Pairings Jam

Technical questions regarding Openings, Middlegames, Endings etc.
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Andrew Bak
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Pairings Jam

Post by Andrew Bak » Fri Nov 27, 2015 7:50 pm

I noticed on the 4NCL website that there was a warning for Division 4 South that "There is some possibility that pairings in later rounds will jam. Every attempt will be made to avoid this."

How does a pairing jam occur? Is it possible to provide an example?

Roger de Coverly
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Re: Pairings Jam

Post by Roger de Coverly » Fri Nov 27, 2015 7:55 pm

Andrew Bak wrote: How does a pairing jam occur?
It must be some technical arbiter term. With a high number of rounds and a low number of teams, the league is likely to take on some of the characteristics of an all play all. They would want to avoid circumstances where they cannot pair at all without teams playing twice. Perhaps the term refers to a circumstance where there is only one way of pairing a future round and that is independent of all previous results.

LawrenceCooper
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Re: Pairings Jam

Post by LawrenceCooper » Fri Nov 27, 2015 8:01 pm

Roger de Coverly wrote:
Andrew Bak wrote: How does a pairing jam occur?
It must be some technical arbiter term. With a high number of rounds and a low number of teams, the league is likely to take on some of the characteristics of an all play all. They would want to avoid circumstances where they cannot pair at all without teams playing twice. Perhaps the term refers to a circumstance where there is only one way of pairing a future round and that is independent of all previous results.
I don't know if a computer program exists that is able to check if legal sets of pairings exist for the required remaining number of rounds but it would be very useful in such cases. I am aware though that manual pairings are probably being used in Division Four.

Kevin Thurlow
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Re: Pairings Jam

Post by Kevin Thurlow » Sat Nov 28, 2015 10:52 am

You probably need manual pairings in the penultimate round, so as to ensure you can pair the last round. It's a function of having a number of rounds which is only slightly lower than the number of players. It probably wouldn't happen in this instance but I had an event where a couple of people withdrew late in the tournament, meaning that two of the remaining players had played all the others, so it needed some imagination to pair the last round, obviously two of them had to play again.

Even if you can pair the last round, you don't want to have one of the leaders having to play the bottom team.

John McKenna

Re: Pairings Jam

Post by John McKenna » Sat Nov 28, 2015 4:08 pm

... so it needed some imagination to pair the last round, obviously two of them had to play again.
Was it also obvious that they would play, again, with colours reversed?

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Tristan Clayton
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Re: Pairings Jam

Post by Tristan Clayton » Sat Nov 28, 2015 6:22 pm

Isn't pairings jam what they put in a Swiss roll?
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David Williams
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Re: Pairings Jam

Post by David Williams » Mon Nov 30, 2015 10:24 am

My brother-in-law told me once of a golfing weekend with a group of friends. Sixteen of them, who played five rounds of golf in groups of four, and he was bemoaning the fact that, although the aim was to play with or against as many of the others as possible, in practice you always ended up with the same person three times, and never played at all with several.

Five rounds, play with three others at one time, fifteen others to play with? Naturally I immediately cut short the conversation and retired with pen and paper. And after a bit of effort I managed to present him with a list of pairings that worked - next time everyone played with or against every other member of the group once and once only.

But subsequently numbers changed, and what looked superficially easier was actually more difficult. For example, if there were more players, it seemed to be impossible to avoid some people playing together twice, even though there are more people to play with. I was left thinking that there is a branch of mathematics that either I'm not familiar with, or hasn't been invented yet.

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Michael Farthing
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Re: Pairings Jam

Post by Michael Farthing » Mon Nov 30, 2015 10:39 am

This problem originally surfaced as "the Kirkman schoolgirl problem" which originally centred on a schoolmistress who had 15 girls whom she took on a walk each day (including weekends - she was very conscientious) arranged in five rows of three. The mistress wanted her girls to have different companions each day during the week and hence the problem. For anyone interested the mathematics of this (and more generalised cases) is discussed in WWR Ball: Mathematical Recreations and Essays.

This incidentally also has a chapter on well-known chess board problems (putting eight queens on the board so that none attacks another; designing a knight tour of the board so it visits each square once and once only etc etc).

MartinCarpenter
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Re: Pairings Jam

Post by MartinCarpenter » Mon Nov 30, 2015 10:56 am

The field of maths definitely seems to have been invented - looks to fall under combinatorial design. (https://en.wikipedia.org/wiki/Combinatorial_design.).

Not really important in chess but it gets really fun in bridge with the movements for pairs events. Someone published a huge book about those.

Kevin Thurlow
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Re: Pairings Jam

Post by Kevin Thurlow » Mon Nov 30, 2015 12:07 pm

"Was it also obvious that they would play, again, with colours reversed?"

yes. Happily, every time I've had to do that, (although only once through a pairing jam), the players have been quite amenable to the idea.

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