PAIRING RULES

601. PURPOSE

The purpose of these Pairing Rules is to standardize the conduct of Swiss System and Round-Robin tournaments for CFC rating. Since even the practices of the best tournament directors vary, specific variations are provided in certain cases. Moreover, there must be legitimate flexibility to deal with the particular requirements of individual tournaments and to take advantage of experimentation for the improvement of the pairing rules. Therefore, other variations of the basic system are allowed, but only when announcement is made in advance of the first round.

602. VARIATIONS

The director may choose to use any of the variations listed in the following rules or variations other than those listed (if he feels they are in accord with the goals of these Pairing Rules), but only if written and also, whenever possible, oral announcement is made in advance of the first round.

610. RATINGS-CONTROLLED INDIVIDUAL SWISS-SYSTEM TOURNAMENTS

Introduction

The Swiss System permits a relatively large number of players to take part in a relatively short tournament. The Swiss System is frequently used in large weekend tournaments in which a hundred or more players can participate in one tournament of, say, four or five rounds. It is also used in longer tournaments extending over one or two weeks with several hundred players and, say, ten to thirteen rounds. A higher ratio of rounds to players will bring about more accurate results, and where a particularly large field is anticipated, several sections (such as expert, amateur, and beginner) can be run simultaneously.

The purpose of the Swiss System is to produce a clear winner in as few rounds as possible; therefore, in pairing, the system consistently works to reduce the number of players with perfect or high scores. The fundamental laws of the Swiss System are that in each round players with the same score must play each other whenever possible and that no contestant may play the same opponent more than once.

In the first round, all the entrants have equal scores of zero and play together in one group. Then, in the second round, the players are divided into three groups: (a) the first-round winners, (b) the players who drew their games, and (c) the first-round losers. The players in each group are paired.

The same system of grouping is continued throughout the tournament. Thus, in the fourth round, those who tallied 3-0 in the first three rounds are paired, those who scored 2.5-0.5 are paired, etc., down to the group that scored 0-3 (see Rule 6 on Scoring).

The Round-Robin tournament is undoubtedly the best kind of competition when nearly all the contestants have similar ratings. Nothing can match the Round-Robin for an all-master tournament, but a ratings-controlled Swiss System tournament is a more effective and fairer type of competition than any other when there is a wide range of playing strength among the contestants and when there are more players than can be handled in a single Round- Robin of reasonable duration. Thus, although it is only an imperfect approximation of the Round-Robin, the Swiss System has practical advantages for large tournaments which outweigh the variables introduced by the system in the parings.

Pairing Cards

611. The director makes out a pairing card for each entrant. On it the director records for each round the colour of the player's pieces, the opponent's (name and) pairing number, the player's score in the game, and the player's cumulative tournament score (see Rule # 616) (see Section 18 for sample forms).

Ratings of Players

612. The rating entered on a player's card is his last-published CFC rating (unless use of a given Rating List was specified in the advance publicity). A foreign entrant without a CFC rating may be given his most recent FIDE rating, or, if he has none, his national rating. (United States Chess Federation ratings may be used without change. British Chess Federation ratings can be converted by multiplying by 8, then adding 600. Ingo ratings can be converted by subtracting 8 times the Ingo rating from 2840.) Entrants without any official ratings may be given estimated ratings based on whatever information the director wishes to use.

Pairing Numbers

613. After the entry list is closed, all cards are arranged in the order of the players' ratings, the cards of entrants without even estimated ratings being placed at the bottom.

VARIATION 613.1: Unrated players, for their actual strength to be reflected more accurately in the pairings, may be arranged -

(a) just below the average rating of the tournament or section, or

(b) about one-fifth of the way up from the bottom.

Players with identical ratings and players without even estimated ratings are arranged by lot. Then the pairing numbers of all players are entered on the pairing cards, starting with the highest-rated player as #1. These pairing numbers generally remain unchanged throughout the tournament.

Late Entrants

614. The director may accept and pair entries after the announced closing time, but a later entrant defaults any round he has missed for which it is inconvenient or too late for the director to pair the entrant for play. The director may also assign a pairing score, to be used only for the purpose of pairing the entrant, if the director feels that pairing each defaulted game as a loss would be unfair to the other players.

