A friend just called and wanted to discuss pairing the following 2nd round middle score group for a team tournament. How do you think it should be paired. Logic explanation would be interesting. Result is the team score. Note, my friend only sent the middle score group and renumbered the pairing #s for only this group which is why the colors for round 1 are unusual.
P# Rating Result Color opp.
2272 1/2 W 4
2267 1/2 B 5
2219 1/2 B 6
2092 1/2 B 1
2089 1/2 W 2
2068 1/2 W 3
Without examining the rule book again in more detail and assuming there are an even number of 1.0 scores, I don’t see anything wrong with this set:
6 vs 1
2 vs 4
3 vs 5
6 will get white twice in a row, but not a big deal yet. 4 will get black twice in a row, but still no problem since it’s just the second round.
The only way to get the colors right is via an interchange—4 for either 3 or 2. Both the interchanges are inside the 200 point limit, but you want to make the cheapest one that you can, so I would do 4 for 3. Since 2 and 5 have played, the only pairing which gets all the colors correct given the interchange is 1 vs 3, 2 vs 6 and 4 vs 5.
Since we are looking at equalization rather than alternation the limit is 200 points.
I agree with Tom with
3-1
2-6
4-5
**** further discussion of a variant of the question ****
If the colors were only being alternated instead of equalized (80-point limit for interchanges) I would have done the following (giving 1 the strongest available opponent in the 2nd half):
5-1
2-6
3-4
The GKarRacer pairings look to be mathematically equivalent, but my personal preference would be to avoid pairing the top against the bottom since it is not yet necessary.
6-1
2-4
3-5
I posted a little too quickly. Not sure where my mind was at. I set that like a tournament bracket in seed order. The normal pairings (not in color order) would be 1-4,2-5,3-6. Obviously you can’t do that since that would duplicate the first round.
As suggested 3-1, 2-6, 4-5 makes sense.
I agree with wintdoan and jwiewel. The colors might as well be made to work.
It’s possible, though, that colors should be considered less important in a team tournament. I assume “team” means team-vs-team. To be sure, even without balancing colors on each board of each team, there would still be overall color balance for the teams a whole. Board 1 might get two blacks, board 2 two whites, etc, but (assuming there is an even number of players on each team), each team would get (for example) white on 2 boards and black on 2 boards.
Still, that doesn’t really feel right. It would be nice to balance the colors for each individual player, not just for each team as a whole.
Here’s another idea. I don’t know if the following has ever been tried, or even suggested. Why not, when two teams due the same color are paired each other, exchange boards 1 and 2 on one of the teams, so that board 1 on team A plays board 2 on team B, and vice versa, and ditto for boards 3 and 4?
Then you would never need to transpose team pairings to improve colors.
Bill Smythe
Wouldn’t switching board order on one of the teams raise havoc with eligibility for board prizes? As soon as you’ve swapped the top two boards, doesn’t that mean that the team’s “board 1” player would now be eligible only for the second board prize?
Hmm, that’s true. Oh well, not all new ideas are good ideas.
I suppose, though, that if a board 1 player were assigned to board 2 in this manner and for this reason, his game score could be regarded as still counting toward a potential board 1 prize. Still, I’ll admit that sounds a bit fishy.
But it reminds me of a concept that was tried in Illinois team tournaments two or three times:
If there is an odd number of teams, instead of giving a bye to the lowest-ranked team, give a trye to the bottom three teams.
Pair board 1 of team A vs board 2 of team B, board 1 of team B vs board 2 of team C, and board 1 of team C vs board 2 of team A. Do the same thing (or, better yet, mirror image) with boards 3 and 4.
The team score for each team is calculated in the standard way – a win if the team’s players score a total of 2.5 or more, a draw if 2.0, or a loss if 1.5 or less.
This way, no team needs to sit out – all the players get games.
Board prize considerations wouldn’t be too important, because only teams in the bottom score group(s) would be involved in tryes.
Bill Smythe
Excellent problem Ernie. I would make the interchange between 3-4 and transpose 5-6, as suggested above.
Now, for some real fun, let’s change the problem to:
Go.
