Pairing question - FIDE vs USCF

Running Chess Tournaments
1

Given the below crosstable through 4 rounds:

#   Rtng    Rd 1    Rd 2    Rd 3    Rd 4    Total
1   2100    W 9     B 8     W 2     B 3
            1.0     2.0     3.0     3.5     3.5

2   1987    B 10    W 5     B 1     W 7
            1.0     2.0     2.0     3.0     3.0

3   1889    W 4     B 9     W 8     W 1
            0.5     1.5     2.5     3.0     3.0

4   2274    B 3     W 6     B 5     B 10
            0.5     1.5     1.5     2.5     2.5

5   1918    W 11    B 2     W 4     B 6
            1.0     1.0     2.0     2.5     2.5

6   1901    W 12    B 4     W 10    W 5
            1.0     1.0     1.5     2.0     2.0

7   1803    W 8     B 11    W 12    B 2
            0.0     1.0     2.0     2.0     2.0

8   1915    B 7     W 1     B 3     W 11
            1.0     1.0     1.0     1.5     1.5

9   1882    B 1     W 3     B 11    W 12
            0.0     0.0     0.5     1.5     1.5

10  1826    W 2     B 12    B 6     W 4
            0.0     1.0     1.5     1.5     1.5

11  1809    B 5     W 7     W 9     B 8
            0.0     0.0     0.5     1.0     1.0

12  1600    B 6     W 10    B 7     B 9
            0.0     0.0     0.0     0.0     0.0

The FIDE pairing engine in SwissSys gives these pairings for round 5:
1 v 5
2 v 3
4 v 7
9 v 6
10 v 8
12 v 11

It seems to me that a more optimal pairing is this:
4 v 1
2 v 3
5 v 7
8 v 6
10 v 9
12 v 11

It could be that I’m just too used to USCF pairing rules (WinTD agrees with me). Admittedly I’m not as familiar with the FIDE pairing system as I’d like to be. Given some time soon I will study them up more. For those that do understand it better, what is it that makes the above preferred? Or is it?

2

I thought for FIDE color was king.
1 v 5 gives the leader his due color and still allows 4 to have white, while 4 v 1 gives the leader a bad color while allowing 5 to have his due color. Don’t mess with the top guy if you can avoid it.
If the algorithm is to go bottom up to avoid rematches then 8 v 7 / 10 v 9 would have been corrected to 9 v 7 / 10 v 8 before 4 v 6 / 9 v 7 was corrected to 4 v 7 / 9 v 6. I’m so used to look-ahead followed by top-down that I had to think a while to come up with a plausible reason for the 9 v 6 pairing.

3

FIDE takes great priority in colors.

Alex Relyea

4

FIDE pairing rules try to avoid repeated up or down floats if possible. In the previous round #5 played #6, which was 2.0 playing 1.5, so, if possible, he would not be downfloated this round. Since #4 wasn’t downfloated in the previous round, and has the same color problem as #5 (score trumps color trumps “float” preference), 1 plays 5 and 4 drops.

5

Two papers which may prove interesting to those who care:

A simple description of FIDE vs. US Chess pairing rules

A more detailed example

6

Wow – impressive.

The main thing I noticed was that, despite the extreme difference in the logic and language presented by the two versions, in a large percentage of cases FIDE pairings and U.S. Chess pairings turn out to be identical.

The other thing I noticed was something we all have known for a long time anyway – that small tournaments (or small sections) are harder to pair than large ones, at least in the later rounds.

First, a typo (in the first document, page 2, near the bottom):

A downfloat means the player has been paired against an opponent with a higher score. (So, one player’s downfloat is the other player’s upfloat.)

This reverses the usual definitions of downfloat and upfloat. Maybe part of the sentence got lost in the translation from handwritten to typed. It appears it should be:

A downfloat means the player has been paired against an opponent with a lower score. An upfloat means the player has been paired against an opponent with a higher score. (So, one player’s downfloat is the other player’s upfloat.)

Despite the different logic and language, most of the differences between FIDE and U.S. Chess pairings appear to be due to (a) the elimination of the 200- and 80-point transposition limits, and (b) the avoidance of multiple consecutive downfloats / upfloats.

In fact, all the differences in the example in the second paper (a 5-round event with 14 players) are caused by the floats.

I very much LIKE the idea of eliminating the 200- and 80-point transposition limits. Those limits create artificial boundaries and ambiguities, and raise questions like “which difference are we talking about, this one or that one?”. It makes me think U.S.Chess should simply adopt FIDE pairings and be done with it.