The pairing numbers of late entrants follow in sequence the last number assigned before the entry list was closed, but, in pairing, late entrants are arranged in the order described in Rule #613 regardless of their pairing numbers.

Byes

615. If the total number of players in any round of a tournament or section of a tournament is uneven, one player is given a bye. A player is eligible for a bye if he has not been given a previous bye. In each round the bye will be given to the lowest rated eligible player in the lowest score group. If all rated players in the lowest score group are ineligible, then the bye is given by lot to an eligible unrated player in that score group. If there are no eligible players in that score group, then the foregoing procedure is applied to successively higher score groups.

615a. Notwithstanding 615, where a player is unable to play a round or rounds, the player may, at the discretion of the chief director, be awarded a 0.5 point bye or byes.

Scoring

616. The scoring is one point for a win, one-half point for each player for a draw, zero for a loss. A bye is scored as one point for the byed player. Any game defaulted because of a player's failure to appear within one hour after the starting time (FIDE Article 17.2) is scored as one point for the winner and zero for the loser, and the defaulting player is not paired for the succeeding rounds without an excuse acceptable to the director. Defaulted games (as those of a late entrant or of a player who is excused from being paired in a round after the director has been notified in advance that the player will be unable to play) are scored as zero. The remaining games of a player who is excused, withdrawn because of a default without notice, or expelled from the tournament are scored as zero. The scores of unplayed games are circled on the pairing cards and wallchart (or marked F or D: if the game is to be rated, it should also be marked R - see sections 718 and 733). Each player's final position is determined by the total of his score.

VARIATION 616.1: A bye may be scored as one-half point for the byed player.

Unfinished Games

617. A game that is not finished before it is time to pair the next round is temporarily scored as a draw for pairing purposes unless, clearly, one player is a winner. When an unfinished game is completed, the correct results and cumulative scores are entered on the players' cards.

VARIATION 617.1: A game that is not finished before it is time to pair the next round may be temporarily adjudicated for pairing purposes. Written and also, whenever possible, oral announcement must be made in advance of the first round of the exact procedures to be used. In making an adjudication, the director should seek out the best advice that is available and should give proper weight to the degree of objectivity of that advice. The objective of the adjudication is to predict the probable result of the unfinished game. Therefore, the adjudication should give primary consideration to the position existing on the board, though such additional factors as the respective strengths of the players and the times remaining on their clocks may be considered as well, according to the adjudication procedures announced for the tournament. The players themselves may not be required to declare their evaluation of or objectives in the game or be penalized for refusing to do so.

Basic Swiss System Laws

618. All Pairing Rules are subject to the following Swiss System laws:

(a) a player must not be paired with any other player more than once;

(b) players with equal scores must be paired if it is possible to do so;

(c) if it is impossible to pair all players with equal scores, every player who is not paired with an opponent whose score is the same as his own must be paired with an opponent whose score is as close to his own as possible.

Pairing the First Round (see also Rule #633)

619. After the bye, if any, is given, the pairing cards are arranged in the order described in Rule #613 and are divided into two equal groups. The players in the top half are paired in consecutive order with those in the bottom half. For example, if there are forty players, #1 is paired with #21, #2 with #22, etc.

VARIATION 619.1: If specifically requested by the players involved, minor transpositions may be made in the first two rounds of a tournament at the director's discretion in order to avoid pairing players from the same region, city, team, family, etc. but only to the extent that the results of the tournament as a whole are not substantially affected by this procedure.

Pairing Subsequent Rounds (See also Rule #633)

Score Groups and Rank

620. In these rules the expression score group or simply group, is used in reference to a group of players having the same score. Sometimes a group may consist of only one player whose score is unequalled by any other player.

Individual rank is determined first by score, then by rating, in the order described in Rule #613.

Order of Pairing Groups

621. In general, the order of pairing is from the group with the highest score down to the group with the lowest score. Occasionally, in the late rounds, the pairing of the lower score groups may have to be adjusted to conform to the basic Swiss System laws (Rule #618), if many of the players in those groups have met before.

