That's the classical birthday "paradox" but that's not what happened here.

Here, a random person in the room announced their birthday, and the question is whether someone else in the room shares that birthday. It's a very different situation, where I'm guessing you need around a thousand people for it to be very likely that their birthdays coincide, compared to the twenty or so for the birthday paradox.

Sure, but in this case it was a case of me not knowing one could check their Smile balance. GP posted their balance, prompting me to check mine, and the total was the same. That feels more akin to me going into a room and the first person I talk to having the same birthday as me than just finding 2 people in a room who happen to have the same birthday.