Well, if you work out the combinatorics, there are eight possible ways to pair the round (without pairing any player against an opponent he has already faced). Of these eight:
So it seems you must choose your poison.
By “bad transposition” I mean over 200 points.
For a pairing to be “within 200 points” (the opposite of “over 200 points”) means, I suppose, that at least one of the two players in the proposed pairing is paired within 200 points of the opponent he would have faced in his “raw” pairing.
By “raw pairings” I mean extremely raw – straight top half vs bottom half, without regards to colors and without regards to players having already faced each other.
Now, I suppose it could be argued that the 200-point limit applies only to transpositions made to equalize colors, not to those made to avoid repeat pairings, and that in this case these transpositions are already necessary to avoid repeat pairings, and that therefore the 200-point rule does not apply here. Let the debate begin.
The ancient (and interesting, if I do say so myself) thread Point Count Pairings touches on issues like these.
Bill Smythe
I don’t see this mentioned above, but I would have done the same thing (interchange 3 & 4, transpose 5 & 6), with colors balancing:
White Black
3-1
2-6
4-5
For what it’s worth, here are the Point Count Pairings scores for the original question:
Raw pairings:
4 vs 1: 50,000 undesirability points (same opponent twice)
2 vs 5: 50,000 undesirability points (same opponent twice)
3 vs 6: 50,000 undesirability points (same opponent twice)
Total undesirability points: 150,000
Pairings suggested by most respondents:
3 vs 1: 127 undesirability points (player 1’s transposition score)
2 vs 6: 21 undesirability points (player 2’s transposition score)
4 vs 5: 175 undesirability points (player 5’s transposition score)
Total undesirability points: 323
The only other plausible pairings (in my opinion):
2 vs 1: 175 undesirability points (player 1’s transposition score)
3 vs 5: 21 undesirability points (player 3’s transposition score)
4 vs 6: 127 undesirability points (player 6’s transposition score)
Total undesirability points: 323
Wow – the last two come out the same. 
:mrgreen:
And note that the same three rating differences are involved. For example, 127 is the rating difference between players 3 and 4, which shows up as player 1’s transposition score in the second pairing set, and as player 6’s transposition score in the third set.
So, it would seem the second and third pairing sets are pretty much equally good. The main difference is that the second set has a top-down appearance, whereas the third has a bottom-up appearance. The second set appears to first try to pair player 1, while the third appears to first try to player 6. I suppose one could give the nod to the second set over the third based on this fact alone.
Bill Smythe
And now, the other shoe. Below are the Point Count Pairings scores for Brennen Price’s revised version.
Raw pairings:
4 vs 1: 50,000 undesirability points (same opponent twice)
2 vs 5: 50,000 undesirability points (same opponent twice)
3 vs 6: 50,000 undesirability points (same opponent twice)
Total undesirability points: 150,000
Bad transpositions, version 1:
3 vs 1: 227 undesirability points (player 1’s transposition score)
2 vs 6: 21 undesirability points (player 2’s transposition score)
4 vs 5: 275 undesirability points (player 5’s transposition score)
Total undesirability points: 523
Bad transpositions, version 2:
2 vs 1: 275 undesirability points (player 1’s transposition score)
3 vs 5: 21 undesirability points (player 3’s transposition score)
4 vs 6: 227 undesirability points (player 6’s transposition score)
Total undesirability points: 523
Bad colors, version 1:
5 vs 1: 203 undesirability points (bad colors 200, plus player 1’s transposition score 3)
2 vs 6: 21 undesirability points (player 2’s transposition score)
3 vs 4: 224 undesirability points (bad colors 200, plus player 3’s transposition score 24)
Total undesirability points: 448
Bad colors, version 2:
6 vs 1: 224 undesirability points (bad colors 200, plus player 1’s transposition score 24)
2 vs 4: 203 undesirability points (bad colors 200, plus player 2’s transposition score 3)
3 vs 5: 21 undesirability points (player 3’s transposition score)
Total undesirability points: 448
The other four possible pairing sets have both bad transpositions and bad colors, so they’re not even on the table.
