Sizu Riatto
Chance Didn’t Have to Be This Hard · Chapter 6

Birthday Problem

Matches are common because a group holds many pairs: 23 people make 253 of them. Works for any number of equally likely values, not just birthdays.

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From the book, Chapter 6. A class of 30: 70.6% chance two share a birthday; with 23 it’s 50.7%, with 50 97%. Someone sharing one given person’s birthday is only 7.6% in a class of 30. Within a day of each other, 14 people are enough (53.7%). For four-digit PINs, 119 people give an even chance of a match; for 6-from-49 lottery tickets, 4,404.

Assumes every value is equally likely and people are independent. Real birthdays are a little uneven, which makes matches slightly more likely. “Within a day” treats the year as a circle, so 31 December is next to 1 January. Everything stays in your browser: no sign-up, nothing stored or sent.