# Proposal: New megaminx scramble notation



## Carrot (Jul 14, 2014)

There's no doubt about the Pochmann scrambling system for megaminx was a great improvement from what we had before, but I still find it "hard" to get the scrambles correct. In my opinion the scrambling notation should help the scrambler get the scramble right over a system that is more uniformly correct with other notation systems.


Rxx Dyy = xy (never Dxx Ryy, which should be obvious for people who knows how to scramble megaminx)
odd lines being pushed slightly to the right to avoid "line slips"

example:

```
-+ ++ ++ ++ +-  U'
 +- -+ +- +- -+ U
+- -- +- -+ +-  U
 +- -+ ++ -+ -+ U'
-+ -- +- -- -+  U'
 ++ +- -- ++ +- U'
-+ ++ -+ -- --  U
```

Same using the current notation:

```
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
```

Bookmarklet for a scrambler using this notation for google chrome. (this overlays whatever website you are on and will almost certainly break the timing function if you are on cstimer, qqtimer or another timer, but hey, Speedsolving is still functional haha)

```
javascript: (function(){ var script=document.createElement('script'); script.type='text/javascript'; script.src='http://competition.odderen.dk/zoe/megaminxScrambler.js'; document.getElementsByTagName('head')[0].appendChild(script); })();
```



Spoiler: You don't know what a bookmarklet is?



basically, bookmark the code as if it was a website URL, simple as that, then when you click it, the scrambler should appear.


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## scottishcuber (Jul 14, 2014)

Seems like a really good idea. It's nice and concise. 

Grouping the pairs of + and - makes it really easy to read. Nice.


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## AJ Blair (Jul 14, 2014)

This seems perfectly reasonable. I agree that it's incredibly difficult to consistently scramble correctly. This is easy to read and seems much harder to mess up or lose your place in due to the offset and the pairing. 

Great idea!


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## ryanj92 (Jul 14, 2014)

This is a really neat idea, reminds me of 'concise' clock scramble notation - chop off anything that is the same in every scramble, for brevity 
Also the line offset thing is so simple but so effective


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## bobthegiraffemonkey (Jul 14, 2014)

This will make scrambles so much easier on the eye, I hope this gets implemented.

Edit: I quickly made a (probably horribly written) scrambler in R for this, which I will be using for scrambles since I want to use Firefox with working timers. I'll post it if anyone wants, but I'm not sure of how much interest there would be since I think you need R installed to use it, but maybe someone can correct me.


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## Iggy (Jul 14, 2014)

Great idea, so much easier to read.


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## Carrot (Jul 14, 2014)

Thank you for the positive feedback so far!

Import scrambles to CStimer: Copy the textbox from here (it always gives fresh scrambles on refresh) -> CStimer: choose "input" in left scramble dropdown box -> paste and have fun! (50 scrambles) 

Also, personally I use >=U' and <=U, to keep each line the same length on the right hand (reduces line-slips caused by U and U' lengths). I know it's very unconventional to use </> instead of U/U', which is why I didn't mention it in OP.

```
-+ ++ ++ ++ +-  <
 +- -+ +- +- -+ >
+- -- +- -+ +-  <
 +- -+ ++ -+ -+ <
-+ -- +- -- -+  <
 ++ +- -- ++ +- <
-+ ++ -+ -- --  >
```


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## brian724080 (Jul 14, 2014)

Great idea. I think it will also be easier to put on a smartphone application due to screen display size restrictions. However, I might not be right because I don't use a smartphone. Also learned that those javascript bookmarks are called bookmarklets


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## Lucas Garron (Jul 14, 2014)

I like how readable that notation stays when it's compact, and how the pairs always start with the same side.


```
-+ ++ ++ ++ +-  U'
 +- -+ +- +- -+ U
+- -- +- -+ +-  U
 +- -+ ++ -+ -+ U'
-+ -- +- -- -+  U'
 ++ +- -- ++ +- U'
-+ ++ -+ -- --  U
```

Is this a proposal for the community, or for the WCA?

For official scrambles, we need to make sure the notation is easy to read (and remember) even for people who are not familiar with the puzzle. If we want to group moves, I'd prefer something like the following:


```
(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
```


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## 10461394944000 (Jul 14, 2014)

Carrot said:


> Thank you for the positive feedback so far!
> 
> Import scrambles to CStimer: Copy the textbox from here (it always gives fresh scrambles on refresh) -> CStimer: choose "input" in left scramble dropdown box -> paste and have fun! (50 scrambles)
> 
> ...