Regarding floats, the maximum number of downfloat / upfloat pairs that should occur in any round of an N-round tournament should be 2N-1 (one for each score group). Since the odds of any score group having an even or odd number of players is only 50-50, in the average case there should be about N/2 such float pairs per round. And this number is independent of the total number of players. With 14 players or with 300, there should still be about 4-5 float pairs going into the last round of a 5-round event.

That’s why small sections are the most difficult. 5 pairs (10 players) is a huge percentage of 14, but a tiny percentage of 300. It comes as no surprise to me that, in the second paper, the explanation of the round 5 pairings takes almost three full pages.

Do I like the idea of avoiding consecutive downfloats for a player? Actually, yes I do. In my directing days, I would always mark floats on a player’s pairing card, so that I could avoid multiple floats if I wanted to. (I didn’t always want to, though – it would depend on the situation.)

Let’s all seriously consider the idea of using FIDE pairings in our own tournaments. Both SwissSys and WinTD support FIDE pairings, as far as I know.

Bill Smythe

7

Thanks!

Thanks so very much for catching that! I will make the correction.

To that, I would add one other point: The transpositions and interchanges made to improve color allocation are deterministic and prefer to disrupt the lowest players in the bottom half of the scoregroup (S2). Interestingly, that means that if there must be players not getting due color (because, e.g., more players need white than black), they will be on the higher boards. (Not only are there no rating difference limits, but in fact the transpositions and interchanges ignore ratings completely.)

8

Or not. FIDE pairings were designed for professional tournaments. They expect

(a) relatively few unrated players (or more generally, players with the same ratings)
(b) effectively no “pairing preferences” like not pairing teammates or players from the same state

Re (a) Players with the same rating (and more specifically the unrateds) are assigned pairing numbers based upon alphabetical order. Now if there are only a handful of players with the same ratings, that’s unlikely to make much of a difference, since after round one, they will generally be in different score groups. If 25% of the players have the same (NA) rating, then that may be a big deal.

Re (b) In the typical score group, there is one and only one correct pairing, which involves finding the permutation of the RHS players that corrects as many colors as possible and keeps the high boards as intact as possible. There’s a lexicographic order that determines the desirability. In a typical relatively large score group, it’s generally not that hard to find the correct permutation because most RHS players can play most LHS players. No longer true if there are pairing preferences. I welcome you to compute the number of possible permutations that might have to be examined in a 30 user score group.

9

Yes and no. FIDE will go to great lengths to reduce the number of bad colors, but generally does not push the bad colors to the bottom of the score group.

In fact, in his paper Ken gives the following example:

1 WB
2 BW
3 WB
4 WB
5 BW
6 WB

– where FIDE would transpose 5 and 6, pushing the transpositions to the bottom, but pushing the bad color to the top – in fact, to first board, where player 4 would get the wrong color.

Ken himself noticed this, in his reply upthread:

Bill Smythe

10

15 factorial, or about 1.3 trillion, excluding interchanges. Or 29 double factorial (292725*…53*1), about 6.2 quadrillion, including interchanges.

You wrote a FIDE Dutch algorithm for WinTD, right? Obviously you found a way to eliminate many of the candidates, probably billions at a time, whenever it was obvious they wouldn’t help.

To be sure, when you allow pairing preferences (don’t pair teammates, schoolmates, family members, etc) the algorithm will no longer be deterministic. That’s not so bad, is it?

I’m not particularly concerned about players with identical ratings, including unrated. Even if the order of such players is not re-randomized every round during a single tournament, the identicalness is not likely to be carried over from one tournament to the next, because the unrateds will now have ratings, and the identically rated players will have new, no longer identical, post-event ratings, so it’s hardly likely there will be lifetime albatrosses around anybody’s necks or anything like that.

So, how about adopting FIDE pairings to the extent of eliminating the 200- and 80-point restrictions and avoiding consecutive downfloats? These would be worthwhile changes. We could call them “semi-FIDE” pairings or something similar.

Bill Smythe

11

By FIDE’s logic, absolutely. The whole point of having a specific method for assigning pairing numbers, doing transpositions in a certain order, doing interchanges in a certain order, doing floats in a certain way is to remove discretion (on the part of either the TD or the pairing software) and/or randomness (which can be misinterpreted as “discretion/favoritism”).

WinTD has a “FIDE-style” option which ignores rating differences (except 0 means 0, i.e. a “free” swap) but otherwise uses the US Chess rules. However, unlike FIDE’s system, it will try to minimize the distortion of positions across the whole score group, while FIDE has the lexicographic preference to avoid distortion at the top of the score group.

12

Does WinTD also have an option to avoid consecutive downfloats for the same player?

Bill Smythe