Pulling Players Down into Lower Score Groups

Running Chess Tournaments
1

Rule 29 covers Swiss Pairing rules and procedures. Summarizing, Rule 29 calls for players to be paired by descending “rank” (i.e. score followed by rating). Players with the same score are to be paired against one another, with the “top half” by rank of a score group paired against the “bottom half”, in rank order. If the number of players in a score group is odd, an “odd player” is selected who is paired against a player with a lower score. This is usually the lowest ranked player in the score group, but someone else may be chosen in order to facilitate the pairing of the two score groups involved. Other players in a score group may need to be treated as “odd” players, such as when there is someone who cannot be paired against anyone else in his score group because of previous games, team restrictions, etc. Rule 29 permits the director to pair those players with lower score groups too.

People who read this forum mostly know all this. I am just setting the stage for my problem. Here it is:

In reading Rule 29, I find no reference to the situation where a score group can be paired intact with no “odd players”, but must be broken up and “odd players” created in order to enable the pairing of a lower score group.

For example, consider the situation where after several rounds, the even number of players with a score of S can, by good fortune, all be paired against other players with a score of S, with no odd players. However, further down near the bottom of the chart, there is a player X whose lowest ranked possible opponent is Y, someone in score group S. X has already played everybody else who is lower ranked than Y. If X is not paired with Y, than X will have to be paired against someone even higher ranked than X (which is basically just the same problem again), or else with someone who he has already played, which violates the highest priority rule of Swiss pairing (27A1).

So, my question is: is it acceptable to pair X with Y? X is higher-ranked and is being turned into an “odd player” in order to make it possible to pair someone further down, not because of any problem in his own score group. If it is acceptable, where in Rule 29 does it state that this is acceptable, or do you have to just fall back on the “priorities” in Rule 27?

Practically speaking, at what point in the Rule 29 “algorithm” may one “pull down” players out of higher score groups to solve pairing problems that develop further down, and what are the rules about which players may be “pulled down”.

2

Yes, if the lowest-ranked opponent that Y hasn’t already played is X you can pair Y against X even if X is in a higher score group.

Rule 29A says that players may be paired outside of their score group if they “must play odd players paired from another score group (29D).” Rule 29D says “There will often be situations where some players cannot be paired within their score group. This … can … happen when players within a score group have already played each other. … At least one player, and possibly more, will have to be dropped to play in a lower score group.” Although 29D doesn’t explicitly say that if it’s not possible to find a suitable opponent for such a player in a lower score group it’s acceptable to pair the player in a higher score group, this can be inferred from the fact that Rule 27A1 (avoiding players meeting twice) is higher priority than 27A2 (pairing players within a score group).

3

What I often do is to look at the top and bottom score groups before looking at the middle score groups. If I see that the players in the bottom score group can’t be paired against each other I’ll figure out what players need to be dropped from the next higher score group before pairing that score group.

Rule 29D says, “In such situations, the first priority (other than avoiding restricted pairings) is to have players play as close to their score group as possible.”

4

What algorithm does one use when doing manual pairing. For example, lets say after a lot of rounds, the bottom player in the ranking has to player several score groups up in order to be paired. If you wait until you get to the bottom, and then undo a higher pairing, you will move down one player. But what about the other pairing in the undone pairing. He won’t have anywhere to go but way down also, even though that wouldn’t have been necessary if you had been able to look ahead. Do you have to undo all the pairings and redo them all in order to avoid that?

5

That’s why I try to look ahead and make sure the bottom score group can be paired before I pair the middle score groups. If I’ve paired the higher score groups and then discover a problem pairing a lower group I figure out which pairings are forced in order to fix the problem and repair the affected score groups. I don’t have a precise algorithm for this; it’s ad hoc.

I’ve heard that FIDE does have a precise algorithm for how pairings are made. I’m sure I’ll learn the gory details at the FIDE Arbiters Seminar, or I could “cheat” and read the FIDE regulations.

6

Looking ahead is good. If the lowest score group (or two) is (are) tiny, you might want to take a look down there when starting to pair the group just above the tiny group(s), or maybe even the two groups just above the tiny group(s).

Above all, don’t make the beginner’s mistake (when doing manual pairings) of writing down each pairing as you make it. That makes it more difficult to undo pairings if necessary.

First, make all the pairings. This will result in a pile of pairing cards where the top card has white on board 1 against the second card, the third card has white on board 2 against the fourth, etc.

Next, write the pairings on the pairing sheet. Do this simply by going through the pile (above) and writing each name (along with player number and/or rating) on the sheet.

Next, post the pairing sheet and holler “pairings are up”. Soon the players will be out of your hair and starting their games.

Finally, at your leisure, write the pairings on the pairing cards. (This does not have to be done until the games have started.)

Eventually, write the pairings on the wall chart too, and then keep the wall chart updated, game by game, as results come in. Then the players will think you’re doing a good job.

Bill Smythe

7

When I was a “young pup” as a TD (back in 1977), Dan Semonoff taught me to pair the top score group first, then the bottom score group. Then, go back to the next highest score group, then the next lowest, and work your way to the middle.

