Results for: Pick a number from 1 to 10 | Hacker News Reader

Results for: Pick a number from 1 to 10

nfrom1to10.appspot.com

148 pointssolipsist67 comments

I just updated the results page with a breakdown per-interface. There are more metrics involved, but it'll be a little while before those get pulled together. (The volume of data was unexpected, to say the least, so there weren't any stats helpers in place prior to "launch".)

As for "revealing" the answers ahead of time, the whole question of "Pick a number from 1 to 10" and the common result being 7 is well known (ish), so I'm not too worried. Plus, the results aren't visible until you choose. PLUS, there were over 80k votes before that first graph was available, and over 140k by the time I put the per-interface breakdown up.

Hopefully, the volume will outweigh the people who try to manipulate it. (There's also IP tracking, which will eventually be used to help filter out anomalies, in addition to geolocating.)

I know, it's not exactly precise science, but it's a fun experiment that was simple and kept the friction to a minimum. I'm not exactly trying to write a paper. :)

Thanks to everyone who voted and spread the word, especially jedberg who posted it to Reddit.

Can you do it again for 1 to 100? I'd like to improve my success probability for this http://xkcd.com/628/

Just make her pick a number between 1 and 10, you'll have at least 10 times more success probability.

And it will be 10 times less impressive.

So clearly we should have her pick a number between 1 and 1000!

I guess 42 will be a spike in the results - but it would be interesting to verify ;)

Are you implying than the average HNer or Redditer has a different bias wrt the average girl?

43 is actually not bad. I would think that most people would pick something somewhere in the middle. A somewhat similar distribution as with the 1-10 results. Odd numbers more often than even numbers. Prime numbers even more often.

Stipulate that both digits must be distinct and odd, then guess 37.

or distinct and even, then guess 68 (think this was an old david blaine trick if i recally correctly)

It seems like publicizing some preliminary results of the study before the study is complete would put the legitimacy of the final results very much so at risk.

constructive criticism ... for science

Yes, but so would (presumably extreme) sample bias.

After 80k votes, it seemed prudent to give those asking "so what?" a response.

If (as I'm sure you do) you have the times along with the votes it would be cool to see if there was actually a bias when comparing the before response and after response datasets.

There was something about "for SCIENCE!" that was irresistible.

That bit of "flair" was added almost on a whim. I'm glad I did add it. I think that helped the experiment get the attention it did, especially when it got onto Reddit. It's funny how a simple factor can (probably) have such a big impact.

Also, the unintentional "mystery" of not including any information about the who or why on the site itself may have helped. I noticed many comments on HN and Reddit that speculated about each, which no doubt increased the activity profile. A little bit of personality goes a long way.

Was this only posted to HN? If it was posted on other sites it would neat to check the numbers against refers to see if HN is better at picking random numbers than, say, Reddit.

How do you be "better at picking random numbers"?

Even distribution, instead of bell-curves around popular/bias numbers.

The site asks you to pick a random number, not mentioning anything about trying to achieve a specific distribution.

EDIT: Downvotes and no comments, nice. You guys seem to be misunderstanding something. If asked to picked any number ("random") between 1 and 10, to suggest that the outcome is "wrong" because the distribution isn't uniform doesn't make any sense at all. It would be a completely different experiment if we were asked to pick a number between 1 and 10 such that the outcome after x number of independent trials has a uniform (or gaussian/exponential/etc) distribution. This seems to be what some people are assuming.

The larger the sample, the more likely a truly random input approaches a uniform distribution. Yes, a coin flip could come up heads 10000 times in a row, but it just doesn't happen.

The point of probability is to describe uncertain events. Coin flips aren't described by uniform distributions, they're binomial. Human intelligence can be modeled by a Gaussian distribution. And this site's experiment seems to suggest that picking a number between 1 and 10 can be modeled by a bimodal random variable with means around 4 and 7. Point being: random doesn't necessarily mean uniform.

No, but random does mean uncertain, and the uniform distribution has maximal entropy. In other words, uniformly distributed numbers are most random, colloquially, and so you can improve your ability to generate random numbers by sampling from a more unform distribution.

Also, just because intelligence is described with normal distributions, it is not at clear that it can be.

Reminds me of this programming joke:

   int rand() {
     return 4;
   }

Hey, it returns a random number!

http://xkcd.com/221/

http://dilbert.com/dyn/str_strip/000000000/00000000/0000000/...

This comes from the fact that the first run of six 9's in the digits of pi comes much sooner than expected: http://www.geom.uiuc.edu/~huberty/math5337/groupe/digits.htm... search for 999999 - you'll see it's only 10 lines down. When discovered, this caused a lot of people to conclude that the digits were not random. Of course, with 5 trillion digits now calculated, there is still no bias found toward any pattern. So it is very hard to tell!

It is totally reasonable to assume that "random" from an unnamed distribution means the maximum entropy distribution, which is uniform in this case

Maybe allow corrections for Benford's law as well? http://en.wikipedia.org/wiki/Benford%27s_law

Benford's law applies to those cases where you can assume that the logarithms of the numbers are uniformly distributed.

While it's perfectly reasonable to assume that for, let's say, Microsoft's yearly revenue, Apple's stock price, or a number series with x% average growth (for example, inflation-affected prices), it has nothing to do with this experiment.