Method of Pairing Each Score Group

622. In the second and as many of the subsequent rounds as possible, the players are paired as follows:

(a) any odd men removed from the next higher score group are paired first as described in Rules #623 -625.

(b) within each score group, after the odd man, if any, has been removed, the cards of the remaining players are arranged in the order described in Rule #613 and divided into two equal sections. The players in the top half (with the higher ratings) are paired with those in the bottom half (with the lower ratings) in as close to consecutive order as possible. Transpositions in the bottom half of a group are made to make the pairings conform to the basic Swiss System laws (Rule #618) and to give as many players as possible their due colours (Rule #629 - 631). If it is impossible to meet the two requirements just mentioned, interchanges between the top half and the bottom half may be made, but not simply to preserve alternation of colours. Every effort must be made, however, to observe the principle of pairing the higher rated against the lower rated players in as close to consecutive order as possible (but see Variation # 631.1). Note: Directors differ somewhat in their exact methods for implementing this procedure, but any reasonable method, followed consistently, is acceptable.

Rules on Odd Men

623. If there is an odd number of players in a score group, the lowest ranked player is ordinarily treated as the odd man. However, the pairings in the group must accord with the basic Swiss System laws (Rule # 618).

In removing an odd man to the next-lower group, the prime consideration is that the remaining players in the original group can all be paired with each other. If the lowest-ranked player in the odd-numbered group has already played all the players in the next-lower group, the next lowest-rated player is treated as the odd man and paired with the highest-ranked player he has not met in the next-lower group. This procedure is followed until a player in the odd-numbered group is found who has not played all the players in the next-lower group.

If all the players in an odd-numbered group have played all the players in the next-lower group, the lowest-ranked player in the odd-numbered group is treated as the odd man and paired with the highest-ranked he has not met in the second-lower group. In all cases, when an odd man is removed from a score group, there must be a possible pairing of all the players remaining in the original group. Sometimes two players who have met in a previous round must be treated as odd men because there is no possible way in which either of them can be paired in their original group.

Method of Pairing One Odd Man

624. The odd man is paired with the highest-ranked player he has not met in the next-lower group.

VARIATION 624.1: The odd man may be paired with the next highest-ranked player whom he has not met in the next-lower group and who is due the opposite colour.

VARIATION 624.2: Except in the last quarter of a tournament, a player should not be treated as an odd man or paired with an odd man more than once unless such a pairing cannot be avoided. To implement this variation, an indication should be made on the card of a player who has been treated as an odd man or paired with an odd man. In the last quarter of a tournament, a player may be treated as an odd man or paired with an odd man as many times as necessary.

Method of Pairing More Than One Odd Man

625. If there are two odd men to be paired, the order in which they are paired is determined by their rank according to Rule #620. If both cannot be paired, rank determines which is paired and which is removed to another group.

Pairing Players with Unfinished Games

626. Players with unfinished games (Rule # 617) should not usually be treated as odd men if it is possible to avoid doing so.

Colour Allocation:

General Principles

627. The director assigns colours to all players. His primary objective in a tournament with an even number of rounds is to give white and black the same number of times to as many players as possible, and, in a tournament with an odd number of rounds, to give white and black the same number of times to every player, plus one extra white or black. After the first round the director attempts to give as many players as possible their due colours, round by round (Rules # 629-631).

First-Round Colours

628. In the first round, when the top half of the ranked field plays the bottom half, the colour assigned to all the odd-numbered players in the top half is chosen by lot, and the opposite colour is given to all the even-numbered players in the top half. Only the one lot is necessary in a tournament, as Rules # 629-631 preserve equitable colour allocation.

Due Colours in Succeeding Rounds

629. As many players as possible are given their due colours as described in Rules # 630-31, so long as the pairings conform to the basic Swiss System laws (Rule # 618). Equalization of colours takes priority over alternation of colours.

Equalization of Colours

630. As many players as possible are given the colour that equalises the number of times they have played as White and Black. When it is necessary to pair any two players who are due to be given the same equalizing colour, the higher-ranked player has priority in getting the equalizing colour, whether white or black.