8

This makes sense, and I have heard this advice before, but 29B says “In general, the director pairs the group according to rank, starting with the highest and working down.” The “in general” makes it hard to know how to take that. Pairing top to bottom certainly has consequences. If you reach a point where two players, A and B, can only be paired against player X, and you are pairing top to bottom by rank, then higher-ranking A gets the pairing, and B does not. So it is important. You get the idea that the USCF wants you to pair top to bottom, except … when?

As I have commented before, one of the big problems with the entire tournament section of the rulebook is that it is almost impossible to tell what is actually a capital-R “Rule”, which must be followed, and what is just tutorial, how people usually do it, advice to young pups, etc.

9

I’ll have to see what FIDE does but it seems to me that the only way to specify the pairing rules unambiguously would be to publish a formal algorithm, or computer program, as the standard way of making pairings. For USCF pairings such an algorithm doesn’t exist. I don’t think it would be easy to create one, and experienced NTDs might disagree about what to do in various situations.

To answer your specific question: if two players, A and B, can only play against X and otherwise would have to play someone who they’ve already played, then you’re going to have to violate the rule against pairing people who have already played. You should minimize the number of rematches and you should minimize the number of players who play outside of their score groups. In general it’s more important to make natural pairings (within the right score groups, for example) for players who are in contention for prizes than for tail enders.

10

Another way to do it would be to set out criteria for pairings and leave the design of algorithms to find a pairing that meets those criteria to sofware developers and tournament directors.

11

The criteria would be so complicated and subject to ambiguity that it would be simpler to write an algorithm or program and say “this is the standard”. There are all kinds of situations that you’d have to account for.

Although this is far from a perfect analogy, and playing chess is much more complicated than making Swiss pairings, it’s sort of like asking for a set of criteria for making good chess moves. The criteria might be a set of rules like “1. Checkmate your opponent. 2. If you can’t do that, develop a winning attack, even if there’s no forced mate. 3. If you can’t do that, win material, as long as the opponent can’t checkmate you by force and doesn’t have a winning attack” and so forth. Obviously the criteria couldn’t cover every situation and there would be exceptions to most of the rules. To really play chess well you have to gain experience and not just learn a set of rules. But if your goal is to allow a computer of a given speed to play at a given rating level, you can specify an algorithm or write a computer program that will be good enough for the intended purpose, within limits.

12

There was no rule 29B back then. What I remember of the pairing rules were “top half vs. bottom half, make it work.” I’m not even sure the 80 and 200 point limits for transpositions or interchanges to improve alternation and equalization, respectively, existed back then. From speaking with Tim Redman last year in Irvine, I got the impression that the work to quantify the effect of “wrong” color allocation was done in the time frame in which the third edition of the rule book was edited; it was that research that led to the 80/200 limits.

For what it’s worth, my simplistic description of the FIDE swiss pairing rules is:

  1. Assign each player a due color and compute the number of players who will not be able to receive due color in the score group. (For instance, if the score group contains eight players of whom five are due white and three black, the best you can do pairing the score group is to have one player who does not get due color.)
  2. Make the natural pairings. If the number of players who have the wrong color is the number from step 1, you are done.
  3. Make transpositions in the lower half as far down as possible. (For instance, in an eight player score group, transpose players 7 and 8.) If not optimal, try transposing 6 and 8, then 6 and 7, then 5 and 8, then 5 and 7, then 5 and 6.
  4. If an optimal pairing has not been found, make an interchange between the top and bottom halves, and try again starting at step 2.

The full description can be found at the Swiss System Based on Rating (The Dutch System) section of the FIDE handbook.

13

I’ve never found that necessary, nor do I think it is particularly wise.

You might, however, want to look ahead a score group or two once you get close to the bottom groups, especially if there are tiny score groups (2 players) near the bottom.

In pairing round 4, for example, if there are no 0-pointers and only two 0.5-pointers, it is highly likely that they have already played (and drawn) each other. So you need to look at the 0.5’s before pairing the 1.0’s. Then, if the two 0.5’s can’t be paired against each other, just pair them against the bottom two 1.0’s, then pair the rest of the 1.0’s normally.

It should seldom be necessary to look ahead more than one or two score groups, and then only if there are a tiny number of players in the bottom score group or two.

These rules (or your “simplistic description”) seem to overlook, or ignore, the seriousness of various color problems.

If, for example, it is necessary to assign black to 1 player who is due white, I would rather assign this wrong color to the player who is least due white. bye-WB is less due white than BWB, who in turn is less due white than WBB, etc.

Bill Smythe

14

The problem with the FIDE rules is the backtracking, which involves undoing all the pairings from some point, backing up to that point, making some change or relaxing some constraint, and “trying again”, repeating until it “works” The algorithm presented in the FIDE “Dutch” pairing rules document is an exponential algorithm, which is bad news.

If the number of players or rounds is small, this algorithm will find a pairing by brute force, but if there are a high number of rounds relative to players, in the later rounds you can get a situation where there are large “clumps” of unpaired players who cannot be paired because they have all played each other already, and the algorithm will spend astronomical amounts of time concluding that these large clumps are unpairable.

No real pairing program actually runs the pure FIDE algorithm, unless it is restricted to low numbers of rounds. The 14-round Blitz tournament at the US Open would be enough to give a program following the FIDE algorithm trouble. It wouldn’t be able to finish the pairings in time beyond probably round 12. A real FIDE pairing program almost certainly has some kind of “backup plan” for avoiding an exponential explosion in high-numbered rounds.