I'm pretty sure each line of a WCA scramble ends with U if the previous move was D++ and U' if the previous move was D--, so you dont even need the last U/U'/</>


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## Renslay (Jul 14, 2014)

Lucas Garron said:


> For official scrambles, we need to make sure the notation is easy to read (and remember) even for people who are not familiar with the puzzle. If we want to group moves, I'd prefer something like the following:
> 
> 
> ```
> ...



Agree. There is no need to compress the scramble. With the -+ ++ +- etc. I would forget from time to time if the scramble would start with R-- or D--, and I'm sure I would mix the ++ with a single D++ or R++ (instead of R++ D++).

But the grouping is a good idea. It's easier to see what is the next turn during a scrambling.


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## scottishcuber (Jul 14, 2014)

Renslay said:


> Agree. There is no need to compress the scramble. With the -+ ++ +- etc. I would forget from time to time if the scramble would start with R-- or D--, and I'm sure I would mix the ++ with a single D++ or R++ (instead of R++ D++)



You would get used to it pretty easily with a little bit of practice, in my opinion.


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## Renslay (Jul 14, 2014)

scottishcuber said:


> You would get used to pretty easily with a little bit of practice, in my opinion.



I have no doubt about that, but I won't practice (as I do not do megaminx). However, I can be called to the scrambling table for scrambling megaminxes - and there I would be confused many times with this type of notation. And I'm sure I won't be alone.

Just for the record, it happened that I had to help with the pyraminx scrambles on an official competition. I asked the person next to me what does the notation mean, he explained it in like 10 seconds, and then I had no problem with the scrambling (because Pyra scrambles are actually pretty easy to read and understand).

Just as Lucas said, it's important to keep the scrambling easy to understand and perform, not thinking too much about what symbol means what. I think the "R" and "D" (and "U") letters are important to avoid confusion.


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## Pedro (Jul 14, 2014)

I think having lines with different colors would already help a lot against the "getting lost in the scramble" thing. Also, we could use just one + or - instead of 2, and rewrite 12d2 like this:

12d2) Other moves are applied while keeping 3 pieces fixed at top left of the puzzle:
12d2c) Clockwise 144 degrees move of whole puzzle except for the slice of top left three pieces: R+ (vertical slices), D+ (horizontal slices).
12d2d) Anti-clockwise 144 degrees move of whole puzzle except for the slice of top left three pieces: R- (vertical slices), D- (horizontal slices).


```
(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
```


```
(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
```

Example:

http://www.cuber.com.br/minxscramble.html


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## MaeLSTRoM (Jul 14, 2014)

The issue I have with the current WCA scrambles is that it is very easy to lose track of what line you're on, and I think this is a larger problem than the readability of each individual line. While shortening to a single +/- or similar is a good idea, the issue with each line looking very similar is still present. The line offset idea in the original post is nice, or maybe an extra line space after each 2 lines would be good as well.


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## Lucas Garron (Jul 14, 2014)

MaeLSTRoM said:


> The issue I have with the current WCA scrambles is that it is very easy to lose track of what line you're on, and I think this is a larger problem than the readability of each individual line. While shortening to a single +/- or similar is a good idea, the issue with each line looking very similar is still present. The line offset idea in the original post is nice, or maybe an extra line space after each 2 lines would be good as well.



See https://github.com/cubing/tnoodle/issues/155 for current plans (white/gray row highlights, similar to the WCA results tables themselves).


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## EMI (Jul 14, 2014)

Good idea. I also don't quite like the fact that a scrambler at a competition would have to know which move he has to begin with - it is always useful if people that don't do the event can still scramble the puzzle, and if practise is needed to do so, it makes things complicated. I think a very intuitive notation would be Dw, Rw and U moves.
(This is not a very strong argument though, as I believe many people do Megaminx and the scrambling notation can be explained fast either way. I think it's more problematic with clock.)
Grouping moves and other ways to make distiction between lines / moves easier is definitely a good thing for some events.


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## bobthegiraffemonkey (Jul 14, 2014)

Regarding concerns about the new notation being confusing or unclear to people not as familiar with normal scrambling notation, couldn't there be a short description/example on the scramble sheet?


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## maps600 (Jul 14, 2014)

I think the grouping is a really good idea. However, I do think that the double plus and minus signs after the letter isn't necessary. Only one plus would really be necessary.


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## Divineskulls (Jul 14, 2014)

This was such an awesome idea, I can't wait for it to be integrated into cstimer and qqtimer.