Alternation of Colours

631. After colours have been equalized in a round, as many players as possible should be given, in the next round, the colour opposite to that which each received in the preceding round, the purpose being to continue alternation of colours. When it is necessary to pair any two players who are due to be given the same alternating colour, the highest-ranked player has priority in getting the alternating colour, whether white or black. However, a player should not be assigned the same colour three times in a row. Transpositions, but not interchanges (see Rule #622(b)) may be made to preserve alternation of colours.

VARIATION 631.1: Neither transpositions nor interchanges should be made simply to preserve alternation of colours. If both players are due for the same colour, the higher-ranked player has priority in getting his due colour.

VARIATION 631.2: In the last round of a tournament with an odd number of rounds, when two players who have had an equal number of whites and blacks are paired, or in the last round of a tournament with an even number of rounds, when it is necessary to pair two players who are due the same equalizing colours, the director may allow such players to choose colours by lot. If one of the players is absent when the round begins, his clock is started, and the lot is taken upon his arrival.

Colour for Unplayed Games

632. Unplayed games (including byed games) do not count for colour.

Accelerated Methods of Pairing Early Rounds (Variations)

633. In a tournament where the players-to-rounds ratio exceeds the optimum (16:4, 32:5, 64:6, etc.), the chances of producing a clear winner are decreased.

Accelerated pairings increase the frequency of meeting of the higher ranked players and are therefore also useful in longer tournaments where the winner is unlikely to have a perfect score.

The effect of these variations decreases when the players are of about the same playing strength (as in a tournament divided into sections by playing strength).

VARIATION 633.1: The following method produces more drawn games and makes it less likely that two contestants will finish with perfect scores.

In the first round, after the bye, if any, is issued and the pairing cards are arranged in the order described in Rule #613, the cards are divided into four sections, and the first quarter of the field is paired against the second quarter, the third quarter against the fourth quarter.

In the second and possibly later rounds, if the number of players with perfect scores exceeds the optimum for the number of rounds remaining, the cards of the players with perfect scores are arranged in the order described in Rule #613, and the first quarter is paired against the second quarter, the third quarter against the fourth quarter. The cards of the players in the score group just below are arranged and paired similarly. Players in the other score groups are paired according to the basic system.

VARIATION 633.2: The following method results in only about half as many players having a perfect score as under the basic system and increases the opportunity of a single winner.

In the first round, after the bye, if any, is issued, the pairing cards are arranged in the order described in Rule # 613. Then the field is divided from top to bottom into four groups (A, B, C, D) as close to the same size as possible and paired as follows:

(a) In one section, the players in group A are paired against the players in group B in consecutive order.

(b) In a second section, the players in group C are paired against the players in group D in consecutive order, using Rule #628 to assign colours in each section.

For the second-round pairings, the players are regrouped as follows:

A: winners from section (a);

B: remaining players from section (a), adding 100 points to the ratings of the players who drew;

C: winners and players who drew from section (b), subtracting 100 points from the ratings of the players who drew;

D: remaining players from section (b).

All groups are arranged in the order described in Rule #613. Group A is divided in half and paired. Group B is paired with Group C. (If there are more players in Group B than Group C, the extra players are added to the top of Group D. If there are more players in Group C than Group B, the extra players are paired with the top players in Group D.) Group D is divided in half and paired.

In each second-round group, odd men are treated, colours are allocated, and players are paired as in the basic system.

For the third and all subsequent rounds of the tournament, the rating points added are removed and the pairings made as in the basic system.

640. RATINGS-CONTROLLED TEAM SWISS-SYSTEM TOURNAMENTS

Basic Rules

641. Most of the rules for Ratings-Controlled Individual Swiss System Tournaments apply to teams in Swiss System tournaments. Some rules are modified as indicated below.

Pairing Cards

642. A card similar to that used for Individual Swiss Tournaments is used, but provision is made for match scores and game points.

Order of Boards

643. Team members should be placed in board order according to ratings, and they must play in that order throughout the tournament. The highest-rated player is Board 1, etc. Unrated players may play on any board as long as their position reflects their actual strength in relation to the rated players. The director may authorize in advance of the tournament that players may be placed out of rating order within a specific point limit, such as 25 or 50 points.

