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Megaminx scrambling is hard

So, some people say that it is easy because it is repetitive, but it is hard because of 3 things
1. It is long like this.
R++ D++ R-- D-- R-- D-- R++ D++ R++ D++ U
R-- D++ R++ D++ R-- D++ R-- D++ R-- D-- U'
R-- D++ R-- D++ R-- D-- R++ D++ R-- D-- U'
R-- D-- R-- D-- R-- D-- R++ D++ R++ D-- U'
R++ D-- R++ D-- R-- D++ R++ D++ R-- D-- U'
R++ D-- R-- D-- R-- D++ R++ D++ R-- D-- U'
R++ D-- R-- D-- R-- D-- R-- D-- R++ D++ U
this is a random scramble tho
2. if you get a slow megaminx, uhh yes it is hard.
and 3. If you get a mistake, uhhh goodluck bc uhhh you have to solve it
So what is your best megaminx solve?
Mine is like 4 mins.
You can agree or disagree. It is up to you
 
So, some people say that it is easy because it is repetitive, but it is hard because of 3 things
1. It is long like this.
R++ D++ R-- D-- R-- D-- R++ D++ R++ D++ U
R-- D++ R++ D++ R-- D++ R-- D++ R-- D-- U'
R-- D++ R-- D++ R-- D-- R++ D++ R-- D-- U'
R-- D-- R-- D-- R-- D-- R++ D++ R++ D-- U'
R++ D-- R++ D-- R-- D++ R++ D++ R-- D-- U'
R++ D-- R-- D-- R-- D++ R++ D++ R-- D-- U'
R++ D-- R-- D-- R-- D-- R-- D-- R++ D++ U
this is a random scramble tho
2. if you get a slow megaminx, uhh yes it is hard.
and 3. If you get a mistake, uhhh goodluck bc uhhh you have to solve it
So what is your best megaminx solve?
Mine is like 4 mins.
You can agree or disagree. It is up to you
Unfortunately, it is necessary. Insufficient scrambling tends to cause premade blocks to be common, making the solve a lot easier. The more you practice, the faster you'll get at scrambling- it usually takes me about 35 seconds for a full scramble and my best time is just over 1 minute 10. I'd reccomend getting a decent magnetic megaminx, YuHu V2 is the cheapest one that is used competitively. Also learn an S2L method: Westlund is both the best and easiest.
 
So, some people say that it is easy because it is repetitive, but it is hard because of 3 things
1. It is long like this.
R++ D++ R-- D-- R-- D-- R++ D++ R++ D++ U
R-- D++ R++ D++ R-- D++ R-- D++ R-- D-- U'
R-- D++ R-- D++ R-- D-- R++ D++ R-- D-- U'
R-- D-- R-- D-- R-- D-- R++ D++ R++ D-- U'
R++ D-- R++ D-- R-- D++ R++ D++ R-- D-- U'
R++ D-- R-- D-- R-- D++ R++ D++ R-- D-- U'
R++ D-- R-- D-- R-- D-- R-- D-- R++ D++ U
this is a random scramble tho
2. if you get a slow megaminx, uhh yes it is hard.
and 3. If you get a mistake, uhhh goodluck bc uhhh you have to solve it
So what is your best megaminx solve?
Mine is like 4 mins.
You can agree or disagree. It is up to you
I really want reduced carrot notation to be used by Tnoodle and eventually by the WCA.
 
Idk why but when you go on cstimer and get a carrot notation scramble it doesn’t do it right. On the pochmann scramble in the original post, notice how every D- - is followed by a U’ at the end and vice versa which is how how it should be

-+ +- -- -+ -- U
+- +- -+ -+ +- U
-+ +- +- +- +- U'
++ ++ -- +- +- U'
-- -+ ++ -- ++ U
++ +- ++ ++ -- U
In this scramble it’s incorrect which makes me wonder why this is even the case and unless this is fixed I wouldn’t bother generating carrot scrambles.

