At the end of two rounds, there are five players at 2-0, with the following color histories and ratings:
player A 1900 BW
player B 1850 BW
player C 1800 WB
player D 1750 BW
player E 1700 WB
– and seven players at 1.5:
player F 1825 BW
player G 1775 WB
player H 1725 BW
player I 1675 WB
player J 1625 WB
player K 1575 WB
player L 1525 BW
How would you pair these two score groups? (Assume that one player having already played another is never an issue.)
Bill Smythe
The rules give some latitude to the director for selecting which player is the odd man (to improve color assignment). I don’t see them as being perfectly clear about just how far he can or should go.
However, I would consider choosing the lowest rated player as the odd man to be more important than color alternation. I would treat selection of a different odd man as roughly the same as transpositions and interchanges (80 point and 200 point rules apply) for color equalization.
So, I’d treat E as the odd man and pair him against F:
C vs. A
D vs. B
E vs. F
G vs. J
K vs. H
I vs. L
It seems to me that the rules are rather vague on this question.
Ok, seems simple enough but then I could be throwing myself to the wolves to have a crack at this… 
Let’s see, the main question is whether to drop D or E to the lower score group, and then whether you should pair D against F or G, ok…
Pairing 1
C v A
E v B
G v D
J v F
K v H
I v L
The above pairing would be ideal based on colors due, but since they’ve all had one of each color then I guess you could go with the “straight” pairings, such as…
Pairing 2
C v A
D v B (D gets two whites in a row)
E v F
G v J (J gets two blacks in a row)
K v H
I v L
So you get the “ideal” pairing scenario with just a couple of color “glitches”. As for which one I would choose…
Pairing 2 since I don’t think I’d get as many complaints from the players by giving them 2 colors in a row as I would by dropping D to play against G in the lower score group, even though the colors are better.
Chris Bird
I would go with Chris Bird’s first pairing, where all players receive their due color. I’m not a great fan of treating someone other than the lowest rated player in the score group as the odd man, but the pairing E-F causes two players not to receive their due color. Both transpositions (the transposition to select D as the odd man from the 2.0 score group and the transposition to pair D with G instead of F) are within the 80 point limit for color alternation.
It seems to me that there is a consideration in pairing an odd man that is not present when pairing within a score group. This consideration is that by having the lowest rated player from the upper score group play against the highest rated player from the lower score group that you will likely have fewer perfect scores after the next round. This consideration makes the alternation of colors relatively less important than it is within a single score group. If you only had a 4 round swiss, you’re more likely to get a clear winner this way.
I don’t consider alternation of colors as being as important as this improved chance of getting a clear winner. Equalization of colors is a little more important than alternation, so I’m willing to consider a different odd-man pairing to achieve equalization.
The rules (perhaps intentionally) leave some room for the TD to choose which is the prefered pairing. So this is just my preference and I see the justification either way. I think players will be more likely to NOTICE the change in color alternation, but more likely to OBJECT to the different odd-man. YMMV
Ohhh. I like this post. (This is why I started watching this forum.)
Tim Just, give us the definative ruling!! 
The reason this one is a little tricky is that in order to balance the colors, you have to do two things, each of which is permissible by itself. 29D1b says, “If the conditions in (a) cannot be met, try treating the next lowest-rated player as the odd player, or pairing the odd player with a lower-ranking player in the next score group.” By pairing D against G, you are doing both. I think it’s the correct pairing, but you could make a legalistic argument against it on the letter of the rule.
Not having actually run any tourneys yet, it’s obvious I should voice my opinion (cough). More seriously, my practice runs have pointed out one thing:
In a 4 round event, I think I’d go with Chris Bird’s 1st pairing (with the GD pairing), which avoids color alternation problems. The reason: In an event with an even number of rounds, I seem to sometimes end up in color snarls at the end. This pairing seems to reduce the color “tension”.
With an odd number of rounds, or with 6 or more rounds, I’d be more tempted to go with the strict pairing and hope the color knots work themselves out later.
Since the only way to be truley fair, as far as colors go, is to have a double round robin, I don’t immagine it’s too productive to spend much time worrying about the colors.
It seems like an easy fix in this case, but can you continue do this (as a matter of practicality) two rounds later, taking all of the players into consideration? The answer obviously has to be based on the number of players involved and the amount of time available between rounds. I wouldn’t think it would be wise to make adjustments in round three, unless your certain you can keep making them through the remaining rounds.
Yeh, that’s one reason I started it. It’s WAY more interesting than finances, or the behavior of EB members.