Alternate team members are used according to whatever system is announced in advance.

Team Ratings

644. The rating entered on a team's card is the average of the ratings of the regular team members. In the case of unrated players:

(a) If a top or bottom board is unrated, the rating assigned is 50 (or some other announced number) points from that of the player on the next board.

(b) If a middle board is unrated, the rating assigned is averaged from the ratings of the next higher - and lower - rated players.

Pairing Rules

645. Teams are paired and ranked first by their match scores, then by their ratings.

Colour Allocation

646. In each team, the colours given to the individual players alternate from Board 1 down. Rules #627-632 for Individual Swiss System Tournaments are applicable to team tournaments, but in each rule the colours referred to are those of the player at Board 1.

Scoring

647. Each member of a team scores game points as described in Rule # 616 for Individual Swiss System Tournaments. A team scores one match point for a win against another team, one-half match point for a draw, zero for a loss, on the basis of game points greater than, equal to, or less than the opposing team, respectively. A team's match score for a bye is one point. Any round defaulted because of a team's failure to appear within one hour after the starting time is scored as one point for the winning team and zero for the losing team, and the defaulting team is not paired for succeeding rounds without an excuse acceptable to the director. Defaulted rounds (as those of a late-entering team, or of a team which is excused from being paired in a round after the director has been notified in advance that it will be unable to play) are scored as zero. The remaining games of a team which is excused, withdrawn because of a default without notice, or expelled from the tournament are scored as zero. The scores of unplayed games (rounds) are circled on the pairing cards and wallchart. Each team's final position is determined by the total of the match points scored by the team.

650. INDIVIDUAL ROUND-ROBIN TOURNAMENTS

Basic Rules

651. Each player plays one game with each of the other players. In a double Round-Robin he plays each of the other players twice, once with white and once with black.

Pairing

652. After being divided into sections (e.g. by similar rating), if any, players are assigned numbers by lot within their sections. The pairings, order of rounds, and colour allocation in each game are shown in the International Tables or Rounds (see pages 6-11 and 6-12 at the end of this section). The player with the first number of each pairing has the white pieces.

Scoring

653. The scoring is the same as in an Individual Swiss System Tournament (Rule #616) except that byes are not scored. When a player or team withdraws or is expelled from a (round-robin) tournament, the problem of how to score the remaining games of that player or team was covered by FIDE in 1970:

"If a player has not completed 50% of his games when he leaves the tournament, his score remains in the tournament table (for rating and historical purposes), but the points scored by him or against him are not counted in the final standings. For the games not played or finished, the player, as well as his opponents, gets a "-" in the tournament table.

If a player has completed at least 50% of his games when he leaves the tournament, his score remains in the tournament table and will be counted in the final standings. For the games not played the opponents will get a "+" (which counts as 1) and the player himself will get a "-" (which counts as 0). The same rule applies equally when a team is concerned instead of a player." [FIDE Interpretation to (then) Article 21 (1970)]

660. TEAM ROUND-ROBIN TOURNAMENTS

Basic Rules

661. Rule #651 for Individual Round-Robin Tournaments applies to teams.

Order of Boards

662. Rule # 643 for Team Swiss System Tournaments applies.

Pairing

663. Rule # 652 for Individual Round-Robin Tournaments applies to teams.

Scoring

664. Each member of a team scores game points as described in Rule # 653 for Individual Round-Robin Tournaments. Match points for each team are scored as described in rule # 647 for Team Swiss System Tournaments, except that byes are not scored. Each team's final position is determined by the total of the match points scored by the team. See FIDE Interpretations Art. 21 (1970, 1973) for scoring the remaining matches of a team that does not complete the event.

670. TIE-BREAKING

Methods to be Used

671. Although tie-breaking should be avoided if possible, in those cases when tie-breaking must be used, such as to award a single trophy, the following methods are to be used unless written, and also, whenever possible, oral announcement is made in advance of the first round. The director is the final authority on breaking ties in cases unresolved by these methods.

