The birthday paradox: why 23 people are enough to share a birthday
The birthday paradox: a bet you should take in any room of 23 people
Put 23 people in a room. A year has 365 days, so two people with the same birthday sounds unlikely. Yet it is the better bet. At the 2014 football World Cup, half of the teams of 23 players had two players with the same birthday.
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You are on a bus tour with 22 other travellers, and Rono is the tour guide. At the first hotel, he collects all 23 passports for check-in.
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Each passport shows a date of birth. Rono makes a bet with the group: two of you have the same birthday, the same day and month. The loser pays for the coffee at the next stop.
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You take the bet against him. 23 birthdays in a year of 365 days leave more than 340 days empty. Surely no two of you land on the same day.
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Rono reads the dates one by one. Near the end of the pile, he stops. Miva's passport says 9 June. So does the passport of a man from the back row. Rono wins.
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It was not a long shot. Take many groups of 23 people: in a little more than half of them, two people share a birthday, about 51 times in 100. This surprise is called the birthday paradox.
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Football gave it a real test. At the 2014 World Cup, each team had 23 players. In 16 of the 32 teams, two players shared a birthday. That is half of the teams, as the math says.
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You pay for the coffee. Then you take the pile and look for your own birthday, 2 October. With 22 other people, you feel sure that someone has it too.
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Go further
A word, and a day left out.