Which transposition is better?

Running Chess Tournaments
21

The original question of this thread prompted me to read the sections about the Look Ahead method (29E6a) and the Top Down method (29E6b) more carefully than I ever had before. There is something about these rules that seems confusing … or maybe I’m thinking about it the wrong way.

The text for the Look Ahead method says (assuming most players in a score group are due for white) that the pairings should be checked for games where neither player is due for white. So far so good. “If such pairings exist, as many of such pairings as possible are changed by making switches to higher or lower boards, involving the minimum possible rating differences.” Although it is not stated explicitly, it seems pretty clear (I think) that you only want to switch with boards where both players are due white. Otherwise you are destroying a “good” pairing where one player is due white and one due black, or where one is due white and one neither. Example 2 in the next section (29E7) confirms this: the boards which already have “good” pairings are not considered for transpositions in the Look Ahead method. (Again, 29E6a does not say this explicitly.)

But now look at 29E7 Example 1, where it discusses the Top Down method. It starts by correcting the top board, BWB vs BWB, by a transposition with the next board, BWB vs WBW. No wonder this method doesn’t work as well, if it advocates correcting one pairing by “uncorrecting” one that should be left alone. Shouldn’t we be able to apply the same implicit common sense here, and say that when we try to correct the top board, we should only make switches with other boards that have color problems? In the example, there are no other boards with color problems, so the pairings should stand, just as they did using the Look Ahead method.

The questions that I’m still not sure about are: (1) If we use the same common-sense logic with both methods, is one really better than the other? and (2) Can we arrive at the same pairings by just applying 29E4 (equalize as many colors as possible, and then alternate as many as possible) without adding the complexity of Look Ahead and Top Down?

22

With top down you also want to try to keep the rating sequence within colors if possible. For example

1900 (due W) - 1600 (due W)
1800 (due W) - 1580 (due B)
1750 (due B) - 1550 (due B)

A simple transposition of the 1600 and the 1550 leaves the bottom three players in reverse sequence (per 29E7, example three that is permissable, though not the best).
1900-1550
1800-1580
1600-1750

A top-down transposition of the 1600 and 1580 and then the 1600 and the 1550 puts the 1600 on the bottom board (where he has to go as that has the only top-half player due black).
1900-1580
1800-1550
1600-1750

The look-ahead method finds
1900-1550
1800-1580
1600-1750
and then uses 29E7 (ex. 3) to get back to
1900-1580
1800-1550
1600-1750

The result is the same either way (if you follow ex. 3).

A big difference between top-down and look-ahead can be seen with
1900 (due W) - 1600 (due W)
1800 (due W) - 1580 (due B)
1700 (due W) - 1550 (due B)
1625 (due W) - 1540 (due B)

Look ahead says that there are no switches that can be made and leaves the pairings alone. Top-down can result in the 1600-1580 switch, then the 1600-1550 switch, and then the 1600-1540 switch, resulting in
1900-1580
1800-1550
1700-1540
1625-1600
This has the virtue of putting the color conflict on the bottom board of the score group, but it looks ugly.

A big plus for top-down is that it can be used for a non-computer-using TD to fairly quickly do a large scoregroup without having to lay all of the cards out and review the pairings.
With the advent of computers that plus is fading quickly.
Also, top-down is more useful early in the tournament, as later you have to worry more about not pairing players that have already played each other (often necessitating spreading the cards out anyway).

In my pre-computer days I know that in smaller tournaments (say 100-150 players in a section) I found using the look-ahead method to search for good candidate pairings to switch from was actually faster than doing the multiple switches involved with top-down, and I felt the pairings were better. However, it did require a fair amount of space to spread those pairings cards out on.

23

If you pick one of the methods and stick with it you will be OK. Since both methods give the TD legal pairings, the only question is one of quality.

I suspect if you get a group of TDs together to discuss which set of pairings was best you would get a lot of nit picking and no real solution to the quality question. Not getting TDs to agree on which pairing rules should be given the overwelming nod, when push comes to shove, has been a challange for many rulebook editions.