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## Carrot (Jul 15, 2014)

For people saying the ++, +-, -+, -- is too hard. it's 4 (+2=6) unique moves... 3x3x3 is 18. Pyraminx is 16. Skewb is 12.
Also, think of it as a coordinate system, first digit is the y axis, the second is the x axis, that should give you a direction vector (+- = (-1,+1) = Up - left = R++ D--; ++ = (+1,+1) = up - right = R++ D++). It just happens that directions are already handled like this, so north-east is always called north-east, not east-north. So +- could be treated like North-west, people with a megaminx in front of them should see how North-west would translate as R++ D--. (North=+, East=+)



Spoiler



Don't treat above as a tutorial or anything, it's just some messy explanation of a few ways to intuitively understand how the -+ system works. (it's recommended to think in order to interpret what I wrote, haha)



(note: The (R+ D-) ... etc notation would not really help me not getting lost, so I wouldn't see why change anything from what it is to that, but that's just my opinion)



Lucas Garron said:


> I like how readable that notation stays when it's compact, and how the pairs always start with the same side.
> 
> Is this a proposal for the community, or for the WCA?
> 
> For official scrambles, we need to make sure the notation is easy to read (and remember) even for people who are not familiar with the puzzle. If we want to group moves, I'd prefer something like the following:



Community.



10461394944000 said:


> I'm pretty sure each line of a WCA scramble ends with U if the previous move was D++ and U' if the previous move was D--, so you dont even need the last U/U'/</>



I call hoax until documentation is provided.


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## Stefan (Jul 15, 2014)

Carrot said:


> I call hoax until documentation is provided.



https://github.com/cubing/tnoodle/b...scrambles/src/puzzle/MegaminxPuzzle.java#L331
The value of variable *dir* is reused for the U-turn.

I don't remember why, though. It was probably in my proposal and maybe I just really preferred 2/5-turns over 1/5-turns.


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## Lazy Einstein (Jul 15, 2014)

Just a quick weigh in here.
I find this notation very easy to follow compared to the normal notation. I don't lose my place as easy. I really like the idea of every other line being adjusted forward to prevent confusion. 

I hope this get implemented because it fills a need in helping to correct commonly made mistakes in scrambling.


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## Ranzha (Jul 15, 2014)

Lucas Garron said:


> For official scrambles, we need to make sure the notation is easy to read (and remember) even for people who are not familiar with the puzzle. If we want to group moves, I'd prefer something like the following:
> 
> 
> ```
> ...



What about Square-1?


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## vcuber13 (Jul 15, 2014)

Ranzha V. Emodrach said:


> What about Square-1?



What about it?


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## Lucas Garron (Jul 15, 2014)

Ranzha V. Emodrach said:


> What about Square-1?



Good question. Two relevant facts for Square-1:

- There are different kinds of turns, and the (possible valid) amount of turning depends on the position.
- There is already a widely used notation to describe Square-1 algs that can be used for our method of scrambling.

I don't remember anyone ever saying we should change Square-1 notation, and I certainly haven't seen alternate proposals.

A closer example is clock, which we did change.


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## Mikel (Jul 15, 2014)

I think a method to distinguish lines such as an offset or white/gray alternating lines would be great. I would recommend it for 6x6 and 7x7 along with megaminx.


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## EMI (Jul 15, 2014)

Lucas Garron said:


> Good question. Two relevant facts for Square-1:
> 
> - There are different kinds of turns, and the (possible valid) amount of turning depends on the position.
> - There is already a widely used notation to describe Square-1 algs that can be used for our method of scrambling.
> ...



Not to the good imho.
Square-1 is hard to scramble, but because of the puzzle, not the notation. The only way to make it easier would be to replace "/" with an "R2" and make (x,y) mean x *pieces* to the left, instead of x*30°. I'm not sure if that is easier though. We should probably just use Lego robots for it


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## qq280833822 (Jul 16, 2014)

Integrated in cstimer. See "megaminx" -> "Carrot"


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## uberCuber (Jul 16, 2014)

EMI said:


> make (x,y) mean x *pieces* to the left, instead of x*30°. I'm not sure if that is easier though.



I would argue that that is harder/slower: with the current notation, I can follow a square-1 scramble quickly and easily without ever looking down at the puzzle. When I see a 4, I have a sense of how "far" that is and don't have to watch myself turning the puzzle. But if (x,y) referred to the number of pieces, then how "far" a 4 is depends on the state of the puzzle, requiring me to look down at the puzzle a lot, making me go slower and also potentially lose my place in the scramble more easily.


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## qqwref (Jul 16, 2014)

Yeah, the number of pieces is harder to be fast with, even though it might seem easier for new people. Back when I did Square-1 sim the hardest part for me was dealing with the U/D turns by piece instead of by angle.

I do like this Megaminx notation. Although I wish we had a scrambling setup that could reach most of the puzzle states.


