What to do with "What is the best method of scrambling a rubik's cube?"

Question

The question in question is this one: What is the best method of scrambling a rubik's cube?. The gist of the question is this:

... what is the best, most random way, to scramble the solved cube?

I voted to close it as opinion-based. In the Close Votes review, one reviewer agreed with me, but three didn't. Curious as to why it wouldn't be closable, I asked in chat but did not get a satisfactory explanation.

Currently, it has four answers:

• The (currently) top-voted accepted one. This answer offers a method which is used by an official organization. It makes no argument about how it would count as "most random", but simply shows some pictures demonstrating how it looks pretty random.
• The (currently) second-voted one. This answer is a frame challenge to the idea of "most random", which then proceeds to offer some scramble methods the answerer is partial to.
• One (currently) tied for third. This answer offers two methods of scrambling and asserts the second is better "as it has no statistical bias towards 'easy' scrambles" without fully explaining why.
• The other (currently) tied for third. This answer is a pure product recommendation for what the answerer considers the "best tool".

Taking into accordance the above, what should be done with this question? Should it be closed or left open? If it's off-topic and thus closable, should a historical lock be applied?

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I (obviously, due to my initial close vote) have an opinion on the matter, but am keeping this question as neutral and fact-based as possible. Thus, an upvote on the discussion post does not indicate a stance on the matter: please submit arguments as answers which can be voted on separately.

Answer 1

Leave it open.

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I'm going to start this answer in a controversial way, by quoting part of the site tour which actually doesn't usually apply here on Puzzling:

Focus on questions about an actual problem you have faced.

Obviously, this guidance is much better suited for sites like Stack Overflow or Software Engineering or Parenting than less practical sites like ours. Most Puzzling questions are not at all related to actual problems in real life, and are more about having some fun creating and solving puzzles together. However, this sentence reflects a philosophy which drives the Stack Exchange network and which was originally, at its foundation, the driving force for this site too.

Puzzling SE started off as a site for questions about puzzles, and early questions posted here include, for example, What is the maximum number of solutions a Sudoku puzzle can have? and Why is a single-corner twist not a valid position on a Rubik's cube? - theoretical questions about the nature of certain types of puzzles. After some very bumpy months in 2014, our site and community shifted largely away from these types of questions, and towards "questions" which are puzzles themselves, with "answers" which are attempted solutions. But there's still a place on our site, albeit a smaller one, for questions about puzzles, including practical ones based on real-world puzzling problems: meta consensus has always been that these questions are equally welcome as questions that are puzzles.

I believe it was an ex-moderator of this site who once made the very thought-provoking observation that, if the original purpose of this site was to help people learn about puzzles, then it's actually achieved that purpose in an unexpected way, because we learn by doing. (They expressed this better than I can, but I can't find the exact quote now.)

Why am I blathering on about ancient history? Well, the question you're asking about is ancient itself, asked in the final hours of the site's private beta stage. But more importantly, sometimes it's important to step back and remember who we are, how we got here, and why we have the rules we do.

Imagine you're a Rubik's cube enthusiast who wants to learn more about cubing. What would you be looking to get from a site like this? We have some questions about how to solve specific positions or whether they're achievable, but those are mostly of quite limited interest, useful to the OP but not so much in general. We have some questions about terminology or optimal/extremal positions; those are interesting but not so much practically useful for a cuber. In a very quick glance through our rubiks-cube posts, this was the most actually-useful one I could see. How best to scramble a cube is a basic problem which any cuber might wonder about, and surely a useful FAQ for any site hosting Rubik's cube questions.

The other answers on this meta so far are both focused on the highly theoretical nature of randomness. I'd rather focus on the practical problem which might be faced by real cubers every day, and on the useful answers which provide: (1) an officially approved program and online interface from the World Cube Association which they use for "good" scrambling; (2) a caution not to bother overdoing the number of twists, with an approximate upper bound on the necessary number for a "good" scramble; (3) another online tool, without much commentary; (4) another answer which basically repeats points from 1 and 2.

• Can these answers be improved? Quite possibly yes.
• Do the answers contain useful information for an average beginning cuber? Surely yes.
• Is the question itself a useful one for cubers to know the answer to? Absolutely yes.

I submit that it doesn't matter that true mathematical randomness is almost impossible to achieve in real life. On the other hand, an answer from this theoretical, mathematical, point of view could potentially make a good addition to the set of answers already existing on this question. But such pedantic mathematical points (and I say this as a proud pedant and pure mathematician myself!) don't mean that the real-world problem is useless, even if it's not solvable in an ideal mathematical sense. It's still an actual practical problem, and our site is richer for hosting such information about it.

Answer 2

Leave it open.

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While questions of the form "What is the best X?" ought to be closed as "opinion-based", I think this question can easily be salvaged simply by removing the word "best" from the post. There is no ambiguity in the question, "How can a Rubik's cube be scrambled efficiently, especially by hand?" which is the basic question the OP is interested in.

I disagree with the reasons provided by Taco タコス in their answer. Randomness can be pinned down well-enough in mathematics: the field of probability is essentially based on giving precise meaning to the word "random". Naturally, "it looks random to me" is not a good criterion for randomness, but isn't that why OP wants to know how they can do better? It would be a shame to turn down the question for this reason.

As long as one carefully defines the probability space and random variable(s) one is using to generate a scrambling of the cube, there is no issue with answers being reduced to subjective interpretations of randomness. I would say that a good answer to the question should make these definitions clear, because the "sense" in which one algorithm outputs a random scrambling of the cube may not be the same "sense" in which another does (for instance, see Bertrand's paradox).

Considering that there are organizations that run cube-solving competitions, this is surely a question that has been considered seriously by many people. The organizers of any genuine competition would most likely seek a (mathematical!) guarantee that no contestant will unintentionally benefit from a scrambling algorithm that they intend to use. I presume some of these algorithms are even freely available to examine for ourselves. At least one of the current answers to the question links to such a resource, which is good, in my opinion.

Regarding the fact that most (all?) of the current answers do not explain how and why the algorithm they describe (or link to) provides a "randomized" scrambling of the cube... I'm not sure.

• Perhaps one can ping them requesting them for details?
• It's likely that some people may know of a "credible" resource without knowing all the details behind it. I don't know how much of an issue this is for Puzzling SE. Certainly, none of the answers would pass muster on Mathematics SE, but this isn't that site.
• Maybe you could bounty the question with a message saying you're looking for more concrete answers (in whatever sense you find satisfactory)?

Answer 3

Close it.

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The question lacks key elements that would prevent opinionated answers, but, it's more than this. Since the question is focused on "randomness", answers will mostly be subjective, as the author points out:

... The best way I can think is to hold it behind my back and turn randomly until, when I look at it, it looks random enough.

Unfortunately, randomness, true randomness is very hard to replicate:

... While randomness seems ideal for making totally unbiased choices, there’s a problem: the lack of bias only really appears in an infinitely long set of random numbers. In any given collection, there can be astonishingly long patterns.

I only bring this up because, as human beings, we are really bad at determining "randomness". As a result, without some additional requirement (such as requiring a minimum of $N$ turns to solve), how can one prove that their random scramble is any more optimal than another? Even given the aforementioned additional requirement, there are likely to be many different ways to reach a specific configuration from a solved cube.

As a result, I believe the question should be closed.

References

Matthews, R. (n.d.). Is anything truly random? BBC Science Focus Magazine. Retrieved October 26, 2021, from https://www.sciencefocus.com/science/is-anything-truly-random/.

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_{I provided the emphasis in the given quotes.}