Actually, I think the rule IS rather clear:
29D. The odd player.
29D1b. …switches to correct colors should stay within the appropriate limits (29E5). …
29E5 consists of 29E5a, the 80-point rule, and 29E5b, the 200-point rule.
In other words, the rules for cross-score-group transpositions are the same as for “ordinary” transpositions – up to 80 points to alternate, up to 200 points to equalize.
This argument seems weak, for two reasons. First, an 80-point difference is statistically unlikely to make a difference as to which player wins. Second, the reason for pairing lowest vs highest isn’t really to reduce the number of perfect scores. It’s to make the lowest player in the group likely to lose (since he is in the bottom half) and the highest in the group likely to win (since he is at the top). Reduction of perfect scores is just a bonus for those of us who run plus-score events. 
I’m sure Tim will say that such decisions are up to the TD, and that the rules should not force that much rigidity down the throats of TDs. And I agree.
I’m interested, though – what would WinTD or SwisSys do? Anybody care to try it?
That’s a good point. We have, in effect, a compound (three-way) transposition.
Player G, for example, ends up with an opponent 125 points higher-rated than in the “raw” pairings. (Other differences do not exceed 75 points in this example.) But a 125-point switch on ONE side of a transposition does not invalidate it. In the case of a simple (two-way) transposition:
[code]raw pairings:
A vs C
B vs D
final pairings:
A vs D
B vs C[/code]
– the size of the transposition is defined as the SMALLER of C-D or A-B.
Bill Smythe
No matter what you do (or don’t) for color alternation in round 3, you’ll have the same potential problems for color equalization in round 4. That’s really a non-issue. Whichever pairing you use, every player will have 2 of one color and 1 of the other color after round 3.
With several rounds, there isn’t as much need to reduce the number of perfect scores after round 3. So I’d be MORE inclined to change the pairing for color alternation if there were several more rounds to be played.
A couple of things I’m not completely clear on: The rule book gives certain things that MAY be done to improve color alternations and equalizations. These include transpositions, interchanges, and different odd-man pairings. Is there an implication that these things MUST be done? SHOULD be done? Or is it only that they MAY be done when when the TD feels the situation warrants it? Also, I’ve always felt that transpostions are to be prefered to interchanges and that odd-man changes are to be avoided as much as possible. Is this the general opinion or am I in the minority?
I agree that it is clear that any switches SHOULD be within those guidelines. BUT see my previous question: does switches “MAY be done” imply that they “SHOULD be done”? Or is the TD supposed/allowed to take other things into consideration?
I thought the whole goal of swiss system pairing was to have a clear winner (not several people with perfect scores) without having to eliminate players for loses or draws. This isn’t just a bonus – it’s one of the central principles behind the swiss system pairing rules.
If you only had a 4 round event, the pairing E vs. F (125 pt. difference) gives you a slightly better chance than G vs. D (25 pt. difference) of only having 2 perfect scores after round 3 – thus giving you a better chance of having a clear winner after round 4. I’m not really following your reasoning in this: You say that the point is to make the lower rated (higher ranked) player more likely to lose but is NOT to reduce the number of perfect scores? One does imply the other so I’m afraid your statement doesn’t make sense to me.
I agree that this is an important goal, but it is not the only one. (If you look up the history of the Swiss system, you will find that this was a big deal in the early days when many tournaments had indivisible prizes. This is hardly ever the case any more except in scholastics.) An equally important goal is to provide fair conditions for all the players. A plus-2 or plus-3 color imbalance is not “fair” in the view of most players. Sometimes it is unavoidable, but the best way to reduce its likelihood is to balance as many colors as possible each round.
True, but totally irrelevant to the question. There will be no extra color imbalance either way. The discussion is whether to change pairings for color ALTERNATION. I already said I’d possibly make the change for EQUALIZATION. But this is the 3rd round’s pairings and colors are balanced up to this point. Whichever pairing is selected, all of the players will have either 2 whites and 1 black or 2 blacks and 1 white.
The alternative pairing means player G will play a 125 point higher rated opponent. Many people will not think that’s “fair”.
You are mistaken. Every time you give a player the wrong alternating color, you increase the likelihood of being forced to make a very undesirable pairing (plus-2 color allocation and/or three in a row) in the next round. Exactly how undesirable depends other factors, such as the number of rounds. (Which is why the TD should have some discretion in such cases.) I agree that the “125 point” argument carries some weight, but the transposition rules for the odd man are not (and never have been) well defined.
