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With any DNA match I like to key in the cM value into DNA Painter are look at the percentage probabilities.

Among them for the 338cM are 1/2 1C or 1C1R both @ 49%
OR
2C or 1/2 1C1R or 1C2R both @ 46%

So these give a good idea of where the link occurs which is probably at or since Great Grandparent level.

As a rough guide, my 100cM ish matches tend to by 3C.

Beyond that, below 50cM they can be anywhere from 4C to 7C, its so imprecise and hence needle in haystack.

Also if the families concerned are from a close community then there can easily be Cousins marrying Cousins, so what I term Cross Pollination between the tree branches can very easily have occurred which in tern will screw with any assumptions.  ie In one tree I made for a family friend I found that one Grandparent pair were 2C to each other.

DNA division is not necessarily equal, so do bear this in mind in assumption made.

You could always create a family tree to put into DNA Painters WATO tool to see the hypothesis that it suggests.

Guy wrote:-

I would also suggest creating quick and dirty trees, i.e. using sources like online trees to build an unchecked data set to provide names to matches. (it goes without saying that any such use requires extra research later to prove the assumptions being made in the quick and dirty tree but it can be helpful if care is used).
As you keep triangulating and discounting maternal matches you will also build a dataset of possible paternal matches and by elimination will eventually produce pointers to the paternal lineage.
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We must work in a very similar manner for this is what I also do.

Rather than clutter up my main tree with Floating Branches or unattached DNA matches and their family, I start a new tree.

ie
Surname of Match 01, I put them in and their parents and grandparents if known and rather than expand it I copy it and rename it as Surname of Match 02.

I then work on expanding the tree but if it turns out to be a brick wall I leave it, go back to the basic 01 tree, copy it again but this time name it as 03.

Then I continue as usual but hoping I am on the right track, repeating the starting over copy and rename as necessary. 

If I get it right I Tree Share the DNA matches tree with Roots Magic, then import the matches tree into my Main tree in Roots Magic and then Tree Share back to my Main tree in Ancestry.

BTW
I avoid using Thrulines, but do use Common Ancestors provided I work through each person in the suggestion line by line verifying each with the usual supporting references.

My nemesis is the Belcher’s I have a standalone tree of them with about 600 people all originating from John Belcher and Ellen McMahon both born about 1780.

Many of their offspring emigrated to Bradford where one of their sons John b1834 in Louth married Mary Ann Gargin (also born in Ireland).

I have 12 DNA matches that I have linked into the tree and to each other, only one has Belcher as their birth surname.

There are many other DNA matches that are shared with those already in the tree and hence it is still very much a work in progress.

Gurney, Bottomley, Padgett, Gilmartin, Grace, Jordan and Rawcliffe are some of the family names that link back to the Belcher line.

My mystery is that I have two high DNA matches that link back to the Belcher family and so far my attempts to find how I fit have come up short.

I have even loaded the Tree into the WATO tool in DNA Painter but the various hypothesis do not work when other proven DNA matches are taken into consideration.

So I am seeking anyone who is also researching the Belcher’s of Bradford and their descendants.

Please PM me if you have information about any living person, otherwise feel free to post.

At the lowest 4% probability that is a 3C at Great Great Grandparent level.

Do you have as wide a tree as possible at this level?

Including all offspring and brining each of them as far forward to present day as you can?

I have a 240cM match and my nearest fit is a NPE that produced my Great Grandmother.

A tree based upon the match which has a few others who are Shared does give the right relationships and DNA Painter’s WATO tool works well with my own hypothesis.

Conversely I have a 96cM match that is shared with other matches in my tree to my maternal Grandmothers side of the family and none have the match in their trees and despite building four different trees on the likely candidates no link has yet been found so I too am at the stage that in his past an NPE occurred and one if his forebears was secretly adopted.

So just stick at it, build a few standalone trees each based on likely candidates and wait to see what hints come in.

It may be a long shot but do upload your DNA data to the comparison sites on the chance that they to have done this and with the tools available on them it could be possible to narrow the options.