The full rules are available in various places. For instance there is a section at the Swiss Perfect page.
1. The Lazy Person's System
In practice it is sometimes difficult for a Director of Play to apply the rules fully. When the draw has to be changed at the last minute and severe complications arise, at some point reality dictates using a short cut.
However some DoPs don't leave it to the last minute to take this step, they launch straight into the Lazy Person's System (LPS). It works by pairing a score group (a group with everybody on the some score) like this:
How many of these steps are correct? Some of them. The first pass in a group is top against bottom half. And players should not play each other twice. The incorrect steps are: the players floated are not necessarily the highest and lowest in the group; the highest rated player in a pairing does not necessarily get the colour due; pairings should be arranged to maximise the number of correct colours rather than just to avoid repeat pairings; and there is a protocol for rearranging the cards, not just moving the cards that are easiest to reach.
2. Why does it matter?
First let us take a step back and look at the Person of Limited Mental Capacity's System. The PLMCS says that in a game of chess the best player always wins so the pairing system is largely unimportant - the best player beats everybody, the second-best beats everybody else etc. So the better you are the more games you win, it doesn't really matter who you play.
As we have seen in the rating system you can't win all the time; if you are 100 rating points better than somebody you can expect to beat them 64% of the time; 200 points better and you win 76%. In a Swiss tournament you only meet a section of the field, so a less accomplished player meeting a weak field can get more points than the best player against a strong field.
There are issues beyond merely the strength of the field; for instance getting a certain number of Blacks or Whites, or getting them at the right stage of the tournament.
Thus the pairing system should not give unfair advantages. The LPS however does not satisfy that criteria, for instance in a group of players performing equally well and progressing at the same rate it will always downfloat the same person. There will always be some inequities in a system where players don't play all the field, but real pairing rules increase the chances of a fair outcome. The LPS gets as far as seeing that some rules are needed, but as we shall see doesn't go far enough.
Moreover the LPS or other home-made systems are not written down anywhere, so when a slightly complicated position arises the DoP is unable to justify jumping one way or the other.
For instance suppose it's the second-last round of the tournament and in a group of four players there are two legal sets of pairings. One pairs 1v3 and 2v4 but gives two players the "wrong" colour. The other gives everyone the right colour but pairs 1v2 (the two highest rated) together.
What do you do? Incidentally the two loudest complainers in the club, who detest each other, will get a very easy and a very hard game, in opposite permutations, in each of the two scenarios. It's also the club championship and the winner takes the last spot in the a prestigious tournament.
All I can say is that you'd better remember what you did last time in the same position. If anyone can show that you appear to change the rules from week to week or event to event then there'll be blood on the carpet, if you play at a carpeted venue.
3. The real system.
Current rules prescribe a hierarchy of factors, namely
There are still some things not covered above, like how do you choose between equally valid pairings and who gets what colour, but we'll get to that.
4. Absolute and relative criteria, and loopholes.
First the loopholes. Rules 2, 5 and 6 don't apply in the last round of a tournament to players on 50% or more. Rules 1 and 2 are absolute criteria. Except for the above loophole they cannot be broken. The remainder are relative. Given a choice the higher rule takes precedence, e.g. it's more important to give someone the correct colour than to avoid floating someone twice.
5. What flaws are there in the LPS or other home-made systems?
Apart from being undocumented and subject to the suspicion (or actuality) of corruption, there are a number of flaws.
Having the highest rated player in a group upfloat (or downfloat) means that the same players will tend to float where floating is needed. This may sound inconvenient for the higher-rated player constantly playing high scorers. Actually it's probably more inconvenient for a lower-rated player on a good score, it means that he or she will not get the chance to upfloat and knock over the tournament leader, or is last in the queue to do so. The combination of the colour equalisation and the prohibition on regular floating shares out the floats.
Incidentally how does the DoP remember who has floated? Either by having a very good memory, or more commonly by drawing an arrow on the card. If you see a set of pairing cards without any arrows marked and the tournament is not in the first couple of rounds then it's a good bet that the LPS is being employed.
The high priority of colour equalisation achieves two things. First, it reduces the incidence of players having the same colour twice in a row. It is undesirable for that to happen because it makes pairings harder in the next round.
Perhaps more importantly, it minimises clustering of colours. Initially it might seem that if you get four Blacks and three Whites (or vice versa) the order doesn't matter that much. In practice, though, the key games tend to occur at a particular stage in the tournament, and it is an advantage (or disadvantage) to get a cluster of Whites (or Blacks) at that point.
6. An example - applying the colour equalisation rule.
Now a real example. First, a convention to save space on explanations - when examples are given, a player with an initial higher in the alphabet than another is higher rated, e.g. Brian is rated higher than John.