In terms of it, the more you practice scrambles the easier it becomes, also try to do R++ D- - regripless and R- - D++ as well. That makes it faster. Also you can use my trick of preempting the u move at the end of each line which makes it faster and so you don’t need to look up at the scramble as much.

My best mega solve is 54.68 but that isn’t really relevant to the point im trying to make. But if you grind even for just a month you will lower your times very fast
 
Idk why but when you go on cstimer and get a carrot notation scramble it doesn’t do it right. On the pochmann scramble in the original post, notice how every D- - is followed by a U’ at the end and vice versa which is how how it should be

In this scramble it’s incorrect which makes me wonder why this is even the case and unless this is fixed I wouldn’t bother generating carrot scrambles.
And this is a major problem of carrot why? Why does it have to be that way (last u move being dictated by the d move)? Iirc, this feature of carrot (the one where U moves are not dictated by the d move) would actually be helpful. Megaminx scrambles produce only a very small number of possible states, and having the ending U move not dictated by the last D move would produce more possible states.

Another thing about current Megaminx scrams is that they tend to be a bit luckier than they should be, the scrams are not random state. I do not 100% remember if carrot improves on the problem, I think it does, but considering the WCA forums is down as of now (my source is a post on that forums from someone who did the calculations on the scram distribution between the scrambling methods) I cannot confirm if carrot makes the scrams closer to the luck they would be if they were random state, and once the WCA forums are back online, I will come back and edit any info if I need to.

Edit: Follow up as WCA forums is back, here is the quote from the post.


What is also not commonly known is that you actually scramble the puzzle state (very slightly) better with Carrot, and not just because it has access to more scramble states.

D++ U is equivalent to a 2/5 turn + rotation, whereas D++ U’ is equivalent to a 1/5 turn + rotation; scrambling with exclusively 2/5 turns causes huge biases in edge orientation. To wit, if we look at the star edges, they are around 1.589× as likely to be attached to the centre correctly rather than flipped.

Mixing in a small proportion of 1/5 turns improves scramble quality by breaking this EO bias; if we always do D++ U’ and D-- U instead, the ratio drops to “only” 1.406× (which is still very high). Carrot is in the middle of these two extremes, with a ratio of 1.487×.”

Carrot can improve scramble quality, and having the U move be random is imo an improvement to Megaminx scrambling, not a detriment.
 
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And this is a major problem of carrot why? Why does it have to be that way (last u move being dictated by the d move)? Iirc, this feature of carrot (the one where U moves are not dictated by the d move) would actually be helpful. Megaminx scrambles produce only a very small number of possible states, and having the ending U move not dictated by the last D move would produce more possible states.

Another thing about current Megaminx scrams is that they tend to be a bit luckier than they should be, the scrams are not random state. I do not 100% remember if carrot improves on the problem, I think it does, but considering the WCA forums is down as of now (my source is a post on that forums from someone who did the calculations on the scram distribution between the scrambling methods) I cannot confirm if carrot makes the scrams closer to the luck they would be if they were random state, and once the WCA forums are back online, I will come back and edit any info if I need to.

Edit: Follow up as WCA forums is back, here is the quote from the post.


What is also not commonly known is that you actually scramble the puzzle state (very slightly) better with Carrot, and not just because it has access to more scramble states.

D++ U is equivalent to a 2/5 turn + rotation, whereas D++ U’ is equivalent to a 1/5 turn + rotation; scrambling with exclusively 2/5 turns causes huge biases in edge orientation. To wit, if we look at the star edges, they are around 1.589× as likely to be attached to the centre correctly rather than flipped.

Mixing in a small proportion of 1/5 turns improves scramble quality by breaking this EO bias; if we always do D++ U’ and D-- U instead, the ratio drops to “only” 1.406× (which is still very high). Carrot is in the middle of these two extremes, with a ratio of 1.487×.”

