Handbook :: C. General Rules and Recommendations for Tournaments

04.4 The Burstein Swiss Pairing System (Based on Sonnenborn-Berger and Buchholz)

Preface: The BURSTEIN Swiss Pairing System is designed to maximize the fair treatment of the players. This means that players having the same score should have met as equal opposition as possible during a tournament. If the Sonnenborn-Berger and/or Buchholz and/or Median, of all players in the same score-group, is nearly equal, the goal is reached. As a Swiss System is a more or less statistical system, this goal can only be reached approximately. The approach is the attempt to equalize the strengh of the opponents of all players in a given score group. Therefore the pairing of each round will tend to pair players who have high Sonnenborn-Berger (or Buchholz or Median) with players having low Sonnenborn Berger (or Bucchholz or Median) in the same score-group. The ratings of the players should be taken into consideration only when the Sonnenborn-Berger (or Buchholz or Median) is equal (e.g. in the first two rounds); otherwise, only current data of the tournament itself should be the basis for measuring the "strength" of the players and making the pairings thereafter.
1.	Introductory definitions: "R" is the rating of a player "SG" (Score Group) is the group of players having the same number of points. The "due color of a player" is the color he played less times than the other color. If he played the same number of both colors, than the "due color of a player" is the alternate color of which he played in the previous round.
2.	Unfinished games: Unfinished (or temporarily non played) games shall be considered as draws for pairing purposes.
3.	Basic pairings principles:
	3.1	Two players who have played each other shall not be paired again.
	3.2	Before making the pairings in each round, players in every SG (including "floaters" from another SG) shall be arranged in the order of their (1) Sonneborn-Berger (SB); (2) Buchholz; (3) Median (4) rating. The player with the highest SB shall be No. 1 in the SG. Players with the same SB shall be arranged in the order of their Buchholz and so on.
	3.3	For accelerating pairing, in the first two rounds, an ‘imaginary’ point shall be added to the score of each of the players in the top half of the initial list of participants (arranged in the order of their R). This imaginary point shall then be deducted before making the pairings of the third round.
4.	Odd number of players at the tournament:
	4.1	A player who has already received a point without playing shall not receive a bye.
	4.2	The player from the lowest SG, who has the lowest SB, will get the bye.
	4.3	If there are players with the same lowest SB in the lowest SG, then the player with the lowest Buchholz will get the bye and so on.
	4.4	The bye has no color.
5.	Color Allocation:
	5.1	In the first round the color assigned to player No.1 shall be decided by drawing a lot. All other odd numbered players in the top half of the initial list shall receive the same color.
	5.2	The difference of the number of black and the number of white games shall not be greater than 2 or less than –2.
	5.3	A player shall not have the same color three times in a row.
	5.4	After pairing two players’ colors shall be assigned based on giving descending priority to:
		giving both players their due color equalizing the numbers of black and white games played before alternating the colors of both players regarding the first difference of their color history going back from the previous round to the first round. Assigning his due color to the player with the higher SB assigning his due color to the player with the higher Buchholz, and so on.

6. Paring procedures:

6.1

In each SG priority shall be given to pair the highest player (i.e. the player with the highest SB) with the lowest player in that SG that he has not already played. The second highest player shall be paired with the second lowest player, etc.

6.2

To illustrate the procedure, suppose there are six players in a SG, ordered 1 through 6 as described in rule 3.2. There will be 15 combinations of pairing within the group, in the following descending order of priority:

1	1*6	2*5	3*4
2	1*6	2*4	3*5
3	1*6	2*3	4*5
4	1*5	2*6	3*4
5	1*5	2*4	3*6
6	1*5	2*3	4*6
7	1*4	2*6	3*5
8	1*4	2*5	3*6
9	1*4	2*3	5*6
10	1*3	2*6	4*5
11	1*3	2*5	4*6
12	1*3	2*4	5*6
13	1*2	3*6	4*5
14	1*2	3*5	4*6
15	1*2	3*4	5*6

6.3

If there is an uneven number of players in the SG, the same procedure is followed and the remaining player is floated to the next SG (provided he is not a floater from another SG) and is paired within this SG according to the same procedure.

6.4

To illustrate the procedure, suppose there are five players in a SG, ordered 1 through 5 as described in rule 3.2. There will be 15 combinations of pairing within the group, in the following descending order of priority ("F" = floater):

1	1*5	2*4	3*F
2	1*5	2*3	4*F
3	1*5	3*4	2*F
4	1*4	2*5	3*F
5	1*4	2*3	5*F
6	1*4	3*5	2*F
7	1*3	2*5	4*F
8	1*3	2*4	5*F
9	1*3	4*5	2*F
10	1*2	3*5	4*F
11	1*2	3*4	5*F
12	1*2	4*5	3*F
13	2*5	3*4	1*F
14	2*4	3*5	1*F
15	2*3	4*5	1*F

[If, for example, No. 2 is a floater from another SG, combinations (3), (6) & (9) are not valid].

6.5

In each SG maximum number of players should get their due colors. Suppose, for example, that the due color of players 2, 4 and 5 is white, and that of the others is black; then the valid combination is No. (4) in rule 6.2 or No. (2) in rule 6.4.

6.6

If the SG from which the floater has been dropped is such that a complete pairing of all remaining teams in the SG cannot be made (or if the floater has already played every player in the next SG), then the floater shall be moved back to its original SG, trying the next possible combination according to the order of priority. If a complete pairing of all teams in two adjacent SG’s cannot be made, then these two SG’s shall be considered as one SG, and rules 6.1 – 6.5 shall accordingly apply.