# I recently finished my science experiment, and would like to share the results with you.



## Mr.Roux86 (Mar 3, 2020)

I have just finished working on my cubing science experiment, which I can officially call The Effect of Scramble Distance on Human Solvers.

What does this mean? Well you might have heard that a Rubik’s cube can always be solved in 20 moves no matter what (this is called God’s number). This is true, but not every scramble takes 20 moves. 20 is only the maximum, we can go lower. This is the distance of a scramble. Distance 20 is the highest possible distance, but the average distance is 18. In my experiment, I tried to see if there was a correlation between distance and solving times. Do people solve worse on distance 20 scrambles vs distance 18? In my research paper, you can see trend lines, not only for every person who took the survey, but also trends for certain demographics within cubing itself. 

Here is my formal abstract:
The purpose of this project is to investigate the relationship between the 'scramble distance' of a Rubik's Cube and the time it takes for human solvers to complete the scramble. I hypothesize that if scramble distance and human solving times are directly related, then a higher distance scramble will lead to higher human solving times. My procedure for this task is to have volunteers solve a variety of predetermined scrambles and record their times doing so. I will compare this data across a variety of participants to see how solve times relate to God's number and the scramble distances before it. I also would like to see if there are additional trends based on solving methods and experience.

Is there a trend? Yes, but it’s not that simple.

I am not going to write an entire essay for now, but if you want to know an overview of everything I studied, you can watch this video which shows most of my information in a power point presentation.

Video: 




If you want to go further in depth, and know absolutely everything I studied, then you can read my research paper.

Paper: https://docs.google.com/document/d/1YPwHi6JEOOJnFFQIeQaTU4hJnfZE_6XD_TsrDpllqMk/edit?usp=sharing

Thank you so much to everyone who participated, in the end, 133 people helped me with this, and I am very thankful for that.


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## 2018AMSB02 (Mar 3, 2020)

Thats really cool! It was fun doing it and I even had some of my friends that barely know how to solve a cube participate.


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## Micah Morrison (Mar 3, 2020)

Yeah I had a lot of fun and would love to do something like this again!


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## xyzzy (Mar 3, 2020)

Error bars! You _need_ to include error bars!

You can draw trend lines all you want, but we can't tell how much you're overfitting if you don't also include the error bars. (You can draw a smooth curve through _any_ finite set of points, which is why curve fitting is interesting/meaningful only if the curve is "simple" in some sense, e.g. linear or exponential.)


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## Mr.Roux86 (Mar 3, 2020)

xyzzy said:


> Error bars! You _need_ to include error bars!
> 
> You can draw trend lines all you want, but we can't tell how much you're overfitting if you don't also include the error bars. (You can draw a smooth curve through _any_ finite set of points, which is why curve fitting is interesting/meaningful only if the curve is "simple" in some sense, e.g. linear or exponential.)


Yeah sorry. I understand I am missing some things, but it's a little too late for that.


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## ProStar (Mar 3, 2020)

Great paper! I think that the scramble distance doesn't effect solve times though, if you look at the averages, the times are almost identical. The difference between the fastest and slowest scramble sets is ~.8 seconds. The reason for that could be simply because people don't consistently average exactly the same time, but merely very close to the same time. Also, I think the greater variance in slower solvers is due to the fact the slower solvers are usually inconsistent overall. I remember when I was averaging 35 seconds, I would get 25s and I would get 40+, while now(I avg 19) I usually get 16-19(with of course some fast singles coming occasionally, but those normally don't occur).


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## Mr.Roux86 (Mar 3, 2020)

ProStar said:


> Great paper! I think that the scramble distance doesn't effect solve times though, if you look at the averages, the times are almost identical. The difference between the fastest and slowest scramble sets is ~.8 seconds. The reason for that could be simply because people don't consistently average exactly the same time, but merely very close to the same time. Also, I think the greater variance in slower solvers is due to the fact the slower solvers are usually inconsistent overall. I remember when I was averaging 35 seconds, I would get 25s and I would get 40+, while now(I avg 19) I usually get 16-19(with of course some fast singles coming occasionally, but those normally don't occur).


Yeah, I am not 100% sure if solving times are affected by my data range (distance 20-13). While it would be pretty useless data, it would be cool to see every distance (distance 20-1), because there has to be a correlation at some point. A person will solve a 1 move scramble much quicker than a 13 move scramble. I would guess that there is a certain point to which people would no longer recognize that a scramble is a few moves from solved, and the trend would have a very sharp drop off point.


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## Filipe Teixeira (Mar 3, 2020)

data science is fascinating
good job dude

there is a ton of effort put into this


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## efattah (Mar 3, 2020)

Some guy did a presentation on ZBLL at US nationals a few years ago (2016?), and he gave the example that top level cubers can see a 6-move scramble and reverse it. Beyond 6 moves it becomes exponentially harder.


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## PetrusQuber (Mar 3, 2020)

Wait so I’m a cuber on the top level?


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## Filipe Teixeira (Mar 3, 2020)

efattah said:


> Some guy did a presentation on ZBLL at US nationals a few years ago (2016?), and he gave the example that top level cubers can see a 6-move scramble and reverse it. Beyond 6 moves it becomes exponentially harder.


I can reverse a 20 move scramble


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## ProStar (Mar 3, 2020)

Filipe Teixeira said:


> I can reverse a 20 move scramble



I can reverse a 9x9 scramble


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## kubesolver (Mar 3, 2020)

efattah said:


> top level cubers can see a 6-move scramble and reverse it.





PetrusQuber said:


> Wait so I’m a cuber on the top level?


No. That's not a logical conclusion.


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## PetrusQuber (Mar 3, 2020)

It was kind of a sarcastic comment about the two not having a correlation.


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## Apolo (Mar 3, 2020)

I did the solves and happy to see the results


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## Daxton Brumfield (Mar 3, 2020)

Very neat! It is too bad I was only able to take like half the survey before I had to go do something


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## JackJack13 (Mar 4, 2020)

efattah said:


> Some guy did a presentation on ZBLL at US nationals a few years ago (2016?), and he gave the example that top level cubers can see a 6-move scramble and reverse it. Beyond 6 moves it becomes exponentially harder.


i think that was chris tran and i agree with that in fact it happen to me today.


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