Swiss system

The rules that every Swiss shares

The International Chess Federation (FIDE) sets out basic rules that apply to any Swiss system. Four of them carry the format.

1. The number of rounds is declared beforehand.
2. Two participants do not play each other more than once.
3. Participants are, in general, paired with others on the same score.
4. If the number of participants is odd, one of them is left unpaired and gets a bye.

That bye is worth as many points as a win, unless the tournament's rules say otherwise, and a player cannot be given it twice.

Chess adds rules about colours. A player's games with White and with Black may not differ by more than two, and nobody gets the same colour three times running.

The last basic rule is about trust. The pairing rules must be transparent enough that the person in charge of the pairing can explain them.

Before round one: a number for every player

A Swiss needs a starting order. FIDE's handling rules rank the players before the first round by strength, usually their rating, then by title, then alphabetically. The highest ranked gets number 1, and so on down. This is the tournament pairing number, and it stays with the player throughout.

The number is not a seeding in the knockout sense. Nobody is placed in a bracket. It is used to order players inside a group who are on the same score.

It can be corrected if the data were wrong, but not after the fourth round has been paired.

How one round is paired

FIDE's own pairing method is called the Dutch System. Before each round the players are put in order by score, and within the same score by pairing number.

Everyone on the same score forms a score group. The group is split into a top half and a bottom half, and the first player of the top half meets the first of the bottom half, the second meets the second and so on.

Take eight players on the same score, numbered 1 to 8, as a worked example. The halves are 1 to 4 and 5 to 8, so the pairings are 1 against 5, 2 against 6, 3 against 7 and 4 against 8.

Two things disturb that tidy picture. If a pair has already played, or the colours would break the rules, the order of the bottom half is changed and the pairing is tried again. And if a score group has an odd number of players, one of them "floats" down to play someone from the next group.

Pairing starts with the top score group and works downwards until everyone is paired.

Two rounds, followed through

Here is a made-up eight-player event, to show the sorting at work. It ignores colours and assumes no draws.

Round one. Everyone has zero points, so all eight are one score group: 1 against 5, 2 against 6, 3 against 7 and 4 against 8. Suppose players 1, 2, 7 and 4 win.

Round two. There are now two score groups.

Nobody meets an opponent from round one, so no adjustment is needed. After round two there will be two players on two points, four on one and two on none, and the third round is paired the same way. Player 7, who caused the upset, is now being tested against the others who won.

What the pairing is trying to achieve

The Dutch System ranks its aims, and the order explains most of what looks odd in a published pairing.

Three things may never happen. Two players may not meet twice. A player may not get the free-point bye twice. And two players who both must have the same colour may not be paired, except among the leaders in the last round.

After that come quality aims, in order of priority. The first is to keep as many players as possible inside their own score group, so that as few as possible float. Then come the colour preferences. Then the system tries not to float the same player in consecutive rounds.

The order matters. Playing someone on your own score outranks getting the colour you are due, which is why a player sometimes gets Black twice in a row.

FIDE insists the result be reproducible: different arbiters, or different approved programs, must arrive at identical pairings. And it is not allowed to alter the correct pairings in favour of any participant.

Colours

Which of two paired players gets White is also settled by rule. Each player has a colour preference, worked out from the games already played. It is absolute if they have had one colour twice more than the other, or the same colour in their last two games. It is strong if they are one game out of balance, and mild if they are level, when the wish is simply to alternate.

For each pair, both preferences are granted if they can be. If not, the stronger one wins. If they are equal, the colours are alternated from the last time the two had different colours, and after that the higher-ranked player's preference is granted.

Before round one there is no history at all, so a single drawing of lots sets an "initial colour", and the rest follows from the pairing numbers.

Why a few rounds are enough

Here is the arithmetic, on the simplest assumption that no game is drawn. Each round halves the number of players with a perfect score.

Real tournaments have draws and play more rounds than that minimum, which is why the rule is only that the number is fixed in advance. Extra rounds also do a second job: they sort the middle of the field, which the minimum number leaves bunched together.

The weak point: round one

In the Dutch System's first round the top half of the list plays the bottom half. FIDE's own text says what follows. In tournaments with a wide range of strengths, the results of the first rounds "are usually quite predictable", and only a few per cent of games end in anything other than a win for the stronger side.

