It is my theory that most (if not all) people of European descent can trace their lineage to some form of royalty.
Since every generation doubles the number of grandparents, if we go back 20 generations, that makes 1,048,576 potential grandparents at that level alone, with the number doubling every generation.
It typically takes 30-35 generations to get back to A.D. 1000. At 30 generations, you could have 1,073,741,824 potential grandparents!!
At this level, there are very often combined lines, which reduces the number of grandparents at each level. Still, estimates place the number of people living in Europe in A.D. 1000 at about 56 million. This makes it very likely that at least one of your ancestors was royalty.
Who Do You Think You Are Magazine posted an article about this, a portion of which is quoted below:
The power of the mathematics of genealogy is vastly underrated. From just a few royal bed hoppers who lived many hundreds of years ago there are estimated to be millions of descendants walking amongst us today.
The 13 monarchs who reigned between 1066 and 1485 fathered at least 40 bastards between them. Henry II leads the field with around 20. Descendants of Edward III, legitimate or otherwise, are believed to be in excess of 4 millions. Some experts believe that practically everyone alive with British ancestry will have a connection with this king.
So statistically, there is a good chance that you are descended from royalty. This may not be from the direct, legitimate line so you may be at some remove from the throne.
So did National Geographic:
The most recent common ancestor of every European today (except for recent immigrants to the Continent) was someone who lived in Europe in the surprisingly recent past—only about 600 years ago. In other words, all Europeans alive today have among their ancestors the same man or woman who lived around 1400. Before that date, according to Chang’s model, the number of ancestors common to all Europeans today increased, until, about a thousand years ago, a peculiar situation prevailed: 20 percent of the adult Europeans alive in 1000 would turn out to be the ancestors of no one living today (that is, they had no children or all their descendants eventually died childless); each of the remaining 80 percent would turn out to be a direct ancestor of every European living today.