Hacker News Reader

Comment by DeathArrow | Hacker News Reader

Why are people bad at coming up with random numbers?

I had a math teacher who trolled the entire class.

We (the class) wanted to go outside instead of having a regular lecture. He made a deal that if we win his game we go outside, otherwise we had to be extra focused for the rest of the period.

Everyone in the class had to pick a random number between 1 and 100 and write it down. He told us that he would get one guess for each pupil (around 30) and if he managed to guess all numbers he would win. If any number was left we go outside.

Knowing how bad humans (and especially 12 year olds) are at picking random numbers, and knowing which numbers were mostly picked, he guessed all numbers with still a handful of guesses left.

If he had done it enough times with different kids in the past, he would have the perfect data to know the likelihood of certain numbers picked and him winning.

That from a teacher's perspective seems like a fascinating idea to try out.

Those odds are 4 quadrillion to one, if the numbers are picked randomly.

I think it's much better because the teacher doesn't have to match guesses to students. For example, for each student the odds are 30/100, roughly one in three. And any duplicates can be matched by a single guess.

I think odds should be 0.3 to the power of the amount of students.

E.g. teacher picking 1-30 and then each student has 0.3 odds of picking 1-30 or 31-100.

The issue is I think all it would take to beat the teacher is one unusual student.

That formula is missing something because for over 100 students the teacher can't lose. (they get over 100 guesses and there are only 100 numbers possible)

If the teacher does have 100 guesses then they wouldn't lose right.

Then it would be 1 to the power of 100.

I guess I should've clarified that the 0.3 refers to being able to choose 30 out of 100 numbers?

More precisely, if there are N students, the probability is (min(N,100)/100)^N. This is 1 for N ≥ 100. And the probability at N=30 is indeed a tiny 2e-16, which shows that the children's "random" picks were far from uniformly random.

(Incidentally, even with N=99 the probability is 0.37 ≈ 1/e, and the probability is lowest at N=37 ≈ 100/e. This is not a coincidence.)

Reverse it, and it becomes clear.

The teacher picks 30 numbers out of 100. Then each student (independently) picks one number. If random, that is 0.3 ^ 30. Obviously, the students are not picking random.

If I had to pick for the teacher:

multiples of 10: 10,20,30,40,50,60,70,80,90

double digits: 11,22,33,44,55,66,77,88,99

Not sure where to go next.

3 and 7 are most common digits people come up with with a random number 1-10

i would pick a 3-7, 30-37, 70-77, then some other fews from there like 1, 100, 50 etc

This sounds like a great teacher. The fact that you got this gem to think about years (decades?) later tells so much about his craft.

2 decades now. He was the best teacher I had. Sadly only for 2 years as he came temporarily out of retirement when our math teacher at the time died.

Mathematical randomness is not exactly a skill required for survival. In fact, our ability to produce random numbers is so bad that our brains consider true randomness to not be random, as this blog post from Spotify shows: https://engineering.atspotify.com/2014/02/how-to-shuffle-son...

Doesn't Spotify basically need to pay nonrandom royalties on stuff inside any given playlist such that streaming some content costs them more than others, while the users payment is constant? If that is true it defies belief that they would avoid cost optimization on their side and give users a truly random shuffle. Especially if they can argue that users don't know randomness when they see it

I'm not sure that has anything to with the algorithm described in the blog post. I posted it because it's a popular, often-referenced example for this type of problem. The problem exists outside of Spotify, in any music player. And I believe that back when this was written, Spotify was paying the same amount of money for all streams, as it was way before the whole problem with people streaming white noise to launder money arose that they currently try to combat by essentially not paying artists with little exposure at all.

Spotify's shuffle is hilariously bad though (to the point that there exist outside tools to pre-shuffle your playlists). I see that article more as an "excuse" for their bad engineering.

I'm sure there are people who will get angry if they get two songs in a row from the same artist on a "random" playlist, but I'll much rather have that than the pseudo-random Spotify nonsense that will only play similar tracks next to each other or just ignore 90% of the playlist.

We're bad at generating randomness because we're bad at detecting randomness.

Given a sequence, and asked to grade how closely it fits sampling from uniform random, we typically get it very wrong.

For example we underestimate how often streaks or clustering happens in uniform data.

We are wired to find patterns. This gives us an advantage for some tasks, but for assessing the randomness of data, makes us very bad.

Reminds me of a rather lively IRC debate I had on a programming channel about how 1,2,3,4,5 was a perfectly fine random sequence of digits. Some just flat out refused to accept that, even though I repeatedly highlighted that it was just very unlikely.

As always there’s a relevant xkcd: https://xkcd.com/221/

At Pomona College, there’s a bit of folklore around a talk a math professor gave in which he “proved” that all numbers are equal to 47.¹ Consequently, students started noticing 47 everywhere since psychologically, it’s a popular number to choose as a “random” number between 1 and 100,² although some of the coincidences (the number of trees on the quad, the exit number on the 10 to get to Claremont) don’t fit into that schema.

⸻

1. Spoiler: there was a divide by zero in his proof.

2. Why? Because it’s near the middle of the interval and is prime, two things that will happen if you unthinkingly just grab for a number.

https://memory-alpha.fandom.com/wiki/47

> The number 47 makes frequent recurrences in dialogues and on computer screens in Star Trek.

> The origin of the significance of 47 can be traced to Star Trek: The Next Generation and Star Trek: Voyager writer Joe Menosky, who attended Pomona College in California. There is a club at Pomona called The 47 Society, which claims that there exists a mathematical proof that all numbers are equal to 47.

> Joe Menosky first started including references to 47 in his scripts in the fourth season of TNG, and the in-joke quickly caught on among the rest of the staff. Since then, references to 47 have been included in many episodes and movies of all the modern series.”

Reply on news.ycombinator.com