The Birthday Paradox Experiment (2018) | Hacker News Reader

The Birthday Paradox Experiment (2018)

pudding.cool

75 pointsthunderbong70 comments

An analog of the birthday paradox that gets me all the time is what I think of as The Locker Room Paradox. This is where when I go into the locker room after working out and the guy who comes in behind me ends in the locker right next to mine. So there’s two of us in a big empty room awkwardly jostling away.

>awkwardly jostling away

I imagine it’d be more fun in a group setting?

(Apologies for the fun-ruining comment.)

For it to be a true analogue if the birthday paradox, it would have to happen rarely to you individually, but surprisingly often to one pair of people in the locker room when there are a smallish number in there.

Assuming you don't have an automated system to give away locker keys, wouldn't this be explained by the fact that gym front desk is more likely to give out the lowest number available and as you took X, they will give out X+1 for the next person?

I've never been to a gym where you're assigned a locker for the day (or given a key). Either you have one permanently assigned (rare) or you go in and find one that isn't occupied.

Ohh, I see! At my gym, locker keys are given to you by the front desk and you put in something as deposit (such as your gym card or whatever you wish) and on your way out you give the key and you get your deposit back.

But why? Seems like it would be inconvenient to gym-users to add these extra steps to getting in and out of the gym. Especially if you have to wait behind other people just to get or return a key. What is the benefit of such a system?

In the case of my new gym (see my earlier reply above), far as I can tell, they are just saving money on modernization. There are similar other penny-pinching measures there, such as treadmills which apparently offer TV and Netflix, etc., but have no channels, no connectivity and no ability to cast over Bluetooth from your phone.

I asked them about the latter issue, and they said that it might get fixed next year; but there are years-old Google Reviews of the gym citing this promise!

It's a relatively small gym so I assume they don't have the resources to improve the system and quite frankly I too would prefer if they spent the money on more equipment

That's interesting. At every gym I've been to, you either bring your own lock or they have locks where you can set a temporary code.

Sadly, my new gym assigns keys in numerical locker order. The Google Reviews are full of lamentations about it. However, the gym is right next door to my new place, so I am inclined to overlook these and other shortcomings.

Logistically, it makes sense for them, as it presumably cuts down on maintenance and cleaning. But it is super-annoying to squeeze past several other sweaty folk when there are two entire locker corridors empty and adjacent.

There’s also the Aisle at a Show Paradox: as a tall guy, no matter where I stand at a concert I always seem to end up being the guy people decide is the aisle and jostle their way around me when transiting from one area of the venue to the other.

I haven’t tested this hypothesis yet but I suspect I could be wandering the desert and out of no where someone will try to slink past me while saying excuse me and spilling my canteen all over.

I think it is closer to the reason why it is surprisingly difficult to throw a rock through a wire fence even when the rock is much smaller than the holes in the fence. We tend to underestimate the area of interaction between the rock and the fence.

If you take a locker in the middle, there will be 8 lockers right next to yours, which may represent a sizable fraction of the total number. Combine that people are not random and that they tend to forget about the times where it doesn't happen and it may seem like it happens all the time even when it is uncommon on average.

I really like the fact that it's using the previous user birthdays. Unfortunately today is my birthday and I think a lot of people are entering today's date as their birthday, I got 6 matches... :)

Happy birthday :)

Nothing unfortunate about having a birthday today.

Happy Birthday!

Happy birthday to you and me, fellow Scorpio.

Plenty of November birthdays because it's cold in Februrary (11 - 9 = 2).

Also: Valentines Day. I always figure that must have an effect.

I always assumed it was because of Valentine's Day.

I have FOUR significant people in my life with November 15th birthday, so I just groaned when I saw the author’s birthday.

And happy birthday phito :)

Thanks for all your birthday wishes <3

At the end, if you ask for more nerd stuff, it displays a histogram of submitted birthdays. There’s two big outliers: one in November and one in January.

It looks like many people submit January 1 or the current date.

I'm a bit confused. Maybe i did not pay enough attention but... Does it stop the first simulation when there are _any_ 2 people with a same birthday, or when someone has _my_ birthday? I think the latter will take more people on average.

