Significance of Non-Surname Matches?

[Skilly]

The three current members of my Surname Project have matches of 34/37, 34/37 and 31/37 with each other and 35/37, 34/37 and 31/37 with two members of another Surname Project. Those two members are 37/37 with each other and 36/37 with one other member of that project. In short, our three members in Haplogroup R1b1b2 match as closely with those three members of the other project as we do with each other. They are also Haplogroup R1b1b2. Conventional research verifies that we three are 6th and 7th cousins, but we have only one possible and very remote connection to the other surname that we know of.

What is the likelihood that the six of us share a common ancestor when there are two different surnames involved? Is this pure coincidence or something we should explore further?

Many thanks for any input you might offer.

[~Elizabeth~]

The three current members of my Surname Project have matches of 34/37, 34/37 and 31/37 with each other and 35/37, 34/37 and 31/37 with two members of another Surname Project. Those two members are 37/37 with each other and 36/37 with one other member of that project. In short, our three members in Haplogroup R1b1b2 match as closely with those three members of the other project as we do with each other. They are also Haplogroup R1b1b2. Conventional research verifies that we three are 6th and 7th cousins, but we have only one possible and very remote connection to the other surname that we know of.

What is the likelihood that the six of us share a common ancestor when there are two different surnames involved? Is this pure coincidence or something we should explore further?

Many thanks for any input you might offer.

I have read a post somewhere on the forum that the lady's uncle and brother were off by 2. 65/67, I think. Upgrade to 67 if you can.

[~Elizabeth~]

A 64/67 between a Miller and a Smith is way better than a 34/67 between a Miller and a Miller. And if that matching Smith and Miller don't closely match another of the same surnames, then maybe they will both match another surname like Logan or Brown.