Berger-Swiss: A Hybrid Pairing System for Chess Tournaments

[Mats Winther]

I was challenged to design the best pairing system ever and thought it was impossible. But now I've done it: Berger-Swiss.

Players are divided by rating into Berger groups, with six players and five rounds as the default. You can also choose eight players and seven rounds. Players with even TPNs, their ranking numbers based on rating, move down to the next group, while those with odd TPNs move up. As a result, players with nearby ratings will not meet during the Berger phase. The Berger groups are then shuffled separately. If the players cannot all be divided into Berger groups, the players with the highest TPNs instead form a Swiss group. With six-player groups, this group contains seven to eleven players. The tournament then begins.

When the Berger phase is over, players carry their points and tie-break scores into the Swiss section of the tournament, which can then continue for any number of rounds. This format works very well because players do not need to be paired against opponents with the same score from the outset, as they do in a traditional Swiss tournament. It is better to introduce that principle at a later stage, when the strongest players will naturally meet as they compete for the top places.

Playing in Berger groups with participants of similar playing strength is much more stimulating. Players know in advance whom they will face in the next round and which color they will have, so they can prepare. One problem with Berger tournaments arises when a player withdraws. In that case, the program creates a Swiss group comprising the affected Berger group and all the Berger groups below it, together with the existing Swiss group, if there is one. These players therefore switch to Swiss pairings earlier, while the Berger groups higher up continue as usual.

The Berger phase also allows games to be postponed and completed later, provided they are finished before Swiss pairings begin. This is a practical advantage when a tournament runs over an extended period.

Compared with a Swiss-only system, this format offers a considerably more stimulating tournament experience for players at every rating level. In my view, it is also preferable to Berger groups divided by rating class, since all participants compete in the same tournament. The system combines the advantages of both formats.

Berger-Swiss Tournament System – free online pairing system.

[Chris Goodall]

Why would you want to send a player into Round 6 with a score of 5/5 achieved entirely against players from the lower half of the rating list? What information do you gain from having player 1 beat that player easily, that you haven't already gained from player 1 beating five opponents from the top half of the rating list? If you want to have one representative of each Berger group in the top four going into round 6, surely old-fashioned binary seeding is the way forward: 1-8-9-16-17-24; 2-7-10-15-18-23, 3-6-11-14-19-22, 4-5-12-13-20-21. That's envy-free for linear monotonic win probabilities, since every group sums to 75. In your system 11 would rather like to swap places with 12, who would very very much like to swap places with 13.

[Mats Winther]

Why would you want to send a player into Round 6 with a score of 5/5 achieved entirely against players from the lower half of the rating list? What information do you gain from having player 1 beat that player easily, that you haven't already gained from player 1 beating five opponents from the top half of the rating list? If you want to have one representative of each Berger group in the top four going into round 6, surely old-fashioned binary seeding is the way forward: 1-8-9-16-17-24; 2-7-10-15-18-23, 3-6-11-14-19-22, 4-5-12-13-20-21. That's envy-free for linear monotonic win probabilities, since every group sums to 75. In your system 11 would rather like to swap places with 12, who would very very much like to swap places with 13.

This chess pairing system is not designed to maximize information about relative playing strength, but to create the best possible tournament experience for all participants. This is achieved by ensuring that rating differences within each group are neither too large nor too small. The Swiss phase then serves to distinguish the leading players.

The Swiss system is a brutal pairing format that continually matches players with the same score. Many find it stressful, as you never know who you will face next or which colour you will be assigned. In Berger-Swiss, players are exchanged only between adjacent pairs of Berger groups in rating order.

Example: In a tournament with seven Berger rounds, the first group consists of:

Magnus Carlsen 2823
Hikaru Nakamura 2792
Fabiano Caruana 2784
Javokhir Sindarov 2782
Nodirbek Abdusattorov 2780
Wesley So 2770
R. Praggnanandhaa 2763
Vincent Keymer 2761

The second group consists of:

Wei Yi 2758
Alireza Firouzja 2757
Anish Giri 2752
Arjun Erigaisi 2746
Jan-Krzysztof Duda 2741
Viswanathan Anand 2739
Leinier Domínguez Pérez 2732
Lê Quang Liêm 2732

Before the tournament begins, Nakamura, Sindarov, So, and Keymer will be moved down, while Yi, Giri, Duda, and Pérez will be moved up. (If five Berger rounds are chosen instead, only three players are exchanged between the six-player groups.) The Berger groups will then consist of the following players:

Group 1:

Magnus Carlsen 2823
Fabiano Caruana 2784
Nodirbek Abdusattorov 2780
R. Praggnanandhaa 2763
Wei Yi 2758
Anish Giri 2752
Jan-Krzysztof Duda 2741
Leinier Domínguez Pérez 2732

Group 2:

Hikaru Nakamura 2792
Javokhir Sindarov 2782
Wesley So 2770
Vincent Keymer 2761
Alireza Firouzja 2757
Arjun Erigaisi 2746
Viswanathan Anand 2739
Lê Quang Liêm 2732

The first group becomes somewhat weaker, while the second becomes stronger. However, it is obvious that Carlsen will face very strong opposition in Group 1. The average rating of Group 1 is 2767, while the average rating of Group 2 is 2760.

Depending on the rating distribution in a club tournament, it is theoretically possible for the second group to have a higher average rating than the first. However, that is not important. The point is that players are matched against opponents of roughly equal strength.

This format is both interesting for spectators and engaging for players.

[John Upham]

I was challenged to design the best pairing system ever and thought it was impossible.

Who challenged you?

[Mats Winther]

I was challenged to design the best pairing system ever and thought it was impossible.

Who challenged you?

A person in the Swedish Chess Federation's Facebook group. I initially set out to implement Monrad, but once I had done that, I got a taste for it and began exploring more ambitious pairing systems.

Monrad is not well known outside Scandinavia, but it has long been a popular pairing system in chess clubs and open rapid tournaments. It is essentially a simplified Swiss system in which ratings are ignored and the starting field is randomized before the first round. You ought to try it.
https://mats-winther.github.io/monrad-eng.htm