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How to pick a random number from 1-10

torvaney.github.io

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Re: How to pick a random number from 1-10

#101

Post by mongol »

jancsika wrote: post #31
FabHK wrote: post #19

Earlier quoted context omitted.

That works and is perfectly uniform (if the people are i.i.d.), but requires quizzing around 20, 40, 60 or more people for a number before you can deliver one, while the algorithm described only requires one or two. EDIT: Not quite that many, more like around 9, 18, 27 or so, see below.

I'm not sure I understand. Humans aren't like weighted dice. For example, it's certainly conceivable that a few pairs of these humans misunderstand the goal such that they have a 0% chance of ever choosing numbers that change the respective ordering. Add to that the higher probability that many of these pairs of humans will just toggle their orders each round. Edit: clarification-- the humans don't even have to misun…

Maybe you don't even need to ask them to think of a number. The person whose name is sorted before the other person's name is person 1. And they compare their lengths instead of thinking of a number?

Re: How to pick a random number from 1-10

#102

Post by eridius »

codetrotter wrote: post #56

> The easy thing to do is to ask someone “Hey, pick a random number from 1 to 10!”. The person replies “7!”. Seven factorial is way bigger than 10. Just kidding, sorry. But what I was actually going to say was, when I read the title of the post, before clicking through, I decided to think of a number myself and I chose the number seven. So it was fun to see that same number in the article. 10% chance in theory and in…

AIUI 3 is the most common if you ask someone to pick between 1 and 5.

I was actually surprised to see 3 wasn't the second-most-common for a number from 1 to 10.

Re: How to pick a random number from 1-10

#104

Post by leethargo »

oarabbus_ wrote: post #69

Am I missing something, or is this a textbook case of overfitting? It's a neat project, but at the bottom he prescribes what to do if the person says 1-3, or if they say 4 or 5, etc. Therefore, it's completely overfit to the Reddit data at the top.

The model could be extended by adding a penalty term to the objective. I guess the penalty would need to be nonlinear, as the current objective already minimizes the x_ij (for i != j) implictly? One could also introduce a fixed-cost offset for any nonzero redistribution amount, but that would change the problem type from linear program (LP) to mixed-integer program (MIP).

Re: How to pick a random number from 1-10

#105

Post by another-dave »

codetrotter wrote: post #56

> The easy thing to do is to ask someone “Hey, pick a random number from 1 to 10!”. The person replies “7!”. Seven factorial is way bigger than 10. Just kidding, sorry. But what I was actually going to say was, when I read the title of the post, before clicking through, I decided to think of a number myself and I chose the number seven. So it was fun to see that same number in the article. 10% chance in theory and in…

From the Reddit comments someone wrote:

"Can't have the evens, they aren't random. 1 and 9 are too close to the outside. 5 isn't random, it's right in the middle! 3 is too low. Leaving 7"

It does feel like the type of biased logic that would run through your mind in the moment — interesting to think, if we have such 'fallacies' on simple stuff, what level of blindspots do we have on more complex split-second decisions.

Re: How to pick a random number from 1-10

#106

Post by gmac »

jldugger wrote: post #64
rland wrote: post #41

I actually laughed out loud when I saw the image of the human RNG distributions. 7 is a random number. Who knew?

I feel like you could probably 'fix' it by the following protocol: 1. Ask your participant to write down a random number. 2. After they've written that number down, inform them you will guess at their number, and give them a dollar if you guess wrong. 3. Ask if they'd like to change their random number. 4. Allow them to write down their new number. The before/after would probably change the distribution, and pretty m…

I'm sure the distribution would change, but not sure it would be closer to uniform. It's now a completely different problem: choose a number most resistant to guessing. For example, if the participant hypothesises that your guess will be a "random" number chosen by you, she should always pick 10.

Re: How to pick a random number from 1-10

#107

Post by corysama »

moksly wrote: post #95
corysama wrote: post #21

Earlier quoted context omitted.

In the US TI has established a multi-decade monopoly in schools. Basically, the teachers are only familiar with specifically them, so they require student only use them, so new teachers are only familiar with them. As a result, a new TI-85 equivalent is only trivially upgraded from what I used 25 years ago and costs exactly as much minus inflation.

Wow, why aren’t students using laptops?

In college some students use laptops for taking notes. Not so much in high school. But in both during tests, electronics are strictly regulated to prevent cheating. Teachers know how to factory reset TI calculators. So, they and only they are allowed. Also, teachers know how to instruct how to use TI calculators. So, they are sometimes even required for certain classes.

Re: How to pick a random number from 1-10

#108

Post by testplzignore »

stOneskull wrote: post #70

How about 1 person labels 10 people 1 thru 10 and another person not knowing how they're labeled chooses 1 of those people edit: the first person labels the 10 in a jumbled up way, then the 10 people not knowing how they are labeled then jumble themselves up

This seems like it could work pretty well. It would be interesting to try it out.

I see two possible sources of bias:

1. The way in which a person labels the others won't be random. And multiple people may exhibit the same pattern. For example, let's say that people are biased towards trying to label an "average" person as #1. This might be based on height, weight, attractiveness, etc. Then a given person may have an uneven distribution of labels attached to them. Further compounding this could be that the most "average" person is the one most likely to be chosen by the second person.

2. You would need to come up with a random way to pair up the first and second person. The worst case might be that the same two people are always paired with each other, and each person always chooses the same person in the room. Then you would end up with a series of 10 digits repeating themselves.

Re: How to pick a random number from 1-10

#110

Post by mrpdaemon »

Tagbert wrote: post #62
lerax wrote: post #54

Earlier quoted context omitted.

Very easy to predict.

how so? if you ask me for a number from 1-10 and I use my watch, how do you have any predictive information? Even if you looked at your watch there is no reason it should have the same seconds value as mine. Obviously this is not really something you could automate and if you were to use a clock on an ongoing basis you might be able to predict likely numbers, but that was not in the original scenario.

Ah but there is a reason for my watch to have the same seconds value as yours, and that is if our watches are kept synchronized to an accurate time source, for ex. via NTP. By assuming otherwise you're sidestepping the problem by claiming you already have a reliable RNG.

Heck, even granted you have an unsynchronized watch, your "random" numbers are easy to predict, I'll ask you for a random number once per second and after a few answers I don't need to ask any more to know your answer.

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