17
• Not prompted, but let's say inspired by Hou Yifan's experience. Feb 4, 2017 at 17:19
• @user1583209 Hou Yifan's experience was unfortunate and was brought about partly by Yifan's results and partly by the very generous conditions which Gibtel provided for women players which attracted an unusually large number of highly rated women chess players. Section C.04.2 General handling rules for Swiss Tournaments is explicit - "It is not allowed to vary the correct pairings in favour of any player." If the Gibtel arbiters had varied the pairings from the ones the computer gave to suit Yifan's wishes any title norms for other players would also have been invalidated. Feb 4, 2017 at 20:50
• You have to rate by results so far and players rating. Gender is not a valid factor for swiss pairing. Dec 16, 2019 at 1:43
• @Glorfindel that is a stack problem as you need 50 points to comment but anybody can answer. Jan 7, 2020 at 3:42

In general your questions are all answered in the FIDE Handbook section for FIDE Swiss Rules and its subsections.

For instance, you ask:

For instance FIDE specifies that no player should play three games in a row with the same color. But if there are only two players (who both have played the last two rounds with the black pieces) with 7 points left who are therefore going to be paired. What is going to happen then? Is the FIDE rule of three same-color games going to be violated or are they going to be paired with other players first?

This is answered in C.04.1 Basic rules for Swiss Systems as follows:

f For each player the difference of the number of black and the number of white games shall not be greater than 2 or less than –2.

Each system may have exceptions to this rule in the last round of a tournament.

g No player will receive the same colour three times in a row.

Each system may have exceptions to this rule in the last round of a tournament.

If you take the trouble to read the specifications for the Dutch system, the most commonly implemented system in approved Swiss pairing programs, in C.04.3.1. Dutch System you will find it expands on how this is handled by this system in the last round:

B Pairing Criteria
Absolute Criteria

(These may not be violated. If necessary players will be moved down to a lower score bracket.)

B.1 a Two players shall not meet more than once.

b A player who has received a point or half point without playing, either through a bye or due to an opponent not appearing in time, is a downfloater (see A4) and shall not receive a bye.

B.2 Two players with the same absolute colour preference (see A7.a) shall not meet (therefore no player’s colour difference will become greater than +2 or < -2 nor a player will receive the same colour three times in row)

Note: If it is helpful to reduce the number of floaters or the score of a floater when pairing top scorers B2 may be ignored. If a top scorer is paired against a non-top scorer, the latter is considered a top scorer for colour allocation purposes.

"Top scorer" is defined as follows:

Top scorers are players who have a score of over 50% of the maximum possible score when pairing the last round.

• But how are those "exceptions" handled in practice? Is it up to the arbiter or would this have to be decided before the tournament starts? Feb 4, 2017 at 20:41
• Again the answer is given in the FIDE handbook section. See C.04.2 General handling rules for Swiss Tournaments "The pairing system used for a FIDE rated tournament shall be either one of the published FIDE Swiss Systems or a detailed written description of the rules shall be explicitly presented to the participants." In my answer I gave you chapter and verse from the description for the Dutch system which is the system implemeted in most FIDE approved pairing programs. The program handles the exceptions as described. Feb 4, 2017 at 20:54