Carrot can improve scramble quality, and having the U move be random is imo an improvement to Megaminx scrambling, not a detriment.
It’s not about scramble quality, it’s about consistency with scrambling errors. That last U move being similar to the last D++/- - move just makes it more consistent and easier to follow along than it being random, since it forces you to pay more attention to the scramble. Even though misscrambles are allowed for this event, you can’t force misscrambles every time. So I try to make sure every scramble is right, and it takes me 20s to do a scramble.
 
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my source is a post on that forums
(that's me btw, who else writes so obnoxiously)

One of the points I was trying to make there was that the "extra randomness" isn't actually what causes Carrot to have better scrambling quality. One could easily come up with a scrambling method with even better quality despite a smaller scramble space, e.g.:

1. Pre-generate 2^50 random-state scrambles.
2. For competitions, randomly select scrambles from this pool of pre-generated scrambles.

Never mind that this method has practicality issues and doesn't make sense to use; quality-wise, it completely trounces Pochmann and Carrot scrambles on every reasonable metric (with high probability) despite only ever generating 1/1000000 as many possible scrambles.

There is a limit to how small the scramble space can get while still looking reasonably random, which is around 2^30 to 2^50 depending on how fussy you are. 2^70 is already a decent safety margin on that and going any higher isn't going to directly help.

Carrot wins over Pochmann (in terms of EO (*)) because it introduces a few 1/5 turns, and it would win even more if you forced more 1/5 turns into it. E.g. by always making the U move opposite of the preceding Dxx move – which incidentally also fixes the inconsistency issue that @Garf raised.

(*) There's no substantial difference in the number of free corner-edge pairs between the two. IIRC Carrot is extremely slightly better but the difference is so small it might as well just be noise. The difference between true random state and either of those is much greater: Pochmann and Carrot are both noticeably bad.

---

It's really frustrating thinking about how to improve megaminx scrambles because we have to optimise in many directions at once:
0. Scramble quality. Pochmann scrambles are actually kind of bad if you do only 7 rows. The old 12-gen scrambles were actually very good but also impossible to execute quickly. We probably want to strike a balance here.
1. Ergonomics. Pochmann scrambles are actually pretty fast to do with some practice! (Carrot scrambles use the same moves but with a different notation so they are also good.)
2. Scramble length. 70 moves is kind of long already, but we can't go much shorter without compromising on scramble quality.
3. Robustness to misscrambles. Rejection sampling (see e.g. Roman's thread about this) can be used to improve scramble quality without increasing length, but (to my knowledge) this is not robust against misscrambling.
4. Community acceptance. How do you get the whole cubing community on board with a new scrambling method? (Am I the right person to spearhead that?)
5. Permanence. We don't just want to improve the scramble method by a small amount, only to have to change it again a few years later for another improvement; we need to improve it by so much that we won't ever have to think about improving the scramble method again in the near future.
6. 7. 8. … (probably a fair number of other considerations that are not immediately coming to mind)

The technical problems are hopefully surmountable by thinking harder about them; the social problems are… a bit harder.
 
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Thought it might be useful to see what an old megaminx scramble looked like for reference:

B f3 b d f3 a2 f4 C2 e4 f2 D a4 c b4 f a3 c3 E2 f4 D3 e4 f4 C3 b2 d2 c2 f2 b E2 e4 d2 a3 d4 F3 c3 f4 b2 f3 b4 D2 E2 c b c e B4 F4 E4 d4 c3 f2 D3 e C f2 b4 D4 F E3 d2
This actually looks like a chess game
 
Thought it might be useful to see what an old megaminx scramble looked like for reference:

B f3 b d f3 a2 f4 C2 e4 f2 D a4 c b4 f a3 c3 E2 f4 D3 e4 f4 C3 b2 d2 c2 f2 b E2 e4 d2 a3 d4 F3 c3 f4 b2 f3 b4 D2 E2 c b c e B4 F4 E4 d4 c3 f2 D3 e C f2 b4 D4 F E3 d2
As a hard mega main, I’m glad that I don’t have to use this anymore.
Not that I ever did but ya know.
 
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