The

Swiss pairing system is used in

chess tournaments as a fair method of deciding who

plays whom, and with what

colour pieces, in each round of the

competition. The system consists of a quite detailed set of

rules and

algorithms; what follows is only a simplified overview.

Several criteria are involved in the choice of pairings for each round; a few of these, referred to as "absolute criteria", *must* be satisfied, while the so-called "relative criteria" are applied to whatever extent is possible. The absolute criteria require that no two players meet more than once throughout the competition, that no player receives more than one bye, and that colours are fairly distributed (so that each player, as near as possible, plays half his games as White and half as Black). Various possible pairings will obey these rules in each round; the remaining criteria describe how to choose the most favourable amongst them. Perhaps the most important criterion is that each pair of players are as closely matched (in terms of points scored thus far in the competition) as possible; other rules govern the way in which colours are distributed in those cases where a perfect distribution is impossible, and how to most evenly pair players of uneven strength in cases where this is forced.

The basic Swiss pairing algorithm for each round is as follows: first, divide players into groups so that each group contains all those players on a particular score. (Before the first round has been played, everyone's score is zero, so in this case we simply have one group containing all of the players; in subsequent rounds the players' presumably differing results will separate them into various score groups.) Within each group, rank players according to their professional or estimated rating, and then pair the top half of the group against the bottom half by matching the top player with the player just beneath the middle, the second-highest player with the player second beneath the middle, and so on until the player halfway down the group is paired with the lowest player. (This obviously assumes an even number of players in the group; odd-sized groups are dealt with either by awarding a bye or by moving the odd player into an adjacent group.) Once this "tentative pairing" is done, various carefully defined shufflings are performed until all players are matched with someone they've not yet played, until colour allocations are sufficiently even, and so on. For details of the ugly complexities involved, the reader is referred to `www.swissperfect.com`.