How Ocheso pairs a Swiss round

A Swiss lets a big field play a short event without knocking anyone out. Nobody plays everyone. Instead, each round, players with similar scores meet players they haven't met yet. After five or six rounds the strongest results have risen to the top, and every player has had a full day of games.

The idea fits on a napkin. Doing it well, every round, in every event, is harder than it looks.

What a good pairing has to respect#

Every Swiss round asks the same questions, and they pull against each other. Ocheso answers them in a fixed order, and the rules higher on the list count for far more than the ones below them:

1. No rematches. Two players who have met don't meet again, unless there is no other way to pair the round at all.
2. No impossible colours. A player who has had the same colour twice in a row, or two more games with one colour than the other, must have the other colour next. Two players who must have the same colour aren't paired together.
3. Close scores. Players meet opponents on their own score wherever possible. When someone has to play up or down, the gap is kept small, and a gap of a full point counts four times as much against a pairing as a gap of half a point.
4. Colour preferences. Beyond those hard limits, a player who is due a colour gets it where the rules above allow.
5. Top half against bottom half. Inside a score group, the stronger half by seed plays the weaker half, so the leaders meet late, not in round one.

Organisers will recognise the order: it is how the Dutch system, the most common Swiss in chess, ranks its criteria.

Weighing every pairing at once#

Most pairing programs work like a careful person with a pencil. They pair the top group, move down, and when a choice further down turns out to be impossible, they go back and undo an earlier one. That works in round one. In the last rounds of a small event, when most players have already met each other, it can back up and retry for a long time, or give up.

Ocheso does it differently. For each round it considers every possible game between every two players and gives each one a weight that encodes the five rules above. Then it picks the set of games with the highest total weight, a classic problem in graph theory called maximum-weight matching.

Because every possible pairing is considered at once, there is nothing to back out of. If the round can be paired, it is, and the method always finishes.

Round one, byes and boards#

Before round one, players are seeded by rating, strongest first, and the top half plays the bottom half: seed 1 against the first seed of the lower half, seed 2 against the second, and so on, with colours alternating down the boards.

With an odd number of players, someone sits out. The bye goes to the lowest-placed player who hasn't had one, and it is worth a full point, the common club rule. A double forfeit scores nothing for either player. Boards are numbered from the top scores down, with the bye last.

Breaking ties#

When players finish level, Ocheso applies the tie-breaks the organiser chose, in the organiser's order. If players are still level after all of them, rating decides.

The standings show these values beside every place, so anyone can check why one player finished above another.

The other three formats#

• Round robin. Everyone plays everyone, on Berger tables. With an even number of players there is one round fewer than players; with an odd number there is one round per player, and each player sits out once.
• Knockout. A bracket seeded by rating, arranged so the top two seeds can only meet in the final; when the field isn't a power of two, the top seeds get the byes. A drawn match goes to a tie-break game in its own round, colours reversed, until a game is decisive.
• Arena. No rounds. When you finish a game you're paired with the best opponent free at that moment. A win is 2 points and a draw 1, and two wins in a row start a streak: every result counts double until the streak breaks.

What we don't claim#

Ocheso's Swiss follows the Dutch system's priorities, in the Dutch system's order. It is not a certified FIDE Dutch implementation, and in some rounds it may choose a different pairing from a certified program that is just as valid by the same rules. If your event will be submitted for FIDE rating, pair it with a FIDE-endorsed program. For club nights, school leagues, online series and everything else, it's the pairing we'd want to play in.

Try it#