The further back the MRCA is, the more distribution slash inheritance of DNA is a matter of the luck of the draw. I liken it to walking through a room in which your ancestors throw up hands of confetti while you walk through it; you never know which colored bit will stick
For example..
The children from my 2x great-grandfather's official marriage inherited more of his DNA than the ones from his relationship to another woman (my 2x great-grandmother), which resulted i.e. in a 95cM match with a half third cousin v.s. two matches of 51cM & 42cM with two full third cousins.
An interesting fact which I personally think may be related is that my 2x great-grandfather was in his 30's and early 40's when fathering the kids from his marriage, and late 50's when fathering those with my 2x great-grandmother.
So even though the matches with the descendants of the half-siblings have less segments, the cM is higher than that with matches of the full siblings. Seeing how science has already determined that the quality of a man's sperm degrades the older he gets, it makes sense that this translates to the quality slash amount of DNA he passes on to his children as well.
To me, at least, this has become a factor when trying to determine which relationship a match descends from if there's no tree or one with not enough generations showing. And it's usually correct.