LIM SYSTEM

Approved by the General Assembly of 1987

Amended by the 1988, 1989, 1997, 1998 General Assemblies and 1999 Executive Board.

Approved by the Council on 28/10/2025

Applied from 1st February, 2026

General Pairing Rules

1.      Awarding the pairing-allocated bye

1.1     In addition of what is stated in Article 3 of the Basic Rules for Swiss Systems, the pairing-allocated bye is awarded to the player with the lowest rank in the lowest scoregroup.

2.      Pairing a Scoregroup

2.1     Two players who have not yet played each other are said to be compatible provided that the pairing will not require either player to have the same colour in three successive rounds, or to have three more of one colour than the other.

2.2     The players with the same score form a scoregroup. The Median Scoregroup is the scoregroup with players having the score equal to half the number of rounds that have been played. Pairing begins with the highest scoregroup and proceeds downward until just before the Median Scoregroup, then continues with the lowest scoregroup and proceeds upwards to the Median Scoregroup which is paired last. The Median-Scoregroup is paired downward.

2.3     Before the players in a scoregroup are paired, the players in the scoregroup who have no suitable opponents for the following reasons are identified and transferred to a neighbouring scoregroup:

2.3.1      they have already played all the players of their scoregroup; or

2.3.2      they have already received two more of one colour over an equal allocation and there is no compatible opponent available in the scoregroup to enable them to have a permissible colour; or

2.3.3      they have already received the same colour in the previous two rounds and there is no compatible player in the scoregroup to enable them to have the alternate colour; or

2.3.4      it is necessary to make even the number of players in the scoregroup

Such a transferred player is described as a floater. Rules on how to select the floater, if a choice is available, are given in the section on "Floater Selection Rules" (Article 3).

2.4     The players in a scoregroup, after transfer of players where necessary, are arranged in the order of their pairing numbers and the players in the top half are tentatively paired with the players in the bottom half. These pairings are said to be proposed pairings, to be confirmed after scrutiny for compatibility and proper colour. If the players in a scoregroup are numbered: 1, 2, 3 ... n, then the proposed pairings are (ignoring colours): 1 v (n/2 + 1), 2 v (n/2 + 2), 3 v (n/2 + 3) ... n/2 v n.

2.5     Where a proposed pairing would result in the pairing of players who have already played each other, the lower numbered player of the two is exchanged for another within the same scoregroup. Further exchanges of opponents may be made to allow alternation or equalisation of colours where possible. How players are exchanged is described in the "Exchange Rules" (Article 4).

2.6     Pairing a blocked median scoregroup

If the median scoregroup cannot be paired, it should be extended step by step under the following rules:

2.6.1      if the number of floaters from higher scoregroups is larger than the number of floaters from lower scoregroups the next pairing of the lower scoregroup shall be cracked and the players of this pairing shall be treated as additional floaters from the lower scoregroup. Then the pairing of the median scoregroup is started again.

2.6.2      if the above condition is not fulfilled, then the next pairing of the higher scoregroup shall be cracked and the players of this pairing shall be treated as additional floaters from the higher scoregroup. Then the pairing of the median scoregroup is started again.

3.      Floater Selection Rules

3.1     The "floater" is a player who is transferred to another scoregroup in accordance with Article 2.3, or because a compatible opponent cannot be found for the player despite exchanges in the scoregroup.

3.2     Floater Selection

3.2.1      When pairing proceeds downward, the floater is transferred to the next lower scoregroup. When pairing proceeds upwards, the floater is transferred to the next higher scoregroup.

3.2.2      When making even a scoregroup, determine the due colours of the players and select as the floater a player who would tend to equalise the number of players due different colours.

3.2.3      (In Maxi-tournaments, when pairing downward, the difference in rating between the chosen player and the lowest numbered player in the scoregroup must differ by 100 points or less, otherwise the lowest numbered player in the scoregroup is chosen as the floater. When pairing upwards, the difference in rating between the player chosen and the highest numbered player in the scoregroup must differ by 100 points or less, otherwise the highest numbered player is chosen as the floater.)

3.2.4      If the number of players due White equals the number of players due Black, the lowest numbered player is chosen as the floater when pairing downward, and the highest numbered player is chosen as the floater when pairing upwards.

3.3     If there is a choice as to which player floats to a lower scoregroup, the player chosen is the lowest numbered player in the scoregroup who has a compatible opponent in the lower scoregroup, after excluding the opponents of other floaters who have higher scores or higher pairing numbers than the proposed floater.