Swiss System Tournaments

672. Cumulative System. For each player in the tie, the sum of his cumulative tournament scores after each round is found. (For example, if a player scores a win in round one, losses in rounds two through four, and a draw in round five, the sum of his cumulative tournament scores after each round - 1, 1, 1, 1, 1.5 -- is 5.5). One point is subtracted from the sum for each unplayed win or one-point bye.

Round-Robin Tournaments

673. Sonnenborn-Berger System. For each player in the tie, the sum of the final scores of all the opponents he has defeated, together with half the final scores of all the opponents which whom he has drawn is found (nothing is added for games he has lost or for unplayed games).

If the tie still remains, the results of the games between the players involved in the ties are used.

652. Round-Robin Pairings

In a Round-Robin tournament each player plays every other player one time. The tables here show the pairings for any number of players up to 18.

Each player is assigned a number (the pairing number) which determines the order in which he plays the others and the colour for each game. In each pairing, the first number receives White. For example, in a five player event, player 2 has White against player 3 in round four. This is indicated at the right by 2 x 3.

The pairing numbers should be assigned by chance. A good way is for each player to draw his number from a hat. Or put each number under a potted plant...

It is important that the numbers be assigned by chance and not, say, by rating. In a tournament with an even number of players n, each player with a number n/2 or less receives an extra White.

In some tournaments it is required that players from the same province (region) may not play against each other in the final three rounds of the tournament. Section 2025 contains a method of doing that.