Supposing that after five rounds of a tournament the following players are on 3 points. An asterisk (*) denotes a player due White, others are due Black. The pairings that happened in earlier rounds are Barry-David, Barry-Gary and Anna-Fred, and Gary downfloated in the last round.
| S1 | S2 |
|---|---|
| Anna * | Ed * |
| Barry | Fred |
| Carrie | Gary * |
| David * | Harry |
We start off laying out the cards as top half vs bottom half; you will note that we have labelled these S1 and S2 (as in the printed Swiss rules) for ease of reference.
We can see that under the LPS the draw is done, apart from correcting colours for Fred-Barry (higher rated gets colour due) and Gary-Carrie. Under the real rules, though, this leaves two people with the wrong colour. Can we do better than this, since under Rule 3 as many players as possible need to have the right colour?
It's pretty obvious that the number of people to whom we can give the right colour is all of them, since four are due White and four are due Black. So we have to rearrange it (this is called a transposition), but how?
The rule is that if you imagine the four players in S2 to be numbered 1, 2, 3 and 4 you need to choose the lowest number made up of these four digits which meets the rules. 1234 or Ed/Fred/Gary/Harry (shown in the table) doesn't work because it breaches the maximum-due-colours rule.
There are 24 permutations but we can take a short cut. We know that anything starting with a 1 or 3 won't work (Ed and Gary are due White), nor anything starting with 2 (Anna has played Fred). So the number has to start with 4. We can also see that there is then only one player in S1 due White (David) and one in S2 due Black (Fred) so the number ends with a 2.
Now of 4132 and 4312 the first is lower so we have, after laying out the cards with the players getting the right colours:
| White | Black |
|---|---|
| Anna * | Harry |
| Ed * | Barry |
| Gary * | Carrie |
| David * | Fred |
So if the players thought the tournament was being run by a Lazy Person then Carrie would have expected to play Gary and been right, and Harry would have expected to play David and got a shock. That's another advantage to having standard rules, nobody can get an advantage by understanding what goes on in the DoP's mind, or by having enough spare time to prepare for three or four possible pairings.
7. An odd number of players.
Let's make it more complicated. Suppose Fred had been unable to make it (having previously notified the DoP of course). Then the players to be paired would be
| S1 | S2 |
|---|---|
| Anna * | David * |
| Barry | Ed * |
| Carrie | Gary * |
| Harry |
Note that we lay the cards out with the extra player in S2. The reason is that as before we will sort the digits 1,2,3 and 4 into the legal pairing making up the lowest number, and the player who is left without an opponent will downfloat.
With four players due White and three due Black it is again possible to give everyone the right colour (there is a formula for calculating this but it's obvious). With a bit of thought we see that the number is 4231 and the pairings are:
| White | Black |
|---|---|
| Anna * | Harry |
| Ed * | Barry |
| Gary * | Carrie |
| David * |
Why didn't Gary downfloat? Because (see the original information above) he did so last round. And Barry couldn't play David or Gary because he already has, so if Ed downfloated there'd be nobody in S2 for Barry to play.
8. Isn't this getting a bit random?
Harry, the lowest rated player in the group, plays Anna, the highest rated in the group and David, in the middle, actually gets the downfloat. Whereas had some other players not played each other, or played their previous games in a different order it would have been different. It wouldn't happen in the LPS, you're the lowest rated and you downfloat every time.
Yes it is a bit random, except that it's done by a set of rules rather than drawn from a hat, and I think that's deliberate. It would be quite wrong for a lower rated player to get the easier game every time. As noted above that might be good or bad for Harry depending whether he actually wanted it that way, but it's both fairer and more interesting for everyone to share it round.
9. An aside - lots of people have already played.
We saw examples above where a player in S1 had only one possible opponent in S2 due the right colour. What if there are no such opponents unplayed - then can we give more people the wrong colour?
No. You'll see in the list of criteria that colour is less important than playing someone on the same score, so we can give someone the wrong colour rather than float them. But there's no rule, except in the LPS, that S1 and S2 have to play each other. It's just that S1 v S2 is the first pass.
So by swapping players between S1 and S2 (called an exchange), and then applying the above processes, we can open up a whole new range of possibilities. This can get a bit complicated without introducing much in the way of new concepts so I'll leave it for you to look up in section D of the rules at the Swiss Perfect page. The principle is to make the minimum necessary disruption. First, swap the lowest player in S1 with the highest player in S2 and see if that solves the impasse. If that doesn't work consult the rules for the order in which more exchanges are made.
