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I am writing a pairing program for round-robin/double round-robin/swiss tournaments. I am looking for the rules to follow while generating the pairings. There seem to be no rules in the FIDE handbook. The only rule I know is that in tournaments like the FIDE Candidates players of the same federation are paired together as early as possible. Do there exist any other restrictions, or do I just pair the players randomly such that each player plays every other player in the tournament?

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I am looking for the rules to follow while generating the pairings. There seem to be no rules in the FIDE handbook.

The pairings are the responsibility of the arbiter and the FIDE Arbiters Commission produces a handbook which it maintains for the guidance of arbiters in the commission of their duties.

This handbook collects together various documents some of which appear in other places on the FIDE website. These include -

  1. An annotated copy of the FIDE Laws of Chess
  2. Guidelines for Organisers
  3. FIDE Competition (Tournament) Rules
  4. General Rules and Recommendations for Tournaments
  5. International Title Regulations
  6. FIDE Rating Regulations
  7. Regulations for the Titles of Arbiters
  8. Anti Cheating Guidelines
  9. The Role of the Arbiters and their Duties

Do there exist any other restrictions, or do I just pair the players randomly such that each player plays every other player in the tournament?

For your question the important section is section 7. Pairings in the FIDE Competition (Tournament) Rules. There it says -

7.5 The pairings for a round robin should be made in accordance with the Berger tables (Annex 1), adjusted where necessary for double-round events.

So, no you do not pair the players randomly. You pair using the Berger tables. The allocation of players to start numbers is governed by the other articles in that section -

7.1 Responsibility for the drawing of lots and the actual pairings rests with the CA.
7.2 The drawing of lots for the first round of a round-robin competition shall be arranged by the CO, to be open to the players.
7.3 In L1, L2: round robin competitions and preferable Swisses, the drawing of lots shall take place at least 12 hours before the start of the first round. In L1 all participants shall attend the ceremony of drawing of lots. A player who has not arrived on time for the drawing of lots may be included at the discretion of the CA. The first-round pairings shall be announced as soon as possible thereafter.
7.4 If a player withdraws or is excluded from a competition after the drawing of lots but before the beginning of the first round, or there are additional entries, the announced pairings shall remain unaltered. Additional pairings or changes may be made at the discretion of the CA in consultation with the players directly involved, but only if these minimise amendments to pairings that have already been announced.

In response to -

The only rule I know is that in tournaments like the FIDE Candidates players of the same federation are paired together as early as possible.

This is covered in articles 7.6 and 7.7 which specify that the Varma tables may be used in conjunction with the Berger tables to provide a way of restricting the drawing of lots to ensure this.

7.6 If the pairings are to be restricted in any way - for example, players from the same federation shall, if possible, not meet in the last three rounds - this shall be communicated to the players as soon as possible, but not later than the start of the first round.
7.7 For round-robin competitions this restricted drawing of lots may be done by using the Varma tables, reproduced in Annex 2, which can be used for competitions of 9 to 24 players

The Berger tables and Varma tables appear at the end of the FIDE Competition (Tournament) Rules

  • Thanks for your answer. I've had a look at the Berger tables. Is there any formula/logic behind those tables, so that pairings in round-robins with more than 16 players be generated using the same way? And, do the numbers in the table next to "Rd #" refer to the standings at that round or the starting ranks? – Wais Kamal Mar 5 '19 at 13:05
  • Each player has a start number and the pairings use those. For instance - Round 3 pairing 3-1 means that the player with start number 3 has white against the player who has start number 1. It would make no sense whatsoever to use standings. – Brian Towers Mar 5 '19 at 14:00
  • What about the logic? Is there a logic or is it just a rule? – Wais Kamal Mar 5 '19 at 20:23
  • There is a logic. If you draw up a crosstable and put "1" in the square for each first round pairing, "2" for each 2nd round pairing then you see a pattern. If there 2n players (and n is large) then the first round pairings are 1v2n, 2v2n-1, 3v2n-2, etc., 2nd round 1v2, 2n-1v3, 2n-2v4, etc., 3rd round 2v2n, 3v1, 4v2n-1, 5v2n-2, 6v2n-3, etc., round 4 - 3v2, 4v1, 5v2n-1, 6v2n-2, 7v2n-3, etc. When you come close to edge conditions (i.e. just one pairing left) these formulae probably break down and you just have to see what pairing is left. – Brian Towers Mar 5 '19 at 22:06
  • A 16 player round robin (the maximum in the Berger tables) is 15 rounds. How often (if ever) will you have more? – Brian Towers Mar 5 '19 at 22:06
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For a round robin, the only rule is to ensure that everybody gets paired each round, or only one odd player is out and that changes each round.

There is a simple formula to do it. It is different for odd/even number of players. You do not need any tables as you can generate one as easily as locating an existing table.

The only trick is to ensure White/Black is assigned evenly but that is also trivial to do with paper and pencil. If you set up a blank crosstable with the players listed down and opponents across then the main diagonal down from the left has Xs as nobody plays themselves. The trick is to then put a dot in the square for those who get black. Do every other square on the upper right. Then on the bottom left do the same thing but on the same diagonals not done on the upper right as each player must have a different color when they play!

If you were sophisticated you could try to seed the players and then arrange the players numbers so the pairing formula would tend to match higher players near the end to keep it more interesting. As far as I know that was never done, and I have directed or seen the pairing for those when I played in or directed for many round robin tournaments.

It is possible that FIDE may have other rules. I only did/played in USCF tournaments.

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Example for ten players - old style: n=10

1   2   3   4   5
6   7   8   9    

You go until n-1 and start over, n/2 numbers each line:

1   2   3   4   5
6   7   8   9   1
2   3   4   5   6
7   8   9   1   2
3   4   5   6   7
8   9   1   2   3
4   5   6   7   8
9   1   2   3   4
5   6   7   8   9

Then you basically ignore the left-most numbers and start the same procedure from the end to start.

 1 |    2 9     3 8     4 7     5 6
 6 |    7 5     8 4     9 3     1 2
 2 |    3 1     4 9     5 8     6 7
 7 |    8 6     9 5     1 4     2 3
 3 |    4 2     5 1     6 9     7 8
 8 |    9 7     1 6     2 5     3 4
 4 |    5 3     6 2     7 1     8 9
 9 |    1 8     2 7     3 6     4 5
 5 |    6 4     7 3     8 2     9 1   <- start here

Then the 10 (n):

 1 (10) |   2 9     3 8     4 7     5 6
 (10) 6 |   7 5     8 4     9 3     1 2
 2 (10) |   3 1     4 9     5 8     6 7
 (10) 7 |   8 6     9 5     1 4     2 3
 3 (10) |   4 2     5 1     6 9     7 8
 (10) 8 |   9 7     1 6     2 5     3 4
 4 (10) |   5 3     6 2     7 1     8 9
 (10) 9 |   1 8     2 7     3 6     4 5
 5 (10) |   6 4     7 3     8 2     9 1

For each player color change nearly all rounds. Gives also a nice obvious cross table. Also lots of math in the system.

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