Chess pairings typically do not employ randomization. The exception is the first round in Berger and Monrad, where
the players are drawn randomly into an ordered list that then determines who faces whom in the opening round. From
that point onward, the process is entirely deterministic. In Swiss pairings, chance plays no part at all, since the
starting order is seeded, usually by rating. Thus, the algorithm contains no built-in element of randomness. It is
the players themselves who introduce variation through their more or less unpredictable results.
The Monrad system is named after the Danish chess organizer Poul Monrad, who during the mid-20th century developed and popularized this simplified variant of Swiss pairings. It became widespread in Denmark, Norway, and Sweden, particularly in school competitions, weekend tournaments, and larger amateur events, because it is simpler than the complete Swiss system: players are paired strictly according to their current score, without the more complicated FIDE restrictions.
In Monrad (simplified Swiss), a certain unfairness can initially arise, as one top player may face a strong opponent while another receives a significantly weaker one. For this reason, elite tournaments prefer some form of Swiss pairing. Another drawback is that a player may receive the same colour three times in a row. The probability of this, however, is only around 1-3% in a standard tournament over 5-7 rounds. For the tournament as a whole, the probability that at least one player experiences this is approximately 5-15% in a medium-sized to large field (20-40 players). This is the case in Danish-Swedish Monrad. In the Norwegian system, as well as in the Dutch (FIDE) system, the algorithm prevents this, except in extreme cases. Since Monrad is rarely used in elite tournaments, this restriction is arguably unnecessary.
I have created a Monrad program here: Monrad Pairing System. It can be used online, but the page itself can also be downloaded and run locally. The program uses either cumulative (progressive) score or Buchholz (the opponents’ combined score, also called Solkoff score) to break ties between players with the same final score. Cumulative score is defined so that early wins yield a higher tiebreak, which favours an aggressive playing style. (Starting with a win and then a loss gives 2 cumulative points after two rounds, whereas two draws give 1.5. In a sense, this can be considered fair.)
The Berger system entails that everyone plays everyone, either once or twice. I have created an online program for Berger pairings for 3-16 players according to FIDE specifications. It can be used directly in the browser, but can also be downloaded and run locally: FIDE Berger Tournament System (Round-Robin).
Swiss systems are constructed in various ways. These include double-accelerated Swiss, Haldane acceleration, and FIDE acceleration (now rare). Certain variants, however, perform very poorly, among them Nordic Swiss (see here). A typical problem for intermediate players is that they oscillate between overly strong and overly weak opposition: in one round they face a significantly stronger player, in the next a clearly weaker one, and then once again an overly strong opponent. This oscillation diminishes the enjoyment of the tournament and produces an uneven tournament experience. Furthermore, a player can receive the same colour three or more times in a row. In the Swedish Blitz Championship 2023, Amin received Black three times in a row and then White five times in a row (see here). Nordic Swiss should therefore no longer be used.
In my accelerated Swiss system, this does not occur: Swiss Tournament System. The program features a safeguard ensuring that the same colour three times in a row is effectively prevented. It is distinctly superior to Nordic Swiss, provided that the program proves reliable after thorough testing.
Accelerated Swiss Pairing according to Winther:
Round 1: Players are divided into four rating groups. The highest-ranked player in Group 1 has White
against the highest-ranked player in Group 2. The same applies to Groups 3 and 4.
Round 2: The highest-ranked winner has Black against the highest-ranked winner in the other half. The
second highest-ranked has Black against the second highest in the other half, and so on.
Round 3+: Swiss pairing commences. Players are sorted by score, then Buchholz points, and then original
ranking. Pairings are conducted from top to bottom against the next available opponent.
Colour allocation: The player with fewer games with White is assigned White. With an equal number of games with
White, the lower-seeded player is assigned White. The system guarantees a 0% risk of three consecutive games with the
same colour.
This system is well suited for open tournaments. Elite players have little reason to object, as they face lower-ranked players in the first two rounds. At the same time, it avoids the oscillation from which intermediate players often suffer in other Swiss pairings. The program uses Buchholz as a secondary sorting criterion when pairing players, after score. Buchholz is stable, well-known, and harmonizes with the objective that players who have faced similar opposition should be paired. Buchholz is standard in international Swiss tournaments, making the system compatible with established practice.
Having the winners in the second half receive White against the winners in the first half in round two is, in my view, a good idea — all players will be pleased. From round three onward, players with similar ratings meet each other more consistently. Generally, top players prefer Black against weaker opposition and White against stronger. The program accommodates this by granting White to the lower-ranked player when the number of White games played is tied. I do not yet know how the overall rating distribution affects the pairings, but that can be investigated using the program.
The fundamental problem of Swiss pairing is that it attempts to achieve a fair tournament within a limited number
of rounds, without being able to employ the ideal round-robin format. Therefore, the system must both produce
high-quality pairings and simultaneously be perceived as fair by the players. Many Swiss variants fall short in this
respect, especially when the intermediate bracket oscillates between overly strong and overly weak opposition, or
when the colour allocation becomes unreasonable. Furthermore, FIDE’s current rules are complex and convoluted,
making them less transparent to participants. The proposed variant is an attempt to combine simplicity with
stability: the first two rounds provide a controlled acceleration where elite players meet lower-ranked opponents,
while the intermediate bracket avoids the oscillation that otherwise detracts from the joy of playing. From round
three onward, players with similar ratings meet each other with increasing frequency, lending the tournament a
natural progression. The fact that Buchholz is used as a secondary criterion harmonizes with the objective that
players with similar opposition should meet, and the colour rule (which guarantees that no one is assigned the same
colour three times in a row) eliminates one of the most disruptive elements in certain other systems. A good Swiss
format must be easy to understand, difficult to manipulate, and convey a clear sense of logical progression. The
system is designed with precisely these principles in mind.
© Mats Winther, 2026.