 
FIDE RULES {Motion Denommee/Barron 2004-05 GL8}

04.1. Swiss System Based on Rating Approved by the 1992, 1997 and 1998 General Assemblies. A. Introductory Remarks and Definitions A.1 Rating It is advisable to check all ratings supplied by players. If no reliable rating is known for a player the arbiters should make an estimation of it as accurately as possible before the start of the tournament. (to convert German Ingo or British BCF use rating = 2840 - 8 x INGO = 600 + 8 x BCF) A.2 Order For pairing purposes only, the players are ranked in order of, respectively score rating FIDE-title (IGM-WGM-IM-WIM-FM-WFM-no title) alphabetically (unless it has been previously stated that this criterion has been replaced by another one) The order made before the first round (when all scores are obviously zero) is used to determine the pairing numbers: the highest one gets #1 etc. A.3 Score brackets Players with equal scores constitute a homogeneous score bracket. Players who remain unpaired after the pairing of a score bracket will be moved down to the next score bracket, which will therefore be heterogeneous. When pairing a heterogeneous score bracket these players moved down are always paired first whenever possible, giving rise to a remainder score bracket which is always treated as a homogeneous one. A heterogeneous score bracket of which at least half of the players have come from a higher score bracket is also treated as though it was homogeneous. A.4 Floats By pairing a heterogeneous score bracket, players with unequal scores will be paired. To ensure that this will not happen to the same players again in the next round this is written down on the pairing card. The higher ranked player receives a downfloat ( ), the lower one an upfloat ( ). A.5 Byes Should the total number of players be (or become) odd, one player ends up unpaired. This player receives a bye: no opponent, no colour, 1 point. A bye is considered to be a downfloat. A.6 Subgroups To make the pairing, each score bracket will be divided into two subgroups, to be called S1 and S2. In a heterogeneous score bracket S1 contains all players moved down from a higher score bracket. In a homogeneous score bracket S1 contains the higher half (rounding downwards) of the number of players in the score bracket. The number of players in S1 will be indicated by "p", indicating the number of pairings to be made. In both cases S2 contains all other players of the score bracket. In both S1 and S2 players are ordered according to A2. A.7 Colour differences and colour preferences The colour difference of a player is the number of games played with white minus the number of games played with black by this player. After a round the colour preference can be determined for every player. An absolute colour preference occurs when a player's colour difference is greater that 1 or less than -1, or when a player played with the same colour in the two latest rounds. The preference is white when the colour difference is << 0 or when the last two games were played with black, otherwise black. In this case the (obligatory) colour is already written down on the score card. (This rule is not in effect when pairing players with a score of over 50% in the last round). A strong colour preference occurs when a player's colour difference is unequal to zero. The preference is white when the colour difference is < 0, black otherwise. A mild colour preference occurs when a player's colour difference is zero, the preference being to alternate the colour with respect to the previous game. In this case the colour difference is written down as +0 or -0 depending on the colour of the previous game (white or black respectively). Before the first round the colour preference of one player (often the highest one) is determined by lot. A.8 Definition of "x" The number of pairings which can be made in a score bracket, either homogeneous or heterogeneous, not fulfilling all colour preferences, is represented by the symbol x. x can be calculated as follows: w = number of players having a colour preference white. b = number of players having a colour preference black. q = number of players in the score bracket divided by 2, rounded upwards. If b >> w then x = b-q, else x = w-q. A.8 Transpositions and exchanges In order to make a sound pairing it is often necessary to change the order in S2. The Rules to make such a change, called a transposition, are in D1. In a homogeneous score bracket it may be necessary to exchange players from S1 and S2. rules for exchanges are found under D2. After each exchange both S1 and S2 are to be ordered according to A2. B. Pairing Criteria Absolute Criteria (These may not be violated. If necessary players will be moved down to a lower score bracket.) B.1 Two players shall not meet more than once. A player who has received a point without playing, either through a bye or due to an opponent not appearing in time, shall not receive a bye. B.2 No player's colour difference will become >+2 or <-2. No player will receive the same colour three times in row. Relative Criteria (These are in descending priority. They should be fulfilled as much as possible. To comply with these criteria, transpositions or even exchanges may be applied, but no player should be moved down to a lower score bracket). B.3 The difference of the scores of two players paired against each other should be as small as possible and ideally zero. B.4 As many players as possible receive their colour preference. (Whenever x of a score bracket is unequal to zero this rule will have to be ignored. x is deducted by one each time a colour preference cannot be granted.) B.5 No player shall receive an identical float in two consecutive rounds. B.6 No player shall have an identical float as two rounds before. Note: B2, B5 and B6 do not apply when pairing players with a score of over 50% in the last round. C. Pairing Procedures Starting with the highest score bracket apply the following procedures to all score brackets until an acceptable pairing is obtained. Afterwards the colour allocation rules (E) are used to determine which players will play with white. C.1 If the score bracket contains a player for whom no opponent can be found within this score bracket without violating B1 or B2 then: if this player was moved down from a higher score bracket apply C12. if this score bracket is the lowest one apply C13. in all other cases: move this player down to the next score bracket. C.2 Determine x according to A8. C.3 Determine p according to