In a group of 23, the odds of two people having the same birthday is roughly 50/50. In a group of 70, there's a 99.9% chance. The maths behind it is explained quite clearly here :
https://betterexplained.com/articles/understanding-the-birthday-paradox/
If you want brainhurty maths, try the Wikipedia page, which goes into far more detail than is decent in polite society.
https://en.wikipedia.org/wiki/Birthday_problem
That reminds me of another birthday one.
Son 4 - not christened but on his birth certificate, his first name was just the 3 letter contraction of a fairly common name. He was never, unlike his school,mates (and most classes he's been in had 2 or 3 boys with the same forename) used the long version of the name. His surname is my maiden name although his birth dad had a fancy Italian surname. Son prefers mine. His bday is a day in September.
Doing family history - years after naming son - I discovered son and I have a direct line ancestor. VERY unusally for the times (around 1810) he was actually baptised not with the long form of the name but with the short, informal form. (Baptists not C of E so I guess shortened names were allowed). I have read thousands and thousands of parish records and never, once, seen anyone else christened with the name in its short form, in the 19thC. Not once. Only my grt x 4 or whatever it is, grandad.
It gets better. He was my dad's paternal line ancestor so the surname is the same as my son's.
Better still... it is an unusually full birth record. Most from that date give just date of christening/baptism but this one also gave birthdate. Same birthday as my son.
Very weird. Although the odds would be higher you'd share a name with an ancestor - presumably not so high when my son 'should' have had his dad's surname, and also the unusual short form of the first name given as a birth name. Bday too. My brother gave me a photo of our grandad - in this same line of the family - the other day. Grandad would be about 17 in photo. Son is now 19. And everyone noticed for the first time how much son resembles my dad's dad. Strangely, we never noticed before. Weird to think he might be a carbon copy of this man born nearly 200 years before him on the same day of the year with the same 'nickname as name'.
Not sure if I posted it before, but doing genealogy I found another one.
I got into family history in the 1980s when we traced this same branch of my family. We were always told the surname we had was 'made up' - that my dad's grandad on this paternal line was a foundling from an orphanage and randomly took this surname when he was 19. My great grandma never met his family and assumed it was true. When she realised, years after marrying, that the surname she used might not be 'real' she even went to a solicitor to check she was legally married.
Sure enough when we started to do family history - to try and put all the rumours to rest and find out who were really were - there was no-one born at the right time or several years either side, in Leeds, with the same name as my great grandad used in adulthood. Simply not there. So he was impossible to trace. I started doing genealogy in the 1980s when I lived in Birmingham.
Over years we tracked down Leeds orphanages etc and tried to find records. No luck. We gave up on it - thinking we'd never know our real name. Then in 2011, the 1911 census was released. A 'family friend' of my great grandad - we looked her up on the census. She was suppsoed to be his closest friend who knew all his secrets. It was the first census she was on and the first time we could do this. Her middle name was our surname. She wasn't just a friend, but his cousin. I traced her mother and all her siblings sure enough - there we were. The surname we'd been told all our lives was made up was in fact our real surname. But great grandad's dad died when he was a 3 year old and his mum remarried - a Brummie chainmaker. Not many of them in Leeds in the 1870s! And my great grandad had been invisble in the censuses because he grew up with stepdad's surname. Aged 19 he did change his name - back to his real one. He was a notorious conman and told stories all his life.
Turned out he lived streets away, when he was a young married man, to his mum and stepdad. Great grandad's wife and family, including my grandad, didn't even know these people existed. The story about being dumped as a newborn at an orphanage was a total fiction but 3 generations believed it.
The coincidence? I traced Brummie chainmaker. He was born in the exact place where I lived for 9 years. The chainmaker's cottage he was born in had been demolished in the 19thC and replaced by the little terrace where we lived. We lived in the end house. My step great great grandad was born, according to the census - in the end cottage. I had lived for 9 years on the precise site where my step grt grt grandad was born - counties away and in a city of over 1 million people. It was where we'd lived when we started trying to find out who we were. And we were challenged for most of those years by the fact my great grandad had taken the name of this very man and that was why we couldn't trace him.