Tim Just
5th Edition editor

24

Glad to hear it. Thank you.

I’ve never been to one of these TD Workshops, but I assume they’re held at the U.S. Open. They could have either (or both) of two purposes:

A – to let more experienced TDs fill in less experienced ones on some tricks of the trade.

B – to let more experienced TDs (and less experienced TDs too, I guess) discuss legitimately different options in complicated situations not explicitly covered by the rules.

I’m guessing that, if you’re using my starting question, you have A in mind more than B. Shoe number two, the transpose-WBWB-vs-transpose-BWWB business, is definitely a B question. :slight_smile:

Bill Smythe

25

Your English is perfect. I would not have known it was not your first language, if you hadn’t told us.

I don’t know of anyplace in the rules that says (or implies) that the higher boards get priority in a score group. The only time rating enters the picture is in the “higher-ranked gets due color” rule, which is only number 5 on a list of 5 rules, and kicks in only if the other 4 do not decide the issue.

Isn’t that top-down, rather than look-ahead? Top-down tries to correct the first bad colors, while look-ahead tries to correct the worst ones.

That’s certainly true, but not relevant to the current discussion. In all the examples in this thread, I deliberately made the rating differences much greater among the top-half players than among the bottom-half, precisely to avoid this sort of complication.

Bill Smythe

26

That was a hilarious post. I’m sorry you deleted it.

Bill Smythe

27

Not if the rule (or example) is worded gently enough: “Pairings X and Y are both legal. Pairing X is slightly preferable because it assigns black to BWWB, the player least strongly due white, whereas pairing Y assigns black to WBWB, a player more strongly due white.”

Bill Smythe

28

Yeah, there’s too much ballyhoo about look-ahead vs top-down, and too much confusion about the definitions of both.

29E6a starts out by describing look-ahead as the processing of counting due-whites and due-blacks, and if, for example, there are more due-whites than due-blacks, avoiding pairing due-blacks against each other, as this would exacerbate the disparity. So far so good.

Then, in a later paragraph, it talks about equalization vs alternation, stating, in essence, that it is more important to give the correct color to a player with unequal colors than to one with equal colors. That’s good too, although describing a player with equal colors as “due neither color” is inaccurate and confusing.

But then top-down is described as a method in which the TD is willing to correct one color by uncorrecting another, just to push the bad color further down into the score group. But I don’t think most TDs who work from the top down would actually do this. They might, however, come up with less than best transpositions, just because they were unwilling to look ahead far enough.

Raw pairings:
1900 BWB vs 1590 BWB
1800 WBW vs 1520 WBW
1700 BWB vs 1500 BWB

A typical top-downer might look at the first two pairings and immediately make the 70-point switch, whereas a looker-ahead would sit back for a moment, then see that the 20-point switch is also feasible, and choose the latter because of the smaller rating difference.

When pairing a large score group (50 players) using pairing cards, a TD wouldn’t find it practical to use a full look-ahead approach. But he should at least look ahead a few pairings, to check for disparities between due-whites and due-blacks, and also to look for transpositions that may be better than the first ones that pop out. About 3/4 of the way through the score group, he could start looking ahead all the way to the end of the group.

Bill Smythe

29

True. It would be highly undesirable, probably impossible, for the rules to include a one-size-fits-all pairing algorithm. There would be all sorts of problems:

A. No room would be left for TD discretion.

B. The algorithm would be too complicated for human TDs to implement when the score group is large.

C. Sooner or later, an unanticipated situation would come up in which the algorithm would produce an obviously silly result.

D. Even a slight deviation from the algorithm would provide fodder for chess lawyers.

Even pairing programs face these problems. A couple of years ago there was a thread somewhere in this forum which brought this out. As I recall, WinTD was forced to make a 300-point transposition because two players had already played each other. But then it refused to make an additional 1-point transposition even though it would vastly improve colors on two boards. We finally concluded (guessed) this happened because the transposition was already outside the 200-point equalization limit.

Bill Smythe