Often after a long day of chess, I like to sit back and enjoy a nice, refreshing pint. I find that “bottoms up” fixes many of my problems too!
:mrgreen:
- Enrique
Now let me modify my earlier example, by adding an extra round and putting an unplayed game in there:
1930 xWB - 1630 BWB
1920 BWB - 1620 WBW
1910 WBW - 1610 BWB
1900 BWB - 1600 WBW
As before, there is only one bad color, and it’s on top board. But now, it’s even more desirable than before to leave the pairings alone, because then the player receiving the bad color is the one who is “least” due his due color. (Note that in this case you would give white to the 1630, because equalization takes priority over alternation.) In my opinion, these are the best pairings, even though the bad color goes to the top-rated player in the group!
Maybe by now some of you are beginning to question point-count pairings. That won’t stop me. Let’s even stretch it just a bit more. Suppose the raw pairings are:
1930 xWB - 1630 WBW
1920 BWB - 1620 BWB
1910 WBW - 1610 BWB
1900 BWB - 1600 WBW
At the moment the bad color is on second board. Here I would switch the 1630 with the 1620, thus pushing the bad color up to top board. Why? To reduce the severity of the bad colors. We now have a bad alternation instead of a bad equalization, saving us 120 (200 minus 80) undesirability points, at the mere cost of 20 undesirability points for the 10-point transpositions.
Let’s take it still further:
1930 xWB - 1630 WBW
1920 BWB - 1620 WBW
1910 WBW - 1610 BWB
1900 BWB - 1600 BWB
Now we have a bad equalization on fourth board. The only way to replace it with a bad alternation is to move the bad color all the way up to top board, switching the 1600 with the 1630. But I still say this is better, even though the player not getting his due color will be the top-rated in the group. We have reduced the bad-color undesirability points from 200 to 80, at the mere cost of a 30-point transposition.
How many of you are still with me?
Bill Smythe
Would the pairing programs make the decisions you would in these cases, Bill?
Has there ever been any support in the rules (any rules) for doing swaps that merely shift the location of the bad color?
I dunno, but in your previous post (if I interpreted you correctly) you said that the FIDE Dutch system does exactly that.
Meanwhile, since you’re here, perhaps you could answer the following question (as regards WinTD), from another poster:
Note that he is not talking about “doing swaps that merely shift the location of the bad color”, but rather, doing swaps that replace a bad equalization with a bad alternation.
Bill Smythe
You look for the cheapest swaps (basically lexicographically starting at the end—rating doesn’t matter, it’s just position in the bottom half) which maximize the color improvement. So if you can’t improve the colors, you don’t do the swaps.
OK, thank you.
Now what about the other situation I described –
1930 xWB - 1630 WBW
1920 BWB - 1620 BWB
1910 WBW - 1610 BWB
1900 BWB - 1600 WBW
where a swap between top board and second board would get rid of a bad equalization, and give us a bad alternation instead. Would WinTD do this?
Bill Smythe
Yes.
Aha! You see, everybody, I’m not the only one who would make such a swap. 
Now what about the more extreme version:
1930 xWB - 1630 WBW
1920 BWB - 1620 WBW
1910 WBW - 1610 BWB
1900 BWB - 1600 BWB
Here, to get rid of the bad equalization, we’d have to swap fourth board all the way up to top board, with the following result:
1930 xWB - 1600 BWB
1920 BWB - 1620 WBW
1910 WBW - 1610 BWB
1900 BWB - 1630 WBW
Would WinTD do this, too? I’m hoping the answer is yes.
Or, we could ladder down the transpositions (sort of), by bringing the 1610 (instead of the 1600) up to top board, then dropping the 1630 from top board to second, and taking 1620 from second board down to fourth, and moving 1600 up to third:
1930 xWB - 1610 BWB
1920 BWB - 1630 WBW
1910 WBW - 1600 BWB
1900 BWB - 1620 WBW
This method of removing the bad equalization is, I think, is about equal in quality to the first. In fact, it could be argued that it is a little better, because (even though more transpositions are involved), the largest transposition is one board less than before.
What does WinTD think of this idea?
Bill Smythe
WinTD would do the last one of these. The series of small swaps is considered to be superior to one big one.
Per 29E7 example 3
I am delighted to find that WinTD agrees with me that transposing raw pairings in such a way as to lose a bad equalization and gain a bad alternation is a worthwhile thing to do. The number of bad colors is not reduced, but their “badness” is.
I wonder how many human TDs would do the same?
Bill Smythe
I really hope the answer is “all of them,” but it probably isn’t.
Actually, it seems there are hardly any human TDs these days. 
Bill Smythe
Beep boop bloop beep beep… Pair a round?
And following is the process through which a human TD could go to reach the same conclusion.
Raw pairings:
1930 xWB - 1630 WBW
1920 BWB - 1620 WBW
1910 WBW - 1610 BWB
1900 BWB - 1600 BWB
“1. Hmm, there are 5 due white and 3 due black, so one player due white must receive black. Let’s give black to the player least strongly due white. That way we will end up with a bad alternation instead of a bad equalization.”
“2. Of the 5 players due white, the one least strongly due white is the 1930, because he is due white only to alternate, whereas the others are due white in order to equalize. So we’ll give black to the 1930.”
“3. That means we should pair the 1930 against a player due white. The highest player (in the bottom half) due white is the 1610. So we have:”
1610 BWB - 1930 xWB
“4. Lining up the remaining players in order, we have:”
1920 BWB - 1630 WBW
1910 WBW - 1620 WBW
1900 BWB - 1600 BWB
“5. Transposing the bottom two will now make all the (remaining) colors work:”
1920 BWB - 1630 WBW
1910 WBW - 1600 BWB
1900 BWB - 1620 WBW
“6. So the final pairings, with white on the left, turn out to be:”
1610 BWB - 1930 xWB
1920 BWB - 1630 WBW
1600 BWB - 1910 WBW
1900 BWB - 1620 WBW
“7. Voila!”
Bill Smythe