A6. C.4 Put the highest players in S1, all other players in S2. C.5 Order the players in S1 and S2 according to A2. C.6 Pair the highest player of S1 against the highest one of S2, the second highest one of S1 against the second highest on e of S2, etc. If now p pairings are obtained in compliance with B1 and B2 the pairing of this score bracket is considered complete. in case of a homogeneous score bracket: remaining players are moved down to the next score bracket. With this score bracket restart at C1. in case of a heterogeneous score bracket: only players moved down were paired so far. Start at C2 with the homogeneous remainder group. C.7 Apply a new transposition of S2 according to D1 and restart at C6. C.8 In case of a homogeneous (remainder) group: apply a new exchange between S1 and S2 according to D2. Restart at C5. C.9 Drop criterion B6 and B5 (in this order) for downfloats and restart at C4. C.10 In case of a homogeneous remainder group: undo the pairing of the lowest moved down player paired and try to find a different opponent for this player by restarting at C7. If no alternative pairing for this player exists then drop criterion B6 first and then B5 for upfloats and restart at C2. C.11 As long as x is less than p: increase x by 1. When pairing a remainder group undo all pairings of players moved down also. Restart at C3. C.12 In case of a heterogeneous group: undo the pairing of the previous score bracket. If in this previous score bracket a pairing can be made whereby another player will be moved down to the current one, and this now allows p pairing to be made then this pairing in the previous score bracket will be accepted. C.13 In case of the lowest score bracket: the pairing of the penultimate score bracket is undone. Try to find another pairing in the penultimate score bracket which will allow a pairing in the lowest score bracket. If in the penultimate score bracket p becomes zero (i.e. no pairing can be found which will allow a correct pairing for the lowest score bracket) then the two lowest score brackets are joined into a new lowest score bracket. Because now another score bracket is the penultimate one C13 can be repeated until an acceptable pairing is obtained. C.14 Decrease p by 1 (and if the original value of x was greater than zero decrease x by 1 as well). As long as p is unequal to zero restart at C4. If p equals zero the entire score bracket is moved down to the next one. Restart with this score bracket at C1. D. Transposition and Exchange Procedures Example: S1 contains players 1, 2, 3 and 4 (in this sequence); S2 contains players 5, 6, 7 and 8 (in this sequence). D.1 Transpositions within S2 should start with the lowest players, with descending priority: 5-6-8-7; 5-7-6-8; 5-7-8-6; 5-8-6-7; 5-8-7-6; 6-5-7-8; 6-5-8-7, etc. Hint: put all numbers constructable with the digits 5, 6, 7 and 8 in ascending order. D.2 When applying an exchange between S1 and S2 the difference between the numbers exchanged should be as small as possible. When differences of various options are equal take the one concerning the lowest player of S1. Exchange one player S1 Exchange two players S1 4 3 2 S2 3+4 2+4 2+3 5 a c f 5+6 j l o 6 b e h 5+7 k n q 7 d g i 6+7 m p r The above matrices contain the sequence in which exchanges should be applied. Exchanging one player: a) 4 and 5; b) 4 and 6; c) 3 and 5; etc. until i) 2 and 7. Exchanging two players: j) 3+4 with 5+6; k) 3+4 with 5+7; l) 2+4 with 5+6 etc. After each exchange both S1 and S2 should be ordered according to A2. Remark: if the number of players in a score bracket is odd, S1 contains one player less than S2. So with 7 players S1 contains players 1, 2 and 3, S2 4, 5, 6 and 7. The exchanges needed in that case can be found from the above ones by deducting all numbers in S1 and S2 by 1. The last column of the second matrix has then become obsolete. E. Colour Allocation Rules For each pairing apply (with descending priority): E.1 Grant both colour preferences. E.2 Grant the stronger colour preference. E.3 Alternate the colours to the most recent round in which they played with different colours. E.4 Grant the colour preference of the higher ranked player. E.5 In the first round all even numbered players in S1 will receive a colour different from all odd numbered players in S1. F. Final Remarks F.1 After a pairing is complete sort the pairing before making them public. The sorting criteria are (with descending priority) the score of the higher player of the pairing involved; the sum of the scores of both players of the pairing involved; the rank according to A2 of the higher player of the pairing involved. F.2 Byes, and pairing not actually played, or lost by one of the players due to arriving late or not at all, will not be taken into account with respect to colour, Such a pairing is not considered to be illegal in future rounds. F.3 A player who after five round has a colour history of BWW-B (i.e. no valid game in round 4) will be treated as -BWWB with respect to E3. So WB-WB will count as -WBWB and BWW-B-W as - - BWWBW. F.4 Because all players are in one homogeneous score bracket before the start of round one and are ordered according to A2 the highest player of S1 will play against the highest player of S2 and if the number of players is odd the lowest ranked player will receive a bye. F.5 Players who withdraw from the tournament will no longer be paired. Players known in advance not to play in a particular round are not paired in that round and score 0. F.6 A pairing officially made public shall not be changed unless it violates the absolute pairing criteria (B1 and B2). F.7 If either result was written down incorrectly, or a game was played with the wrong colours, or a player's rating has to be corrected, then this will only affect pairing yet to be made. Whether it will affect a pairing already made public but not yet played should be decided by the arbiter. Unless the rules of the tournament state otherwise: F.8 Players who are absent during a round without notification to the arbiter will be considered to have withdrawn themselves. F.9 Adjourned games are considered draws for pairing purposes only. F.10 F.10 In order to make the final standings the following criteria apply (in descending priority): the highest number of points scored; should this be equal for several participants prize money should be shared; where it concerns the first place: the best result in games played against each other; the highest average rating of the opponents; the drawing of lots.