One in 365 not factoring in variables such as when people tend to screw the most, leap years, etc.

I am not a math guy but I would say it is highly likely probable but not 100% guarantee by any means. That is where I imagine that whole "Chaos Theory" begins to apply.

ETA: Just to clarify my train of thought as I was a few beers deep last night.
In a room of 367 people there is a 100% chance two will have the same birthday. It is impossible to not to.
However in a room of 367 people it is very possible you would have someone not have the same birthday as you but would with another person in the room. I assume the calculation would begin with 365.25*365.25 and go from there. Again not a math guy here.

Has to be factored in. Many baby booms after power outages and drunken holidays. One cycle made the news back when.

To the chaos side I would include war, famine, plagues, real pandemics, weather events, natural disasters, flu and disease seasons, etc.

This doesn’t not meet your original criteria exactly, but (ignoring baby booms) there is a statistical probability of greater than 50% that in a group of 23 people, 2 of them share a birthday. Wikipedia can explain the math in detail, it’s an actual studied problem in statistics: Birthday Problem

As I recall, rather than figuring out the chance of 2 people in a group sharing a birthday, you calculate the chance that no one in the group shares a birthday and then take the inverse of that.

Again, not exactly what you asked, but it might provide a framework to solve what you want.

Calculator

If your group size is 50 people the chances of two sharing the same birthday is about 97%

ETA in a group of 25 people there’s a 57% chance 3 of them share a birthday.

I shared a birthday with a girl in my elementary school class.

When I attended "kindergarten" I was one of 3 w/ the same birthday. Unfortunately can't recall class size.

Google "birthday problem" if you really want to go down a probability rabbit hole.

Here's the money shot... At around 60 people, you're getting pretty close to 100%.

You're already over 50% probability at only 23 people.

Attached File

In what population size?

In a room of 400 people, there is 100% chance some have the same birth days.  If you include the year, that's a different calculation.

My girlfriend that I dated, prior to meeting my wife, has the same birthdate as my wife, just a yr apart.

First part, yes, second part no.  The chance that NO ONE out of 365.25 people had the same birthday as you would be (364.25/365.25)^364.25.  That is to say, each person has a 364.25/365.25 chance of NOT sharing your birthday, and you multiply that chance as many times as you have people to see the chance that they do not have your birthday.  The chance that at least one other person has your birthday is then 1 - that chance.

There is about a 37% chance that none of them will share your birthday, or 63% that one or more people do share it.  This is because many of them will share birthdays with each other, so about 134 days of the year would be expected to have no person with a birthday on it.

Mike

ETA:  This calculation was to show the chance of a person sharing a birthday with YOU, because apparently I can't read a question.  Others have covered probability of whether there are ANY matching birthdays, though not how that is calculated.

So, to figure out if ANY birthdays overlap (though not how many), we can do a similar set of math.

We start with a group of zero people, and start adding people to see if they have the same birthday as anyone already in the group.

The first person obviously doesn't match anyone in the group, since there aren't any.  So his chance of NOT matching anyone is 1, and there are now 364.25 out of 365.25 days left.
The second person now has a chance of NOT matching the previous person of 364.25/365.25, and there are now 363.25 days left.
If no one has a matching birthday, then after N people are added there will be 365.25-N days available.

So you end up with an equation where you have (365.25/365.25)*(364.25/365.25)*(363.25/365.25)*.....*((365.25-(N-1))/365.25)  for N people, where N is 2 or more

And this gives you the chance that you have no matching birthdays.  Since we used a non-integer number of days to account for leap year, the chance will never show up as exactly zero, but will instead become negative when you reach 367 people.  In this case, a negative chance means zero chance.

We had about 50 people come through the range yesterday. One of them had the same birthday as me.

My youngest son and his wife have the same birthday.

The girl I dated in high school had the same birthday as me.

Oops, this was already answered above. Still if you want more details on this sort of statistics, look up the binomial distribution, that covers N trials (number of people you meet) with p chance of success (chance they share your birthday).

Briefly dated a girl that was born the day before me.  Growing up, my sister's friend that lived behind us was born the day before my sister in the same hospital.