3.4     If there is a choice as to which player floats to a higher scoregroup, the player chosen is the highest numbered player in the scoregroup who has a compatible opponent in the higher scoregroup, after excluding the opponents of other floaters who have lower scores or lower pairing numbers than the proposed floater.

3.5     If a proposed floater has no compatible opponent in the adjacent scoregroup, they shall, if possible, be exchanged for another player in their scoregroup; otherwise, they shall be floated to a further scoregroup.

3.6     When pairing a group that includes floaters from a higher scoregroup, the floater with the highest score is paired first, or the floater with the highest pairing number, if scores are equal.

3.6.1      When pairing a group that includes down-floaters (DF) from a higher scoregroup, the floater with the higher pairing number is paired first.

3.6.2      When pairing a group with DF coming from different higher scoregroups, the floater coming from the highest score group is paired first (not always the one with the highest pairing number).

3.6.3      When there are DF and UF (up-floaters) in the same scoregroups (this should normally happen in the median scoregroup) in the upper half of scoregroups or in the median group, first pair the DF, then the UF and finally the remaining players.

3.7     When pairing a group that includes floaters from a lower scoregroup, the floater with the lowest score is paired first, or the floater with the lowest pairing number, if scores are equal.

3.7.1      When pairing a group that includes UF from a lower scoregroup (in the 2nd half) the floater with the lowest pairing number is paired first.

3.7.2      When pairing a group that includes UF coming from different lower groups, the UF coming from the lowest scoregroup is paired first (this is not always the player with the highest pairing number).

3.7.3      When there are UF and DF in the same score group in the second half of scoregroups, first pair the UF, then the DF, and finally the other remaining players.

3.8     When pairing downward, the floater is paired with the highest numbered player available who is due the alternate colour (provided, in Maxi-tournaments, that the ratings of proposed opponents who are exchanged for this purpose differ by 100 points or less). When pairing upwards, the floater is paired with the lowest numbered player available who is due the alternate colour (provided, in Maxi-tournaments, that the ratings of proposed opponents who are exchanged for this purpose differ by 100 points or less).

3.9     Type of Floaters

3.9.1      Due to their origin and their compatibility in the adjacent scoregroup there are four types of floaters listed in descending order of disadvantages.

1. a floater who has already floated to the scoregroup just being handled and has no compatible opponent in the adjacent scoregroup.
2. a floater who has already floated to the scoregroup just being handled and has a compatible opponent in the adjacent scoregroup.
3. a floater who has no compatible opponent in the adjacent scoregroup.
4. a floater who has a compatible opponent in the adjacent scoregroup.

3.9.2      If there is a choice, the floaters should be chosen to minimise the disadvantages using the following priorities:

1. avoid floater(s) of type a
2. avoid floater(s) of type b
3. avoid floater(s) of type c

3.10   A floater who has floated the round just before shall not be floated due to Article 2.3.4 provided:

3.10.1      this will not produce other floaters of the types a, b, c of Article 3.9

3.10.2      this will not decrease the number of pairings of that scoregroup

4.      Exchange Rules

4.1     The proposed pairings of players obtained according to Article 2.4 are scrutinised in turn for compliance with the compatibility statement (see Article 2.1). And,

4.1.1      when pairing downward, scrutiny of proposed pairings begins with the highest numbered player; if the pairing is found not to comply with Article 2.1, the lower numbered player is exchanged until a compatible pairing is found; or,

4.1.2      when pairing upwards, scrutiny of proposed pairings begins with the lowest numbered player; if the pairing is found not to comply with Article 2.1, the higher numbered player is exchanged until a compatible pairing is found.

4.2     In the following example of a scoregroup with six players, and pairing downward, the attempt is first made to find a compatible opponent for Player #1, the highest numbered player in the scoregroup.

Six players in a scoregroup with proposed pairings as follows:

1 v 4

2 v 5

3 v 6

If the pairing 1 v 4 is not compatible, for example, because the players had met in an earlier round, the positions of Player #4 and Player #5 are exchanged so that we have:

1 v 5

2 v 4

3 v 6

If the pairing 1 v 5 is also not compatible, a further exchange is made. The original proposed pairing and possible exchanges made to find a compatible opponent for Player #1 are as follows:

Proposed Pairing (col. 1) and Possible exchanges to find compatible opponent for #1

1 v 4      1 v 5      1 v 6      1 v 3      1 v 2

2 v 5      2 v 4      2 v 4      2 v 5      3 v 5

3 v 6      3 v 6      3 v 5      4 v 6      4 v 6

4.3     After a compatible opponent, for example, #6, has been found for Player #1, the proposed pairing for Player #2 is scrutinised. Exchanges to find a compatible opponent for Player #2 are as follows:

