Thinking about ancestors

There was an archer serving with Henry V at the battle of Agincourt in 1415 named John O'Daly. Was he an ancestor of mine? Perhaps.

I suppose that there were about 20 generations between the battle and today. That means I have a potential of 2 to the 20th ancestors in 1415 -- something just over one million. Of course, the actual number of ancestors is much less as surely there were second, third, fourth up to 19th cousins marrying during that history.

Incidentally, while my father was an Irish Daly, my mother was English, and I am at least as likely to have English ancestors among the 6000 British at the battle as Agincourt as Irish, even though I have a direct namesake that I know was at the battle.

One can only guess at the number of O'Dalys in 1415. The name is supposed to date from the 13th century, so the number should be fairly small, and indeed they should all be fairly closely related. Thus it seems quite likely that I have a direct connection to someone at Agincourt through the male line.

The number of English in 1400 has been estimated as three to four million. If we assume that I had 5000 distinct male English ancestors alive in 1415, that there were 6000 English at Agincourt, and that there were 2 million male English, then the probability that I had at least one English ancestor in the battle is 0.99945 -- almost a certainty. I guess the direct Daly connection is not that impressive after all.