Into Darkest Switzerland

It is time, finally, to venture with gun and camera into the heart of darkness – making Swiss pairings. As our trusty native guide, we’ll use Bwana USCF – Chapter 2 of the USCF Official Rules of Chess (7th edition). Chess players have been running Swiss tournaments for years, so darkest Switzerland holds no terror for Bwana USCF. Still, we must be alert to the possibility the Bwana USCF will try to lead us into occult rituals peculiar to the needs of Chess.

Here are the five main rules that Bwana USCF applies to determine pairings, listed in approximately the order in which they should be enforced:

1. No pair of players who have already met may be paired against each other;
2. Each pair of players should have the same score or, if this is not possible, nearly the same score;
3. Within each score group, the pairings should be arranged so that the top half of the ratings distribution plays the bottom half of the ratings distribution, with each half sorted by rating;
4. Players should have equal, or nearly equal, opportunities to play the white pieces; and
5. Players should not play the same color pieces several times in a row.

The third rule implements a form of seeding that, strictly speaking, makes such pairings Dutch pairings. Dutch pairings make sense especially when the number of rounds in the tourney is just enough to identify a unique winner – that is, when the number of rounds is the same as the number of rounds needed for a knock-out bracket for the same number of players. It has an effect similar to that of conventional bracket seeding, so that the top two players, if neither loses earlier, will meet each other in the final round.

If there aren’t enough rounds to ensure that there can be only one undefeated player, Bwana USCF countenances accelerated pairings, which would split the first-round field into quadrants rather than halves. This doesn’t guarantee that there will be a unique winner, but makes it considerable more likely because it moves up by a round the possible pairing of two top players.

(It seems that pairing systems tend to get named for nationalities associated, in popular imagination, with both orderly precision and low levels of corruption. One encounters variations called Danish and Norwegian also. It wouldn’t do to call a system Congolese or even Italian. If I ever invent a pairing system, I intend to call it the New Zealand System.)

But these five rules are not sufficient to determine, for any particular round pairing, exactly what pairing is called for. So there are a large number of ancillary rules, all intended (when properly applied) to make one particular set of pairings the correct one.

Bwana FIDE (Bwana USCF’s big brother) goes so far as to provide pseudo-code for an automated pairing system, with the hope that, armed with a proper program, every tournament director will produce exactly the same result. Doing this requires each of the ancillary rules to be weighed against all of the others.

It’s making sense of the welter of ancillary pairing rules that makes Swiss pairings appear to be such a black art. And this might explain why they’re often resisted for games other than chess.