I Win This Birthday Bet Every Other Time

Put 23 people in a room and there's a 50.7% chance two of them share a birthday. It sounds impossible — until you stop counting people and start counting pairs. I also built 10,000 simulated rooms to check the math against reality. 0:00 The 23-person bet 0:35 Why your gut says 6% 1:16 Count pairs, not people 1:54 The math: (364/365)^253 2:46 Testing 10,000 rooms 3:18 How fast the odds climb 4:01 PIN codes and one open question Cake graphic: Twemoji (github.com/jdecked/twemoji), CC BY 4.0. #math #probability #birthdayparadox