I don't need to go on the internet.
There are loads of chances for at least 1 chromosome from Edward I or whoever from 800 years ago to be passed down to people who are alive nowadays.
This is Adam Rutherford on the tests and royalty
DNA ancestry tests may look cheap. But your data is the price | Adam Rutherford | The Guardian
"In short: if you really want to spend your cash to discover that you are descended from Vikings (spoiler: if you have European ancestry, you are) or you have blue eyes (try a mirror), go ahead"
So you’re related to Charlemagne? You and every other living European… | Adam Rutherford | The Guardian
And this also makes it more interesting -
"Each subsequent generation, the contribution from an individual from your lineage becomes less. Professor Mark Thomas from University College London describes this dilution as “homeopathic”. After a few rounds of preparation, homeopathic dilutions contain no molecules of whatever the active ingredient is imagined to be. Genetic inheritance works in a similar way. Half of your genome comes from your mother and half from your father, a quarter from each of your grandparents. But because of the way the DNA deck is shuffled every time a sperm or egg is made, it doesn’t keep halving perfectly as you meander up through your family tree. If you’re fully outbred (which you aren’t), you should have 256 great-great-great-great-great-great-grandparents. But their genetic contribution to you is not equal. Before long, you will find ancestors from whom you bear no DNA. They are your family, your blood, but their genes have been diluted out of your bloodline. Even though you are directly descended from Charlemagne, you may well carry none of his DNA."
They are your family. Your blood. But their genes have been diluted.
But you can still trace them as an ancestor as a direct descendant
And some more science
Most Europeans share recent ancestors | Nature
Whether they are a Serb and a Swiss, or a Finn and a Frenchman, any two Europeans are likely to have many common ancestors who lived around 1,000 years ago. A genomic survey of 2,257 people from 40 populations finds that people of European ancestry are more closely related to one another than previously thought, and could help to bring about new insights into European history.