The Swiss system is a combination of all-play-all and knockout. All the players play in every round, but in each round players with equal (or at least similar) scores meet each other.
Any players who join after the first round shall receive no score for the rounds they have missed.
Before each round, the players are ranked in order. They are ranked first by score, then by grade/rating, then by title (e.g. grandmaster), then in alphabetical order. For pairing purposes only, an adjourned game is considered a draw.
Having sorted the players, the next step is to pair them. Each player in the top half plays the player in the corresponding position in the bottom half, e.g. the highest ranked player overall is paired with the highest ranked player in the bottom half. This process is repeated, for the second and subsequent rounds, within groups of players having the same scores (termed score brackets). The score brackets should be sorted in descending order of score.
Two players may not play each other more than once. This is one of the absolute pairing criteria; it may not be violated, and if necessary players should be moved to a lower score bracket in order to meet it. However, if a player wins a game by default, it is not illegal for that player to be paired with the same opponent again.
If the number of players is odd, the lowest ranked player in each round is given a bye, worth 1 point. A bye is considered a downfloat (see later). One absolute pairing criterion is that a player who receives either a bye or a win by default may not be given a bye subsequently.
Where a score bracket contains an odd number of players, the lowest ranked player shall be paired with the highest ranked player of the next lowest score bracket (unless the rules require a different pairing). The former player will then have been given a downfloat and the latter player an upfloat; and they will effectively constitute a separate score bracket. Two relative pairing criteria, in descending order of priority, are that no player should receive an identical float in two consecutive rounds, and that no player shall receive an identical float as two rounds before; however, neither of these apply when pairing players with scores of over 50% in the last round.
To meet relative (and absolute) pairing criteria, it may be necessary to transpose players in the bottom half of a score bracket. Start by numbering those players in order, "1" denoting the highest ranked player. Then list the numbers that can be constructed from the digits denoting the players. Finally, work through the numbers in ascending order until one is found that corresponds to an order that allows a legal pairing.
If transpositions cannot produce a legal pairing, a player in the top half of a score bracket may be exchanged for one in the bottom half. The difference between the rankings of the players to be exchanged should be as small as possible. If this allows more than one possible exchange, choose the one involving the lowest ranked players.
Players should not be moved to a lower score bracket in order to fulfil relative pairing criteria.
Having paired the players, the next step is to decide who plays with which colour. In the first round, the odd numbered players in the top half play with one colour, and the even numbered players in the top half play with the other. The colour played by each group should be decided by lot.
No player may play more than two consecutive games with the same colour, and no player may play more than two more games with one colour than with the other. These are absolute pairing criteria. However, they do not apply when pairing players with a score of over 50% in the last round.
In descending order, a player's preference for one colour may be: absolute, when he has played more than one fewer game with that colour than with the other or has played the latest two games with the opposite colour; strong, when the player has played one fewer game with that colour than with the other; or mild, when the player has played the same number of games with both colours and played with the opposite colour in the previous round. One relative criterion is that, where possible, everyone in a score bracket should be given their colour preferences.
If it is not possible to grant the colour preferences of both players in a pairing, grant the stronger preference. If both preferences are equally strong, alternate the colours to the most recent round in which the players played with opposite colours; for this purpose, those rounds in which a player did not play are moved to the beginning, with the other rounds following in order. If both players have identical colour histories, grant the preference of the higher ranked player.
Finally, there is the question of tie-breakers. There are three methods. Where players are tied for first place, they can be separated by the results of games played between them. The second method is to calculate the averages of the opponents' grades. The third method is to draw lots.
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