C.04.4.1 Dubov System
Approved by the 1997 General Assembly. 

Preface: The DUBOV Swiss Pairing System is designed to maximise the fair treatment of the players. This means that a player having a higher rating performance than another player during a tournament should have more points as well. If the average rating of all players is nearly equal, like in a round robin tournament, 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 equalise the average rating of the opponents of all players of a score group. Therefore the pairing of a round will pair players who have played low rated players before with players having high ratings now. 

1. 
Introductory definitions 


1.1 
"R" is the rating of a player 


1.2 
"ARO" is the average rating of a player's opponents. ARO must be calculated after each round as basis of the pairings. 


1.3 
The "due colour of a player is white",



1.4 
The "due colour of a player is black",


2. 
Pairings limitations 


See Basic Rules, section C.04.1, rules b, c, d, g, f 


2.1 
Apart from the last round a player cannot be transferred to a higher score group two times running and more than three times (if the tournament has less than 10 rounds) or four times (if the tournament has more than 9 rounds) during one tournament. 


2.2 
A player shall not be transferred from the subgroup due to a colour to the subgroup due to the other colour if this would violate the limitations C.04.1.f or C.04.1.g. 

3. 
Colour allocation 


Pairing two players the colour allocation shall regard with descending priority:


4. 
Odd number of players at the tournament 


The player from the lowest score group, who has the lowest R will get the pairingallocated bye. 

5. 
Pairing for the first round 


The player's list calculated before is divided into two equal parts: The players from the upper part of the list are placed on the left and those from the lower part, on the right. The first player from the lefthand list plays the first player from the righthand list, the second plays the second, etc. After that, the colour of the pieces is determined by drawing lots for one of the pairs, for example, for the first pair. In such a case, all oddnumbered pairs have the same colours as the first pair, whereas all evennumbered pairs have the other colour. 

6. 
The standard pairing procedure for the remaining rounds 


6.1 
Standard requirement (Special cases see below chapter 7) 



The number of players having the same score is even and the number of players with due colour white and black is the same. Each player in the score group has at least one possible opponent in the score group. 


6.2 
First attempt 



The players who should play with the white pieces are arranged in order of increasing ARO, the ARO being the same the player with the lower R is placed higher. If ARO and R coincide completely, the players are to be placed alphabetically. For example:
The names of the players are then written down, and only one fact is checked  whether the players have not played their opponents before. 


6.3 
Improvements 



If the players have already played each other, then the "white" player is paired with the first "black" player whom he has not played before, from the lower rows. 


6.4 
Floater 



The aim of the pairing procedure is to pair all players within a score group. 



a. 
the player was not floater from higher score groups and can be paired in the lower score group 



b. 
the player was not floater from higher score groups and cannot be paired in the lower score group 



c. 
the player was floater from higher score groups and can be paired in the lower score group 



d. 
the player was floater from higher score groups and cannot be paired in the lower score group 

7. 
Transfer of players to meet the requirement of Chapter 6 


If the requirement of the standard pairing procedure is not fully fulfilled the following transfers shall be carried out in the order listed below. 


7.1 
If a player has already played with all the players of his own score group, a player from the next possible lower score group is transferred to the score group to be paired who has not yet played with the player in question and can be paired according to the colour allocation rules 



a. 
the due colour is opposite to the due colour of the player in question. 



b. 
if there is a choice, then the player with the highest R is to be transferred. 



c. 
if there are more than one players having the same R then the one with the lowest ARO will be transferred. 


7.2 
If the number of players of the score group odd, a player from the next possible lower score group shall be transferred to the score group to be paired, who has not yet played with at least one of the players of the higher score group and is allowed to be paired according to the colour allocation rules. 



a. 
his due colour is opposite to the dominating due colour of the higher score group. 



b. 
if there is a choice, then the player with the highest R is to be transferred. 



c. 
if there are more than one players having the same R then the one with the lowest ARO will be transferred. 


7.3 
If the number of players in the score group is even and the number ofWhites exceeds the Blacks by 2n, then n "white" players, who have the lowest ARO, are transferred to the black group. If their ARO is equal, the player with the higher R is chosen. Should both (ARO and R) coincide completely, the list of the players is arranged alphabetically, the transfer being made from the upper half. 


7.4 
If the number of players with the same score is even and the number of Whites is smaller than the number of Blacks by 2n, then n "black" players, who have the highest ARO, are transferred to the white group. If their ARO is equal, the player with the lower R is chosen. Should both (ARO and R) coincide completely, the list of the players is arranged alphabetically, the transfer being made from the upper half. 

8. 
Treatment of floaters 


8.1 
Priority of floaterpairing 



The floaters having due colour white are arranged according to chapter 6.2. 


8.2 
Pairing the floaters 



Each of the floaters is paired with the player having the highest R, if possible having the opposite due colour. If there are more than one player with equal R, the player with the lowest ARO is chosen. 

9. 
Final remarks. 


The list of AROs should be published after each round to make it possible for the players to calculate the pairings on their own. 