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## cubernya (Jul 16, 2014)

qqwref said:


> Yeah, the number of pieces is harder to be fast with, even though it might seem easier for new people. Back when I did Square-1 sim the hardest part for me was dealing with the U/D turns by piece instead of by angle.
> 
> I do like this Megaminx notation. Although I wish we had a scrambling setup that could reach most of the puzzle states.


I know it can't reach all, but what percentage can it reach?


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## Lucas Garron (Jul 16, 2014)

theZcuber said:


> I know it can't reach all, but what percentage can it reach?



70 independent choices = 2^70 states
The number of states is about 2^226.

So, pretty much 0%.

Note that this information doesn't tell you anything about whether our scramble program is good or bad. If those 2^70 are indistinguishable from random (to a human), we're totally fine.
(I've been meaning to run calculations to see if certain simple measurements of randomness are satisfied, e.g. amount of separation of adjacent pieces.)


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## qqwref (Jul 16, 2014)

Lucas is right. Even with 77 choices (choosing the U or y direction as well) the number of positions is negligible compared to the number of positions of the puzzle.


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## Renslay (Jul 16, 2014)

Lucas Garron said:


> 70 independent choices = 2^70 states
> The number of states is about 2^226.
> 
> Note that this information doesn't tell you anything about whether our scramble program is good or bad. If those 2^70 are indistinguishable from random (to a human), we're totally fine.



Then why is everybody so hyped about random state scrambles instead of fix 25 move scrambles in 3x3?
(Especially considering the huge argument in this thread: http://www.speedsolving.com/forum/showthread.php?48443-Best-way-to-randomize-a-cube )


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## Lucas Garron (Jul 16, 2014)

Renslay said:


> Then why is everybody so hyped about random state scrambles instead of fix 25 move scrambles in 3x3?
> (Especially considering the huge argument in this thread: http://www.speedsolving.com/forum/showthread.php?48443-Best-way-to-randomize-a-cube )



There is no contradiction. In both cases, the goal is to produce a state that is no easier/harder for a human to solve than a random state.

For 3x3x3 it's really easy to generate a short scramble that is indistinguishable from a (uniformly) random state... namely, because it *is* a random state. (By easy, I mean your smartphone can literally do it in the blink of an eye.)
If you're using a computer/smartphone, there is no good reason not to use random-state scrambles for 3x3x3 – especially since quite a few timers are available for each common platform that will do this for you by default.

25-move scrambles are bad for several reasons. One that is easy to grasp: EO is about twice as likely to be solved (compared to a random state) – this already makes it a bad choice for BLD practice.

For Megaminx, generating a short alg to produce a random state is far from practical (and it would take too long to apply), so *there* the notion of indistinguishability actually becomes relevant.


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## Carrot (Jul 16, 2014)

Stefan said:


> https://github.com/cubing/tnoodle/b...scrambles/src/puzzle/MegaminxPuzzle.java#L331
> The value of variable *dir* is reused for the U-turn.
> 
> I don't remember why, though. It was probably in my proposal and maybe I just really preferred 2/5-turns over 1/5-turns.



*facepalm* why? Why? That's a terrible reasoning, but okay. I was wrong about that, but no documentation was provided why it was reasonable to take that decision. 



qq280833822 said:


> Integrated in cstimer. See "megaminx" -> "Carrot"


Sweet!


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## Stefan (Jul 16, 2014)

Carrot said:


> *facepalm* why? Why? That's a terrible reasoning, but okay. I was wrong about that, but no documentation was provided why it was reasonable to take that decision.



I don't see you complaining about all the other 2/5-turns, so why about these?

For 2/5-turns in general, here's a bit (starting at "Now an improvement..."):
https://www.worldcubeassociation.org/forum/viewtopic.php?p=1458#p1458


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## Carrot (Jul 16, 2014)

Stefan said:


> I don't see you complaining about all the other 2/5-turns, so why about these?
> 
> For 2/5-turns in general, here's a bit:
> https://www.worldcubeassociation.org/forum/viewtopic.php?p=1458#p1458



Mainly because I see the R, D part as the "scrambling" part and the U's as an adjustment in order to break up the pairs that can't be broken up just by the R, D part, so I don't see them as being related. The best argument I can see for for only using 2/5 turns is that you can reach longer and since all permutation groups are even the quality is not decreased.However, I still like the 1/5 turns in the end of half of the lines.

(thanks for the link, but I had already skimmed that a few years back)


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## sk8erman41 (Jul 29, 2014)

I've been using the "Carrot" scramble in CSTimer and gotta say it is waayyyyyy easier, I like it a lot well done


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