Some background on how pairing systems work.
Updated Thu Mar 31 08:59:40 EST 2005 for tsh 2.800.
This section discusses the theory behind scheduling pairings for tournaments. For information about how to implement pairings in tsh, please refer to the section on configuring tsh.
Choosing a pairing system is a balancing act among several conflicting goals. A pairing system should be fair: ideally, players should end up ranked the same way whether you list them by performance rating or wins and spread. A pairing system should be fast: ideally, players should not have to wait to find out who their opponents are. A pairing system should be fun: ideally, the outcome of the tournament should not be determined until the end and in the last rounds contenders should be playing each other.
A fair or fun pairing system cannot be fast, because getting the pairings just right usually involves waiting until the last game finishes each round before deciding pairings for the next round. A round robin seems fairest (everyone faces as close to the same field as they could face, without playing themselves), but is rarely fun, because of the difficulty in predicting who will be in contention at the end of the tournament.
Some directors favour fairness (and simplicity) and divide their players into small groups so that they can all play round robins. This has the advantage that the director doesn't have to do any work to figure out the pairings (but s/he wouldn't have to anyway with this software), but the disadvantages that the prize pools and the potential ratings changes end up being relatively small. Most players prefer the larger ratings swings and prize pools that come with playing in larger groups.
Swiss pairings were invented to deal with the problem of tournaments where the number of players is vastly larger than the number of rounds, and they work well under such circumstances at preventing contenders from playing each other until late in the tournament, if ever. In ideal Swiss pairings, the top half of each group of players who have the same number of wins plays the bottom half. Portland (or Fontes) Swiss pairings improve on the logistics of Swiss pairings by pairing based on results from one round previous: players are arranged into win groups based on how many wins they had in round N-2 when pairing for round N.
With regular Swiss pairings, round N pairings cannot be determined until after all of round N's games have reported in, which can result in games starting 70-75 minutes apart. With Fontes Swiss pairings, games can be scheduled to start hourly, allowing an extra game to be played in a typical daily schedule.
Each pairing command (except for RoundRobin) lets you specify how many repeat pairings a player is permitted. Early in a tournament, this should be zero, as no one should play a given opponent twice if it can be avoided. Later on in a long tournament (at least with typical North American group sizes), it should be greater than zero, so that the tournament is decided based on results between contenders rather than contenders competing to see which weaker players they can beat by how much. You should decide beforehand at what point you are going to allow repeat pairings. A good time to do so is after a break, so that people who end up playing each other two games in a row have a chance to stretch their legs first. You may also use a criterion such as "whenever pairing without repeats would pair the leader out of his quartile", though since that criterion isn't yet implemented in tsh (because no one's asked), you'll have to set that up manually.
Many tournaments end with a king-of-the-hill (KOTH) round, whether earlier rounds are paired round-robin or Swiss. The final KOTH round is customarily paired with no restrictions on repeats (enter a number of permitted repeats one greater than in the previous round), and not Fontes (i.e. based on the results of the immediately preceding, not second preceding, round).
I usually begin tournaments with a fixed three-round schedule that picks players for round-robin quads at random from each quartile, then pair a certain number of Swiss rounds (regular Swiss after session breaks, Fontes Swiss mid-session), allowing repeats at some point, then end with a KOTH allowing one more repeat than in the preceding round.
That does mean that after a break, two consecutive rounds are paired based on the same round's standings, but since the program checks to avoid repeat pairings, this doesn't cause trouble. If you use this scheme though, do not increase the number of repeat pairings permitted in either of the first two rounds of a session: always do so only in the third or fourth round. Increasing pairings at the wrong point in a session can lead to large numbers of back-to-back repeats and player complaints.