Another way to put it is this: Suppose you make the pairing in which two out of six boards have a bad alternating color. Then generate the possible game results. Some of these are going to result in having to assign someone the same color a third time a row in the next round. Now do the same thing with all the colors alternating. There will still be some “very bad” cases in your set of possible results – but not as many, and no “three in a row.”
I did consider the color imbalance question. There is no greater chance of a +2 color imbalance with either pairing (again, every player has a 2-1 imbalance with either pairing after round 3).
I also looked at the two players without alternating colors: D and J. I considered D to be more problematic since he was in the smaller score group. I looked at each of the possible results and did not see any case where a 3-in-a-row color assignment pairing would be the “natural” pairing. I chose not to take the time to examine J for a hypothetical case. Would I take the time in a real tournament? That would depend on the size of the tournament and which round we were in (round 3 of 3 total or 4 total rounds is much easier to check than round 3 of 6). Of course, to be honest, I’d normally just use what the software paired. 
I’m sure you can establish that if there are enough rounds there will be more problems with my suggested pairing – but then I was supposing that there weren’t very many more rounds (hence it would be important to use the default odd-man pairings). Most tournaments I’ve been to seem to have just barely (or not quite) enough rounds to give a clear winner for the number of players. I might give a different answer if part of the question had indicated a 6 round tournament.
I think I’ve demonstrated that there are other things to consider than just color alternation. The TD should consider the other things and make a decision that’s appropriate. Your point about needing to consider the longer-term consequences of color alternation is well taken.
Note that I am not saying that your proposed pairing is “wrong” – it is certainly defensible under the rules, and I would have no problem with a TD who consistently dropped the low man regardless of colors. I think it’s slightly inferior in view of 27A5. For what it’s worth, I dummied this up in SwissSys, and the program preferred your pairing. In a real tournament, I would probably override the program if I noticed this.
I think the rulebook is (wisely) trying to avoid sticky-wicket situations. If a rule says something MUST or SHOULD be done, you could end up in a situation where it would be better NOT to have done it (whatever “it” is), so it’s often better to encourage TD discretion.
I guess I was simply pointing out that players at (or near) the bottom of their score groups are supposed to get tough opponents, while those at (or near) the top are supposed to get easy opponents. Pairing the lowest (or second- or third-lowest) down, and/or pairing the highest (or second- or third-highest) up, usually accomplishes this because there is usually a ratings overlap between the two score groups. Reducing the number of perfect scores is just an added bonus.
Actually, at least in small tournaments (fewer than 20 players), you could INCREASE the color snarls by making the colors work too well in early rounds. If ALL colors alternate in every round, you have created two “camps” of players, those who started with white and those who started with black, and you’ve made only inter-camp pairings, no intra-camp pairings. After a while (in a small tournament), you’ll run out of decent inter-camp pairings, and you’ll have to start making intra-camp pairings, where the colors will be wrong.
An extreme example occurs with 6 players. If all colors alternate in round 2, and again in round 3, you’ll find there are NO pairings at all in round 4 (even without regard to score, color, etc).
It’s slightly less extreme with 8 players. If all colors alternate in rounds 2 and 3, there will be only one set of pairings which alternates again in round 4, and this set will be highly undesirable because of huge score differences.
In a small tournament, it’s better to have a few bad colors in round 3 (where alternation, not equalization, is the only issue) rather than having them forced on you in round 4.
Bill Smythe
Son of a gun… thanks for another illuminating explanation. I’d been practicing with an odd number of players, thinking this would make things harder, but for this problem, it seems to relieve the tension a little, as the players with byes get to float between the two camps. Doing it with an even number of players does seem to make it worse overall. And yes, I’ve been looking only at small tournaments (heck, the last one this club ran had one section with “5 rounds, 4 players”).
One of the posts in this thread mentioned a 3-way transposition, which can be constructed as the “product” of two 2-way transpositions.
Suppose we have six players in a score group:
1920 WBW vs 1520 WBW
1910 BWB vs 1510 WBW
1900 BWB vs 1500 BWB
Almost any TD would transpose here, pairing the 1920 against the 1500. But how should the other two pairings be made?
1920 WBW vs 1500 BWB
1910 BWB vs 1510 WBW
1900 BWB vs 1520 WBW
Or:
1920 WBW vs 1500 BWB
1910 BWB vs 1520 WBW
1900 BWB vs 1510 WBW
The advantage of the first way is that it is just a 2-way transposition, and it leaves one of the “original” (raw) pairings intact.
The advantage of the second way is that, among players due the same colors, it keeps things in order.
Which way would you do it?
Bill Smythe