birthday_cake_candles_tPsychologists and statisticians often illustrate people’s poor grasp of probability by asking….How many people do you need in a room to have a 50% chance of any two of them sharing the same birthday?

According to the laws of probability the answer is surprisingly small, but is it correct? Let’s put this world famous problem to the test…..

According to the maths, you only need 23 people in a room to get a 50% chance of any two of them sharing a birthday. Squash 57 of them in the same room and the probability of a match apparently rockets to about 99% (for the theory, see here).

Let’s put this theory to the test….

First – if you are reading this, please join in, otherwise the numbers get all screwy.

Second, here is my birthday….17 September (no need for a big present, a card containing money will do)…..

Third, if the first person to read this also happens to be born on the 17 September then they should add a comment saying ‘Match! (17ย  September)’. However, if they are born on another day they should simply write their birthday (e.g., 12th March). There is no need to add the year you were born.

Fourth, the next person then looks at the two dates (17ย  September and 12 March) and, again, if they are born on one of these two dates (e.g., 12 March), writes ‘Match! (12 March)‘. If not, they add their birthday to the list.

And so it goes on…..if ANY of the dates already listed matches your birthday then you write ‘Match!’ and say which date it is. Otherwise you add your birthday to the list.

According to the theory, we have a 50% chance of a match with just 23 people and a 99% chance with 57. But will our experiment support the theory?

OK, step forward and share your birthday (and encourage your friends to do the same – we need lots of people for this to work)…..everyone have just one go and no lying!

340 comments

  1. 18 December (and for what it is worth, the 21st person has the greatest chance of being the first one to say “Match”. It does indeed take 23, though, to have a greater than 50% chance of at least one match.)

  2. match October 18 (interestingly enough I was on a retreat weekend a few years ago with about 55 other people and there were four of us all with October 18 birthdays)

  3. 8 April. I had a classmate through grades 1-9 that shared my birthday.

    The regular probabilistic answer depends on the assumption that birthdays are distributed evenly across the year. In reality, they aren’t, which in fact suggests you should need even fewer people to find a match.

  4. 29th November

    No matches on here yet, but there were 3 of us at one point in an office of about 40.

    The theory assumes an equal distribution of birth dates, which I doubt would actually be the case (I would guess dates like last Saturday’s would result in higher number of conceptions), which should therefore make the match more likely

  5. 24th May

    From Junior infants to 6th Class (5 to 12 years old) there was one girl in my class of 5 who shared my birthday ๐Ÿ™‚

  6. So now we know the birthdays of a bunch of readers of this site. A few people happened to give their age as well, but we could get more by running a perception experiment which proposes that people’s age will affect how they see it and asking for ages in the comments.

    Perhaps something similar claiming to be looking for a correlation with where people were born could get us a list of readers’ home towns.

    Then you just need one of those ‘what’s your porn star name’-type quizzes which features mother’s maiden name as a component, and we should have enough information to break into a few bank accounts …

  7. Match — 12 August.
    There’s an anecdote of a statistician trying this game out on a corporate board meeting and being dismayed at getting no matches — until the unnoticed tea lady suddenly spoke up and said she shared the birth date of one of the big wigs.

  8. “I know twins who share the same birthday. What are the chances of thatโ€ฝโ€ฝโ€ฝโ€ฝ”

    I know twins who don’t share the same birthday because one was born in the last minutes of the day and the other minutes later on the next day.

  9. Match – March 19th and first name,
    but surely there should be more matches in
    July, August, and Sept. than any other months
    as in the northern hemisphere, births cluster
    around August in a bell curve pattern.

    The fact that both my match and I posted
    rather late would tend to confirm this.

  10. Have commented before so no birthdate here. Asked around and found in my son’s class of 29 there are 3 pairs of birthdays and in my daughter’s class of 25 there is one pair.

  11. 17th May

    No match here yet, but in my last job working in an office of just four people one of my colleagues shared my birthday.

  12. I already posted, so I’m not going to add my date another time.

    Just a question: isn’t this little game a little flawed when we do it on a blog instead of a room? What would the chances be of somebody adding a MATCH (they found something in common with another reader and might be more likely to post) compared to the chances of adding a new date?

    And how would multiple matches for the same date influence your chance of adding another MATCH for that date?

  13. I already posted once with my date but I wanted to add that I personally know of 6 people with my birthday of October 18 in my town. Also my brother was dating a girl, when he was at college in another city, with the exact same birthday as me down to the year. She was a couple hours older than me.

    I agree with the previous post about how the assumption of birthdays being spread out evenly among the year is not quite true. In my primary school class of 53 there were 9 students with birthdays starting at October 15 and ending at October 26 even though the actual dates were from two separate years.

  14. 30th june – hardly anyone in june ๐Ÿ˜ฅ – however in my first year at uni, when i lived in halls, i shared my flat with someone who had the same birthday, including the year!

  15. 4th January.

    (some people have not said match, even if their bday has already popped up. For example, JeffY, 1st jan has already been said.)

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