This paradox also helps illustrate the bitcoin difficulty.
If enough hash attempts are in the room, one will show up that is above the difficulty. Even though there’s 2^256 possibilities (an impossibly high amount) the birthday paradox explains that only a relatively small amount of total hashes are needed before we find “collisions.” And in this case, because the difficulty is a threshold, there are many possible hash collisions.
Reading this I understood why the probability increases so dramatically. If you've got n people, adding a person actually adds n chances of their birthday repeating.
An examination of the histogram shows significant seasonal variations. The months July - October show higher than expected births and March - May show the most significant decline in births. Perhaps the most reasonable explanation is that conceptions are up in the months of October through January and down in June through August. You be the judge.
The implications for the original questions are that slightly fewer persons are needed to get a single match and slightly more persons are needed to have every day covered if the distribution is not uniform.
npeople, adding a person actually addsnchances of their birthday repeating.