10. A bit harder - someone has to have the wrong colour
In the first round of a tournament we might expect the top seeds to win giving a task a little like this:
| S1 | S2 |
|---|---|
| Ian * | Max * |
| Julie | Ned |
| Karl * | Olivia * |
| Lisa | Peter |
Not difficult at all. The LPS would leave it like this giving a quarter of the field the wrong colour, but those knowing the rules can, by arranging S2 in the sequence 2143, get
| White | Black |
|---|---|
| Ian * | Ned |
| Max * | Julie |
| Karl * | Peter |
| Olivia * | Lisa |
Supposing, though, we have an upset and we have to deal with this:
| S1 | S2 |
|---|---|
| Ian * | Max * |
| Julie | Ned |
| Karl * | Olivia * |
| Lisa | Ziggy * |
Now with five players due White and three due Black we can't give everybody the right colour. But the procedure is the same, we use the digits 1,2,3,4 (Max, Ned,Olivia,Ziggy) to make the lowest number sequence where one player gets the wrong colour. Which happens to be 2134. So we get:
| S1 | S2 |
|---|---|
| Ian * | Ned |
| Max * | Julie |
| Karl * | Olivia * |
| Ziggy * | Lisa |
11. Who gets White?
Another rule in the Lazy Person's System is that if both players had the same colour in the last round then the player with the higher rating gets the other colour.
In the above instance, where Karl and Olivia have identical colour histories (one game with Black) this is correct. However in more complex positions there are a couple of things you need to look at first.
The most important is strength of colour preference. For instance suppose Quentin has a colour history of WBWB and is drawn to play Rachel who starts with a half-point bye and then has BWB. Both are due White but Rachel, although lower rated, gets White as she has a stronger preference; she has actually had one less White.
The next is how recently each player had different colours. The Lazy Person sometimes gets the previous case right, but this one usually throws them. Suppose Sandra has had WBWBW and Thomas has had BWWBW. Both are due Black, both have had the same number of Blacks and Whites. If you think Sandra gets Black because she's higher rated, you're wrong. Thomas gets Black because the most recent occasion on which they had opposite colours, the second round, he was White.
A little obtuse? Not really, it's in black and white in the rules. (When you meet the Director who swears such a rule doesn't exist, bet him a million dollars then point to rule E3.) If it doesn't make sense, think about Thomas getting White. That gives him BWWBWW - four Whites in five games. He wouldn't complain, but supposing it was you and you had to play four Blacks in five games. Whereas Sandra will have WBWBWW which is a more even spread. So this rule minimises clustering of colours.
If both players have the same colour history only then do you go to higher ranked. But note that doesn't necessarily mean higher rated. If one players is on a higher score the player is higher ranked, but if they are on the same score then the higher rated is higher ranked and gets the due colour.
12. Colour preference - some odds and ends.
Having had a colour one less time, like Rachel, is called having a strong preference, whereas merely having had one colour more recently, as Richard did, is a weak preference. A player having had the same colour twice in a row has an absolute preference because under the criteria we cannot give that player the same colour three times in a row. For instance in the above example if Richard had played WWBB then he would have got White against Rachel.
Byes and forfeits are colourless. There might have been an old rule that a bye was White, but there isn't now. Sometimes the LPS treats a forfeit as whatever colour a player would have had if the game was played, if the DoP has already written the colour on the card.
For the purpose of writing history, eliminate byes and forfeits. For instance a player with a half-point bye in Round 2, playing B-WBW and a player getting a forfeit in the fourth round, BWB-W, should both be written -BWBW.
Looking back at pairing S1 against S2, we don't consider how strong a colour preference is, we merely look at what the preference is. Only when we find that we have had to pair two people due the same colour do we look at who gets it.
13. Heterogeneous and remainder groups.
To date we have only looked at cases where everybody in a group is on the same score. These are called homogeneous groups. Where one or more players are on a different score, which comes about through players downfloating from a higher score group, we have a heterogeneous group.
Some weird and wonderful home-made rules have been applied to this circumstance. We have seen in the LPS that the highest-rated player is pulled out of the lower score group and matched against the downfloater. Another approach is to mix the player into the lower score group in rating order and then pair as normal.
In fact the correct rule is to do much as the same as we did earlier except that S1 constitutes the downfloating player(s) and S2 is made up of the members of the lower score group. Most commonly S1 only has one player in it (a downfloater) but there could be more, for instance (with scores in parentheses).
| S1 | S2 |
|---|---|
| Alex (5) * | Jessica (4) * |
| Cathy (5) * | Kevin (4) * |
| Liz (4) * | |
| Mary (4) | |
| Norbert (4) |
In this instance Alex and Cathy are the joint tournament leaders and have already played. In addition Alex has played Jessica and Liz, Cathy has played everyone except Jessica and Mary, and Kevin upfloated in the last round.
