Swiss System Based on Rating 
 
Approved by the 1992 General Assembly. 
 
A. Introductory Remarks and Definitions 

A1.  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) 
 
A2. Order 
For pairing purposes only, the players are ranked in order
of, respectively 
a) score 
b) rating 
c) FIDE-title (IGM-WGM-IM-WIM-FM-WFM-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this criterion has been replaced by another one) 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. 
 
A3. 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. 
 

A4. 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 (  ). 

A5. Byes 
Should the total number of players be (or become) odd, one
player ends up unpaired. This player receives a bye: no
opponent, no color, 1 point. A bye is considered to be a
downfloat. 

A6. 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. 
 
A7. Color differences and color preferences 
The color 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 color preference can be determined for
every player. 
 
a) An absolute color preference occurs when a player's color
difference is greater that 1 or less than -1, or when a
player played with the same color in the two latest rounds.
The preference is white when the color difference is << 0 or
when the last two games were played with black, otherwise
black. In this case the (obligatory) color 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). 

b) A strong color preference occurs when a player's color
difference is unequal to zero. The preference is white when
the color difference is << 0, black otherwise. 

c) A mild color preference occurs when a player's color
difference is zero, the preference being to alternate the
color with respect to the previous game. In this case the
color difference is written down as +0 or -0 depending on the
color of the previous game (white or black respectively).  
Before the first round the color preference of one player
(often the highest one) is determined by lot. 
 
A8. Definition of "x" 
The number of pairings which can be made in a score bracket,
either homogeneous or heterogeneous, not fulfilling all color
preferences, is represented by the symbol x. 
 
 
x can be calculated as follows: 
w=number of players having a color preference white. 
b=number of players having a color 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. 
 
A9. Transpositions and exchanges 

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. 
 
B. Pairing Criteria 
 
Absolute Criteria 
(These may not be violated. If necessary players will be
moved down to a lower score bracket.) 
 
B1. 
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. 
 
B2. 
a. No player's color difference will become >>+2 or <<-2. 
b. No player will receive the same color 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). 
 
B3. 
The difference of the scores of two players paired against
each other should be as small as possible and ideally zero. 
 
B4. 
As many players as possible receive their color 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
color preference cannot be granted.) 

B5. 
No player shall receive an identical float in two consecutive
rounds. 

B6. 
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 color allocation rules (E) are
used to determine which players will play with white. 
 
C1. 
-	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. 
 
C2. 
Determine x according to A8. 

C3. 
Determine p according to A6. 

C4. 
Put the highest players in S1, all other players in S2. 

C5. 
Order the players in S1 and S2 according to A2. 

C6. 
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. 
 
C7. 
Apply a new transposition of S2 according to D1 and restart
at C6. 

C8. 
In case of a homogeneous (remainder) group: apply a new
exchange between S1 and S2 according to D2. Restart at C5. 

C9. 
Drop criterion B6 and B5 (in this order) for downfloats and
restart at C4. 

C10. 
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. 

C11. 
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. 

C12. 
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. 

C13. 
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.  

C14. 
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). 
 
D1. 
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 constructable with the digits 5, 6, 7
and 8 in ascending order. 
 
D2. 
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			Exchange two players 
 
		S1					S1 
	4	3	2			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. Color Allocation Rules 
For each pairing apply (with descending priority): 
 
E1. 
Grant both color preferences. 

E2. 
Grant the stronger color preference. 

E3. 
Alternate the colors to the most recent round in which they
played with different colors. 

E4. 
Grant the color preference of the higher ranked player. 
In the first round all even numbered players in S1 will
receive a color different from all odd numbered players in
S1. 
 
F. Final Remarks 

F1. 
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. 

F2. 
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 color, Such a pairing is not
considered to be illegal in future rounds. 
 
F3. 
A player who after five round has a color 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. 
 
F4. 
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. 

F5. 
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. 

F6. 
A pairing officially made public shall not be changed unless
it violates the absolute pairing criteria (B1 and B2). 

F7. 
If either result was written down incorrectly, or a game was
played with the wrong colors, 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: 

F8. 
Players who are absent during a round without notification to
the arbiter will be considered to have withdrawn themselves. 

F9. 
Adjourned games are considered draws for pairing purposes
only. 

F10. 
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.                                         