Again, ties. Bad transpositions, 523 either way. Bad colors, 448 either way. So we go for the bad colors.
I’m guessing most TDs would go for bad colors version 1 over bad colors version 2, as version 1 looks a little more normal.
Bill Smythe
Hi Bill:
Great analysis. I first tried just transpositions and after 2 changes had 2 bad color problems. I then tried the interchange and was very happy with the result.
3-1, 2-6, 4-5.
I look at the initial pairing changes as just looking at ways to avoid pairing the same opponents. Therefore, in my mind, the interchange of 3 & 4 is not for color so the rating difference restrictions do not come into play. Just my logic to eliminate questions about the rating difference. 29C2 allows either, lists transpositions first, but says nothing about which is preferred. It does state that Interchanges for better colors so I believe my logic is correct. Sometime soon, I plan to look at what the Dutch Swiss System would do. As the FIDE systems give a lot of weight to color, suspect this is the pairing set will be the one I chose.
Hi Bill:
Re point count pairings for the original problem. I see that the variations total is a tie. However, in one the top board has the major undesirable and in the other, the bottom board does. Does point count pairing take this into account? Should it? Perhaps try to push the greatest undesirable towards the middle for easier next round pairings?
When the entire scoregroup is getting adjusted there is a very high chance that multiple adjustments will have the same point count. Also, there is a good chance that the roughly middle of the scoregoups cannot be legitimately given the greatest undesirability.
Cases where the middle can be given the greatest undesirability and are still tied for the lowest point count of undesirability measure are probably rare enough that it is unnecessary to clutter up the rule book. For that matter it may be desirable to give that greatest difference to the top board if it is not the final round and you have a preference for critical and close final round match-ups.
I’ve never been in favor of making transpositions simply to push the bad colors down to a lower board. Unless the total number of bad colors is reduced, or at least the “badness” of the bad colors, there is no point. And point count pairings quickly refute such attempts.
For example:
1930 WB - 1630 WB
1920 WB - 1620 BW
1910 BW - 1610 WB
1900 WB - 1600 BW
Here there is only one bad color, and it’s on top board. Some TDs who use pairing cards, and who refuse to “look ahead” at the rest of the group, might be inclined to immediately grab the 1620 player and put him on top board against the 1930. This moves the bad color down to second board, making it 1920 WB - 1630 WB, but accomplishes nothing overall.
Now suppose this same future-blind TD decides to make a further transposition, by bringing the 1600 player up to second board to improve the colors there. Fine – now the top two boards look nice, but there’s still a color problem on one of the bottom boards. Again, nothing is accomplished overall.
The more intelligent TD, who looks ahead at the entire score group, will quickly realize that 5 of the 8 players are due white while only 3 of the 8 are due black. There will, therefore, be a color problem no matter what, so why bother? The raw pairings are as good as it gets, without transpositions.
Of course, the case which started this conversation is entirely different. Here several transpositions were required just to avoid repeat pairings, and two different pairing sets turned out to be point-count equal. So one might as well simply invoke the pairings that most TDs would probably notice first, and which three actual TDs did notice first right here in this thread.
But there should be no need to clutter up the point-count specifications to accommodate such ties. The simple fact that the “more natural” pairings would be noticed first should suffice.
Bill Smythe
This has been an outstanding thread. This sort of situation occurs regularly. Bravo to all involved in shedding light on this subject.
It is not precisely correct to say that one set was noticed by three TDs first. The numerically equivalent pairings had already been proposed (and thus read and noticed) prior to those three TDs looking at them and preferring the alternative when deailing with a variation of the original situation. Those numerically equivalent pairings are perfectly valid, so it came down to personal preferences considering what is likely to be best in the long run for the tournament.
As time goes on, threads like these are becoming more curiosities than learning opportunities with most TDs simply using pairing programs and accepting their results. That said, I like seeing threads like these so that TDs still look at those computer pairings for sanity checks to verify that they have their settings correct (so that they avoid the “garbage in, garbage out” issues).
The FIDE Dutch system is exactly the opposite. The high board pairings are kept as intact as possible, with the swaps being pushed to lower boards, i.e. color problems are fixed from the bottom up.