Proposed Pairing (col. 1) and Possible exchanges to find compatible opponent for #2

1 v 6      1 v 6      1 v 6      1 v 3      1 v 2

2 v 4      2 v 5      2 v 3      2 v 6      3 v 5

3 v 5      3 v 4      4 v 5      4 v 5      4 v 6

4.4     The exchanges to find a compatible opponent for Player #2 must at the same time leave Player #1 with a compatible opponent. If this cannot be done, for example, if Player #1 and Player #2 have previously played each other and all the other players except Player #6, then the original pairing of Player #1 with Player #6 is retained, and Player #2 is floated. And,

4.4.1      if the scoregroup originally had uneven members and the lowest numbered player was floated to make even the number of players in the scoregroup, #2 is exchanged with the floater, originally #7 in the scoregroup, or,

4.4.2      if the scoregroup was originally even, then the lowest numbered player remaining must be floated in company with #2 to maintain an even number of members in the scoregroup.

5.      Colour Allocation Rules

5.1     Where possible, and by means of exchanges, each player shall be given the alternate colour; at the end of each even-numbered round each player shall have had an equal number of Whites and Blacks. Moreover,

5.1.1      no player shall be given the same colour in three successive rounds, and

5.1.2      no player shall be given three more of one colour than the other.

5.2     After the first scrutiny and exchanges necessary to establish that all pairings in a scoregroup are new pairings, a second scrutiny with exchanges where necessary is undertaken to give each player, if possible, the alternating colour and at the same time, the equalising colour.

5.3     If one of the players in a pairing had the same colour in the previous two rounds, this player must be given the alternating colour. If both players had the same colour in the previous two rounds and compatible opponents in the scoregroup are not available, then one or both players must be floated.

5.4     If both players in a pairing had the same colour in the previous round, then the colours they had in earlier rounds, going back in sequence, shall decide who is given the alternate colour. If players in the median scoregroup or above had identical histories, then the higher ranked is given the alternate colour, or, in even-numbered rounds, the equalising colour. If the players below the median scoregroup had identical histories, then the lower ranked player is given the alternate colour, or, in even numbered rounds, the equalising colour.

5.5     In the odd-numbered rounds, whenever possible, each player shall be given the colour which gives them one more only of one colour than the other.

5.6     In the even-numbered rounds, whenever possible, each player shall be given the colour that gives them an equal number of Whites and Blacks.

When both players of a pairing are due the same equalising colour, and further exchanges are not possible, the colour history will decide who is given the equalising colour, as in Article 5.4. One player will then have two more of one colour than the other colour.

This is allowed but care must be taken not to violate Articles 5.1.1 and 5.1.2, and to equalise the player's colours at the earliest opportunity.

5.7     (In Maxi-tournaments, an exchange of opponents to find, for example, one who is due the alternate colour is allowed only if the ratings of the opponents to be exchanged differ by 100 points or less.)

6.      Exceptions applicable to the last round

In the last round, Article 5 of the Basic Rules for Swiss Systems, requiring players with the same score to be paired if they had not met in an earlier round, shall have priority over alternation and equalisation of colours, even if it is necessary for one of the players to be given the same colour for the third round in succession, or to be given three more of one colour than the other.

Brief examples of pairing

7.      Pairing Round One

7.1     If the number of players is uneven, the lowest rated player in the Pairing List is given the pairing-allocated bye.

7.2     The colour to be given to Player #1 is decided by drawing lots; the other odd-numbered players in the upper half of the Pairing List are then given the same colour as Player #1. Player #2 together with the other even-numbered players in the upper half of the Pairing List are given the other colour.

Depending on the draw, the pairings for the first round in a tournament of forty players would be either 1 v 21, 22 v 2, 3 v 23, 24 v 4, ... 40 v 20; or 21 v 1, 2 v 22, 23 v 3, 4 v 24 ... 20 v 40, where the player having White is mentioned first. This is the only occasion when colours need be decided by lot.

7.3     Players who have won their games are each awarded one point; each of those who have drawn receives 0.5 point. Each of those who have lost receives 0 point.

8.      Round Two

8.1     The players are arranged in groups of the same score.

8.2     If the number of players is uneven, then the pairing-allocated bye is awarded as in Article 1.

8.3     Pairing begins with the highest scoregroup (1 point), continues with the lowest scoregroup (0 point) and finishes with the Median Scoregroup (0.5 point).

Detailed instructions for pairing Round Two and subsequent rounds are above.