It ended up getting posted to Reddit, and has been making the rounds elsewhere. (Over 100,000 uniques, holy cow!)

Unfortunately, the referrer wasn't tracked. I wasn't expecting to get enough hits for it to matter. The expectation was for maybe 100 over a week. IP addresses are tracked, so I'll eventually do a location breakdown.

Assuming you don't delete them, why not use your webserver logs to link datestamp+IP address to referrer-url?

I solved this problem by using software. Using your current brain state is a terrible seed for randomness.

Strangely enough, I got asked to pick a number between 1 and 10 a few days ago in an Irish pub in Germany. Looks like this was a LOT more popular than expected!

For the record, I picked 9 - much to the dismay of the person asking me.

The positioning of the dropdown clearly has a lot of influence on the results. People are horrible random number generators! In this case, people are unlikely to choose the ends (1/9) or the center (5) leading to a bimodal distribution with two modes at 4 and 7.

In thinking back, that's exactly why I picked 4.

I just clicked whatever was closest because I wasn't even thinking about the exercise.

The number picker was random, some people got a drop down, some got a list of numbers, some got a slider etc etc etc

Note however that different types of input systems were used. Refreshes show the following different types:

  * A slider that need to be dragged to choose a value.
  * A list of numbers shown with highlighting on hover.
  * An input cursor that on hover changes to a list of numbers (within a curved border this time).
  * A text field (enclosed in a circular border), allowing manual input.

I'm quite interested in how results varied depending upon input type (possibly more interesting than seeing how they vary by referrer).

Well, why don't you have a look? :) http://nfrom1to10.appspot.com/results/

I picked 3 because it's in the easiest number for me to strike (text box version).

My mouse is typically in the middle of the screen, closest to the higher-scoring numbers in the graphical version.

I'd like to see the results from the same test where you have to type the number as a word for the textbox (e.g., three), and where the numbers aren't laid out in the same numerical order for each user in the graphical version.

Seems like people are so number centric and go for the universal lucky number. Not sure why. How did this help? Were you able to do any behavior analysis based on this small experiment?

I would suggest, go on a weekly result and keep tabs on result variation.

Try posting it on various/diverse communities. This might help to understand alot about visitor behavior on various websites as you can track referring websites too.

If possible graph the picks depending upon the referring websites. Or even a graph based on region, tracking via IP should be easy.

For those who missed the Parent post, check here http://news.ycombinator.com/item?id=2375149

I picked 9. I feel good about doing my part to even out the distribution I predicted :)

I thought people would think 10 was the least random number, so I picked it, :-)

I won! Yay.

can you do this again but with an arbitrary range. I'm curious what happens when you don't have the lucky number effect (i.e. 7)

You didn't count my 11 :(

Did you actually use firebug and submit an 11 to the server? That would be pretty funny.

Yep, sure did.

Nor my 0 (type a ten, press left then backspace the one).

The problem is that it didn't ask us to choose the numbers uniformly. Perhaps I picked from a Gaussian distribution with mean 5 and a strict cut-off at 1 and 10.

I don't think anything can be concluded unless it asked for "choose uniformly at random among the 10 numbers," if we want results robust against question biasing.

"Choose randomly" is generally understood to mean "choose randomly from a probability distribution containing as much entropy as possible given the problem." I mean, I could choose from the probability distribution {0.001, 0.001, 0.998} but it's commonly understood that this isn't what's meant by the word "random".

PS: I chose 2. Eat that, seveners!

Yay, I tried to guess and pick the number which I thought would probably be picked the least amount of people.

10 was a good guess.

The results for 'select' seem strange. That's the only place where random specified/not makes much difference. It also indicates that a lot more people picked numbers under 'select/specified' than any other condition.

Have you checked your logs for possible vote stuffing?

Not yet, though IP addresses are one of the metrics for each vote. I'm still working on efficient ways of going through everything.

Is it wise to publish updated results while the data is still being gathered? Random selection should be blind and independent and its quite possible people may change their vote to favor an 'unpopular' number or vice versa.

I think that the reason that 7 is so high is because it is commonly believed that 3 will is the first one you think of. As a result people choose to pick something higher, hence 4 and 7 being the top two.

I didn't think that much. I just chose 7 because I wanted to choose I high number, but anything higher then 7 would have been to high.

I thought it was commonly believed that 7 is the most often picked - I've seen a "magic" trick based around that before.

Sort of looks to me like people avoid the extremes and also 5 (possibly because it's "right in the middle" and so perceived as "less random"?).

I was talking with a friend when I visited the website, and just completely unconsciously entered any number. It was 7. After submitting I wondered why I did that without even thinking about it.

my favorite number is 4 but I entered 7 because I wanted something higher and this was the highest prime number within that range :)

I'm surprised the number 1 wasn't higher up because of the slider (since it defaults to 1). I guess people aren't as lazy as I thought they were and actually took the effort to move the slider :P

I don't get it. How is the selector relevant to what people choose? You might as well have put a different colored rabbit somewhere on the page and measured responses that way.

I'm getting nothing but "1800".

Momentary stupidity on my part. I told it to cache the expire time instead of the actual value. Oops. Go figure, it was the one time I think "Eh, this is a small change. I don't need to go to a testing version first."

Science has error bars.

Science takes time ;)

contrarian pride for 1 or 10.

Glorious #2 Master Race.

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