We follow the same principle as before. The digits 1,2,3,4,5 (Jessica, Kevin, Liz, Mary and Norbert) have to be arranged to give the lowest number without breaching the pairing rules. One player can have the wrong colour.
The arrangement which achieves this is 41235.
| White | Black |
|---|---|
| Alex (5) * | Mary (4) |
| Cathy (5) * | Jessica (4) * |
| Kevin (4) * | |
| Liz (4) * | |
| Norbert (4) |
If we tried to start the sequence with 1 (Jessica) or 3 (Liz) we would give Alex an illegal opponent, while starting with 2 would upfloat Kevin. There's no problem with 1 as the second digit since one player can have the wrong colour. We still need to look at colour history for the Cathy-Jessica pairing.
A key point to note here is that we pair groups, not players. We do not try to pair Alex from the five players on 4 and then pair Cathy from those left. Whether we can upfloat two, one or zero players due the wrong colour depends on the overall composition of the group, which can be why you will sometimes see the highest-rated player in a group upfloat and sometimes not.
After making the above pairs we have a remainder group of the three players left from our heterogeneous group. This group is then paired in the usual way.
14. The last group.
Eventually you will get to the last group and a couple of things may happen.
First, there may be a player left over. In any other group that player would be a downfloater. In this case that player gets the bye. This is slightly different from the LPS, where a player is pulled out and given the bye before the pairings are made. Here the pairings are made and then a person is left over. Note that this might mean the player with the bye is not the lowest-rated candidate.
The other problem that may come up is that there is no legal pairing available among the final group. For instance the two players coming equal last on 1 point have already played each other. In such a case you will have to unpick the second-last group and re-do it in such a way as to produce two downfloaters. To save time it can be useful in the later rounds to have a quick look at the bottom players to see if this going to happen.
15. Byes and forfeits - miscellaneous.
A bye is a downfloat. This is quite unequivocal (rule A5). In particular the player who gets the first-round bye does not then downfloat into the first-round losers in the second round.
A player who has received a "free" point through either a bye or a forfeit cannot then later receive a bye. This is actually a sub-clause of the absolute criteria (rule B1(b)), so it has the same force as not playing the same player twice.
As noted above, byes and forfeits have no colour for pairing purposes. A forfeit also does not prevent two players being paired again in a later round (rule F2).
The rules do not appear to prescribe a forfeit to be a downfloat, though in all other respects the intention seems to be to treat a forfeit like a bye.
The pairing rules do not mention half-point byes, so the DoP or the club has some scope to make up local rules. My suggestion is to treat them exactly the same way as normal byes unless there is a good reason not to, since it creates extra complications with no real gain to introduce different rules.
16. Unrated players.
A common practice when a player does not have a rating is to put the player at the end of the list. This is tantamount to treating the player as having a rating of zero (or a number less than the lowest rated player). The rules state quite unequivocally that "[i]f no reliable rating is known for a player the arbiters should make an estimation of it as accurately as possible"; that is, manufacture a rating as best you can and rank the player accordingly.
Again this is logical when you think about it. An unrated players is often a beginners who is genuinely the bottom player, but if that's not true why put thirty players in order of rating (strength, approximately) and then shove someone to a point clearly out of the sequence just because you don't know the exact position?
A side issue is that if treated as the lowest-rated competitor the player is then more likely to get the bye, which is not a good way to encourage new players. Of course if the player is really one of the weakest players in the field they will eventually drop to the bottom and get the bye, but why accelerate the process?
17. Computer pairing systems.
There are a number of computer pairing systems around, of which the best known is probably Swiss Perfect.
Occasionally I can't explain pairings produced by Swiss Perfect. However in the majority of cases I find that where I can check manual pairings with SP any disagreement is due to some human error, which becomes obvious when the computer pairings are seen.
My suggestion is that if time permits a DoP should do the pairings manually, check them with SP, and if they are different then after careful thought and in particular checking the two sets of pairings against the criteria in section 3 above, stick with the manual pairings if still convinced of their correctness.
18. There are other ways.
The problems with home-made rules are that they may contain a fatal flaw, and simply that being undocumented they are unlikely to be applied consistently. For these reasons club members should expect DoPs to apply the rules as written.
However the official rules as described here are not the only documented rules in existence. The most common variation seems to be one in which the floater from a group is the player closest to the middle (in rating order)
19. Conclusion.
The intent here is not to cover all possible cases, and I don't claim to understand the system well enough to presume to do that. However I hope that I have included enough to explain typical scenarios and allow identification of gross errors.
The two things to watch out for: the same player constantly floating (typically in conjunction with floats not marked on the pairing cards), and a player due White having Black while the reverse happens to another player in the same score group. These can only be correct where there are restrictions from players having already played each other.
Please notify anything in the above which you believe is incorrect or unclear.
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