The website is being purposefully obtuse and the birthday paradox is a "paradox" because it's sometimes formulated in the same way as the website. In other words, you are completely correct that the intersection of any two birthdays is significantly more likely than the intersection of a particular birthday.

The Birthday Paradox is about a group of people sharing at least one birthday between them. If it was at least 1 person out of 23 people sharing YOUR birthday then the odds would be 1 - (364/365)^23 which is around 0.06 (or 6% chance). So, yes, this scenario is a lot less likely.

Thanks for that. I believe the fact that it asks for a birthday puts people's brain in a mode where the awe at the end is bigger.

Related, having flat tires on a car seems to come in little bursts,like 10 years none and then 2 in a year.

Can confirm, but both times it was a screw or something in my tire so I presume someone dropped some at a point of my commute.

I'd expect flats on cars to be correlated. People tend to buy tires in sets, so age related factors affect them all. Similarly they tend to get driven on the same roads, so are subjected to similar environmental damage.

Also, people are good at noticing patterns that don't exist, so that's a possibility too.

It's interesting how uniform the birthday distribution at the end looks. I'd expect more seasonality (e.g. more babies conceived in the cold, dark months).

Weird how, coincidentally, 3x as many people are born on Nov 15 as any other day

Nope, Jan 1st has about the same amount. So the lazy liars and those wondering what the dialogue says if they share a birthday with the prompt.

is that US Nov 15th?

Cause I was born in Australia on Nov 14th :-D

Wouldn't that be US Nov 13th?

I wonder if modern living has pretty much made this a non-factor. We have things to entertain ourselves regardless of the duration of light outside and so we're no longer left sitting at home in front of the fire bored, we're sitting at home in front of the fire playing with our phones. Less likely to bow-chicka-bow-wow out of boredom.

Remember that the seasons are inverted on the other side of the equator. (Granted, the population splits something like 90/10 but still.)

There are relatively few people living south enough to have "cold and dark winters," anyway. The northern hemisphere is much more concentrated towards the north.

Most people live above 35°S where, at the most extreme, winter days are about 10 hours and a half long (plus about an hour of decent twilight). Temperatures obviously vary depending on region but they don't really get much below 10°C as far as I know.

So really, it's more like mostly bright and somewhat chilly.

Yes, it's also extremely unlikely.

The actual distribution in developed countries is not uniform: there is a spike at the end of September (because many more people make babies at or around New Year's Eve) and a considerable drop on Dec. 25th (because people will avoid that date and provoque the birth some days before in case it might happen).

Also, on the site there is a huge spike on Nov. 15 which, incidentally, is the birthday of the author: maybe they tested it many times?

Why do people not like having their child be born on Xmas?

It's that some small percentage of births are intentionally induced for various medical reasons. Sometimes because the baby is full term but labor is not starting on its own yet. Other times an OB will attempt to rotate a full term baby that's in breach position to avoid needing a C-section surgery. Successful or not, this rotation procedure has a chance of triggering labor (which is why they wait until the baby is at or close to full term before trying it).

Bottom line: hospitals are short staffed on Xmas so they set scheduled procedures which may induce labor for the day before or the day after whenever possible which preserves their limited capacity on Xmas for unscheduled births and emergencies.

My sister’s birthday is a few days after Christmas. She hated this as a child because once her birthday was over there was almost a whole year without any prezzies

15th november are valentine's babies, I'm not surprised about this spike

Any such spike would be over weeks, not heavily concentrated on one day. It's clearly people taking the quiz twice to see what it says if you match the creators birthday.

> The actual distribution in developed countries is not uniform

This is a nice story I've heard many times, but is it actually true? Like what are your statistical sources here?

US births by day data is available here:

https://github.com/fivethirtyeight/data/tree/master/births

For the period 2000-2014 the number of births by month, divided by the number of days in a month, is:

   1  31   5 072 588     163 631.87   
   2  28   4 725 693     168 774.75   
   3  31   5 172 961     166 869.71   
   4  30   4 960 750     165 358.33   
   5  31   5 195 445     167 595.00   
   6  30   5 163 360     172 112.00   
   7  31   5 450 418     175 819.94   
   8  31   5 540 170     178 715.16   
   9  30   5 399 592     179 986.40   
  10  31   5 302 865     171 060.16   
  11  30   5 008 750     166 958.33   
  12  31   5 194 432     167 562.32   
     365  62 187 024     170 375.41

The difference isn't huge but it's significant. There were on average 180k birth in Sept. vs 165k in April and 170k in December.

