Approved by the 1992, 1997 and 1998, 2001, 2006 General Assemblies.

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)

For pairing purposes only, the players are ranked in order of, respectively

a) score

b) rating

c) FIDE-title (IGM-IM-WGM-WIM-FM-CM-WFM-WCM-no title)

d) alphabetically (unless it has been previously stated that this criterion has been replaced by another one)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.

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.

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 ( ).

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.

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.

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.

(a) 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.

(b) 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.

(c) While pairing an odd-number round players having a strong colour preference (players who have had a bye before) shall be treated like players having an absolute colour preference as long as this does not result in additional downfloaters. (GA 2001)

(d) While pairing an even-numbered round players having a mild colour preference (players who have had a bye before) shall be treated and counted as if they would have a mild colour preference of that kind (white resp. black) which reduces the value of x (see A8) as long as this does not result in additional floaters. (GA 2001)

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) 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.

(b) 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.

Absolute Criteria

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

a) Two players shall not meet more than once.

b) 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.

a) No player’s colour difference will become >+2 or <-2.

b) 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).

The difference of the scores of two players paired against each other should be as small as possible and ideally zero.

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.)

No player shall receive an identical float in two consecutive rounds.

No player shall have an identical float as two rounds before. Notes: B2 may not be applied when pairing players with a score of 50% in the last round if this is helpful to avoid additional downfloaters.B5 and B6 do not apply when pairing players with a score of over 50% in the last round. (GA 2001)

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.

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.

Determine x according to A8.

Determine p according to A6.

Put the highest players in S1, all other players in S2.

Order the players in S1 and S2 according to A2.

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.

Apply a new transposition of S2 according to D1 and restart at C6.

In case of a homogeneous (remainder) group: apply a new exchange between S1 and S2 according to D2. Restart at C5.

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.

Drop criterion B6 and B5 (in this order) for downfloats and restart at C4.

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.

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.

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.

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.

Example: S1 contains players 1, 2, 3 and 4 (in this sequence); S2 contains players 5, 6, 7 and 8 (in this sequence).

Transpositions within S2 should start with the lowest players, with descending priority:

a) 5-6-8-7;

b) 5-7-6-8

c) 5-7-8-6

d) 5-8-6-7

e) 5-8-7-6

f) 6-5-7-8

g) 6-5-8-7, etc.

Hint: put all numbers
constructible with the digits 5, 6, 7 and 8 in ascending order.

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 4 3 2 3+4 2+4 2+3

S2 5 a c f S2 5+6 j l o

6 b e h 5+7 k n q

7 d g
I 6+7 m p r

Exchange two players

S1 3+4 2+4 2+3

S2 5+6 j l o

5+7 k n q

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.

For each pairing apply (with descending priority):

Grant both colour preferences.

Grant the stronger colour preference.

Alternate the colours to the most recent round in which they played with different colours.

Grant the colour preference of the higher ranked player.

In the first round all even numbered players in S1 will receive a colour different from all odd numbered players in S1.

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.

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.

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.

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.

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.

A pairing officially made public shall not be changed unless it violates the absolute pairing criteria (B1 and B2).

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:

Players who are absent during a round without notification to the arbiter will be considered to have withdrawn themselves.

Adjourned games are considered draws for pairing purposes only.

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.

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