FIDE's answer is an accelerated pairing, which changes the early rounds only. In the Baku Acceleration Method the list is split in two before round one. Players in the top group are given "virtual points" equal to a win. The virtual points count only for pairing, never for the standings. Because they push the top group into a higher score group, strong players meet each other from the start.

In a nine-round tournament the first five rounds are accelerated. The top group gets one virtual point for the first three rounds and half a point for the next two, and nothing after that.

An organiser may use an accelerated method only if it was announced in advance.

Other approved pairing systems

The Dutch System is not the only one. FIDE's handbook also lists the Dubov, Burstein and Lim pairing systems, a double-Swiss system and a Swiss team pairing system. Only the Burstein System was read for this page.

It has a different aim. Its preface says it is designed so that players on the same score "should have met an average opposition as equal as possible". After a few opening rounds paired the Dutch way, it stops ordering each score group by rating. It orders players by how strong their opponents have been so far, and pairs those who have had a hard run with those who have had an easy one.

The same preface is candid about the limits of the whole family: "a Swiss System is a more or less statistical system", so the goal "can only be reached approximately".

Ties, and why the usual tie-breaks do not fit

In a round robin, two tied players have faced the same field. In a Swiss they have not. One may have met stronger opponents on the way to the same score.

FIDE's tie-break regulations sort the available measures by what they are built from.

The best known is Buchholz: the sum of the scores of each of a player's opponents. A higher Buchholz means a harder set of opponents. FIDE states that Buchholz must not be used in round robins, where it would tell you nothing.

Buchholz comes with modifiers. Cut-1 leaves out the opponent with the lowest score, so that one opponent who collapsed or withdrew does not drag a player down. Median-1 leaves out the lowest and the highest.

Other tie-breaks on FIDE's list look at the game between the tied players (direct encounter), or multiply each opponent's final score by the points scored against them (Sonneborn-Berger). The sum of progressive scores adds up a player's running total after every round, which favours someone who started fast.

Direct encounter needs care in a Swiss, because tied players may not all have met. FIDE's rule is that if one of them would be alone at the top of the mini-table among the tied players whatever the missing games had produced, that player is ranked first.

The organiser chooses an ordered list of tie-breaks, and it must be published before the tournament starts. If the list runs out, the tie is broken by drawing lots, unless the tournament's rules say such ties stay unbroken. A tournament may also settle places by play-off games, and if it does, its regulations must say which places are played off, in what format and at what time limit.

Byes, late arrivals and withdrawals

A long event with a large field has people coming and going, and a Swiss absorbs them in a way a bracket cannot.

• A late entry is paired from the round in which they arrive and gets no points for the rounds missed, unless the tournament's rules say otherwise.
• A player known in advance not to be playing a round is not paired and scores zero for it, unless the rules say otherwise. Tie-break rules call a half-point or zero-point absence a requested bye.
• A player who withdraws is simply no longer paired.

Absences distort tie-breaks that depend on opponents' scores, so FIDE's regulations say how each kind of unplayed round is to be valued when an opponent's Buchholz is worked out.

Once pairings are published they are meant to stand. They may be changed only in listed cases, such as two players being paired who have already met, and only if the chief arbiter judges the change to be in the tournament's interest.

In team events

When teams play a Swiss, a match produces two kinds of score: match points for the team's win, draw or loss, and game points, the sum of what its players scored on the individual boards. A competition decides which is primary, and the other becomes available as a tie-break.

What it is good at, and what it costs

This section is mostly reasoning from the structure.

A Swiss handles any number of entrants in a fixed number of rounds, keeps everyone playing to the end and gives each player opponents of about their own level after the first rounds. Those three things are why open chess tournaments use it.

Its weaknesses follow from the same design. Only the top of the final table is reliable, because the middle has been sorted least. Players on equal scores have had unequal journeys, so tie-breaks carry a lot of weight. The pairings cannot be published ahead of time, which is hard on spectators and on anyone who needs to plan. And the method is complicated enough that pairings are in practice produced by approved software.

It changes from event to event

The one thing to remember: in a Swiss, your next opponent depends on your own score, and your final place among equals depends on your opponents' scores. The number of rounds and the order of tie-breaks are in the tournament's regulations, and both are fixed before the first move.