Edit: also, here, a graph per day:

https://www.reddit.com/media?url=https%3A%2F%2Fi.redd.it%2Fm...

(The source is mentioned but I did not verify it directly).

The scale on that plot is cut off to emphasise small-ish variations. It is practically uniform.

The point of the plot is to show the drop on Dec. 25th; but the numbers are unrelated to the plot and do show actual variations from month to month.

I was going to try it again with February 29th

I tried it and it just gives the same continuation that talks of a shared birthday.

Okay, that was about as clear as mud to me. Maybe I just need more coffee, but nothing about it led me to understand why there is a 50% chance with 23 people. Can someone else explain this?

The odds that someone else shares just your birthday out of 23 people sounds crazy still. It should be 182.5 to get to 50%, right?

It is not that someone else shares YOUR birthday: it is that two people (among those 23) will have the same birthday.

oooooh, got it. That wasn't clear.

I had a hard time believing the birthday paradox when I first heard about it years ago, so I modeled it with Clojure/Incanter and the results were spot on. Really interesting and fun paradox.

Aren't there birthdays that are more likely than others?

There is one birthday that is far less likely than others, courtesy of leap years. All other are roughly similar, with small seasonal variation.

And no moon cycle related variations, despite a popular (false) belief. It always amazes me that the superstition is spread even among (some, of course not all) midwifes!

Incredible site that also is very mobile friendly!

That would not be a surprise to me :)

Most people access they WEB via the phone, I would expect it is up to 80% browse on their phone.

I was going to say that I was disappointed that the page didn't show the formula for the probability and show how it changes as you change the number of people in the room.

Then I checked the wiki page and understood that some of the maths is actually quite fiendish (for non mathematicians anyway) - https://en.wikipedia.org/wiki/Birthday_problem

Also https://matt.might.net/articles/counting-hash-collisions/

While the math is clear, I'm a bit annoyed by the label "paradox" as the whole setup is too simplistic and reductionistic.

The actual chance of being in the same room with someone who shares your birthday needs to include other factors like your socioeconomic background, the cultural environment you are in, your present location, and certain historical facts.

Without having done the math, I'm fairly certain that a member of the baby boomer generation in New York has a higher chance of meeting their birthday sibling than a 12-year-old in a rural part of Australia.

Wait, what?

Are you saying that income influences what time of the year you are born?

The paradox doesn’t talk about meeting your birthday sibling, but meeting two people who are birthday siblings.

So by the time the 12 year old has met ~20 people, there is a 50/50 chance that amongst those 20, there’s a birthday pair.

> So by the time the 12 year old has met ~20 people, there is a 50/50 chance that amongst those 20, there’s a birthday pair.

If you randomly choose the ~20 people from the global population then yes, this will be the case (especially after a number of rounds). And yes, I'm aware this is also the definition of the paradox.

But if you choose the people from your vicinity (i.e the people you are actually likely to meet), the chances will vary based on your individual parameters (which defines the number and quality of the sample size).

Could you explain more what you mean? Other than certain holidays perhaps causing a higher chance of alone time for future mom and dad, I don’t see what you mean, and I don’t understand your last paragraph.

> While the math is clear, I'm a bit annoyed by the label "paradox" as the whole setup is too simplistic and reductionistic.

https://en.wikipedia.org/wiki/Paradox#Veridical_paradox

(also https://www.youtube.com/watch?v=ppX7Qjbe6BM for a 40min video discussing the weird usages of the word "paradox")

Thanks, I was not aware of this classification. I primarily tend to think of paradoxes as "self-contradictory statements" but you just expanded my definition.

Wait, how is the math clear? There was no math presented on the site, I didn't see a single formula

Took a brief look at the Wikipedia article: https://en.wikipedia.org/wiki/Birthday_problem

(2018)

Scripted.

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