Megaminx scramble notation

[StefanPochmann]

I suggest we switch to the following megaminx scramble notation.

First take a 3x3. Hold it with your left hand, thumb on the F sticker of FLU, index finger on the B sticker of BUL, remaining fingers of the left hand help hold/stabilize the cube. Now while holding the cube with the left hand (except for the z2 cube rotations, of course), use your right hand to scramble like this:

r' d' r' d2 r' d' r2 d r' d' z2
r d' r' d' r2 d2 r' d2 r' d z2
r' d2 r' d2 r2 d r' d r' d z2

Now do the equivalent on the megaminx, i.e., hold the upper left corner/edge/corner triple with your left hand and use your right hand to scramble like this.

- R and D mean everything but the L and U layer, respectively, I didn't like the lower case letters.
- "+" means clockwise, "-" counterclockwise, two for two fifth turns.
- Do a 180 degrees puzzle rotation around z at the end of each line.

R- D- R++ D+ R+ D- R- D- R+ D-
R++ D- R-- D- R- D+ R+ D+ R-- D--
R- D+ R+ D++ R- D+ R-- D+ R+ D++
R- D+ R-- D++ R-- D-- R++ D- R-- D-
R++ D-- R-- D- R- D- R-- D+ R+ D-
R+ D- R+ D++ R++ D- R+ D-- R++ D--
R- D++ R-- D-- R-- D+ R++ D+ R+ D--
R++ D++ R- D- R- D-- R+ D++ R-- D-
R- D- R-- D-- R- D- R+ D++ R-- D++
R++ D- R++ D+ R+ D-- R- D-- R+ D+

I have only tried this twice so far, on two megaminxes. The first time it took me about 1:50, the second time about 1:35. And that's for 100 moves. So that's a lot faster than the notation currently used by the WCA, which takes me about 5-6 minutes for 60 moves even after having it done several times. Also, both megaminxes look exactly the same! Proves that this notation is very easy to get right! With the current WCA notation, I'm pretty sure I make mistakes.

I used 100 moves because this is what I've been using the last few years with a similar way to scramble. I don't mind using a different number, but I think 100 is good.

Update: I just did the scramble a third time, again I got the exact same result (so I conclude I didn't make a single mistake in 300 moves and 27 puzzle rotations), and this time it only took me 1:15.

[StefanPochmann]

Did it once more, this time in 1:09, again without mistake. Now I'll go to bed.

[Ron]

Hi Stefan,

Thanks again for your input.

I like your idea a lot!
For me only 2 questions remain:

1) Can we say anything about the "scientific" state of the scrambling of Megaminx?
To put it differently: if we would do 100 moves like this, would the Megaminx be thoroughly scrambled?
Is there any guess about the maximum depth of Megaminx?
How would the current scrambling and your proposed scrambling compare? Harder, easier, roughly the same?


2) Can someone make a scrambler program for this?
The scrambler program should (preferably) show a visual image of the colours of Megaminx after the scrambling (random colour scheme or take the latest Mefferts tiled colour scheme).

Thanks,

Ron

[jaap]

I really like this idea, too.

The only question that remains is whether the number of moves in the scramble has to be increased, and if so by how much.

It is clear that the set of move sequences this new method generates is a subset of those of the old method, so the scramble length will need to be at least as much as before for an equally fair scramble.

I'll need to think about that length issue a bit further, though my gut instinct says it shouldn't make much difference. With this new method we can however use much longer scrambles without using more time. I think the 60 moves we do currently is a compromise - as short as we could get away with to get reasonable scrambles, but probably not quite enough to be really fair.


Here is a really simple scramble length estimation method.

The Mexaminx has 120 corner-edge pairs.
Assumption: A scramble should be at least long enough that every such pair is likely to be separated at some point.
Every move splits 10 of the 120 pairs, or one twelfth.
Assuming that during a scramble the corner-edge pairs that have not yet been separated are fairly evenly distributed over the puzzle, every move will split one twelfth of those, leaving 11/12 of the pairs untouched.
The number of unsplit pairs after n moves is therefore about
120 * (11/12)^n
and this falls below 1 after 56 moves.

While 60 moves is likely to split all the pieces up at some point, they might not be separated as much as the average truly random position. This new method, using 90-100 moves or so, will certainly be better.

Jaap

[StefanPochmann]

1) Can we say anything about the "scientific" state of the scrambling of Megaminx?

I don't know of any analyses, but here are a few ideas that could be analyzed by looking at the effects of many scrambles:

- Number of unbroken CE pairs after N moves, for N up to let's say 200. This should stabilize after a while, and we should find out when it does, and do a few more moves than that.

- Average distance to home position for each corner or edge after N moves. This should also stabilize at some point, and the expected value should be easier to compute than the unbroken pairs value.

To put it differently: if we would do 100 moves like this, would the Megaminx be thoroughly scrambled?

It looks good to me. I have solved the above scramble a few times, with different solution paths, and it felt normal.

Is there any guess about the maximum depth of Megaminx?

I never heard of one.

How would the current scrambling and your proposed scrambling compare? Harder, easier, roughly the same?

I think the same or very similar. The above two statistics could help determine which is better (i.e., stabilizes the values earlier).

Now an improvement...

I thought I use many more "two fifth" turns than "one fifth" turns when I scramble for practice, and I just checked it and it turns out I do 2/5 turns *exclusively*. And they look better, too. Try just the first line of the above scramble:
R- D- R++ D+ R+ D- R- D- R+ D-

It leaves a large part of the megaminx untouched. Now undo that and instead do:
R-- D-- R++ D++ R++ D-- R-- D-- R++ D--

That's the same but all 1/5 turns turned into 2/5 turns. It has effects all around the megaminx. I then tried this scramble:

R++ D++ R-- D++ R++ D-- R++ D-- R-- D++
R++ D++ R++ D-- R++ D++ R-- D-- R-- D--
R++ D-- R++ D++ R++ D++ R-- D-- R-- D++
R-- D++ R++ D++ R++ D++ R-- D-- R++ D--
R-- D-- R-- D-- R++ D-- R-- D++ R-- D--
R-- D++ R++ D-- R++ D++ R-- D++ R++ D++
R++ D++ R++ D-- R++ D++ R-- D++ R-- D++
R++ D-- R-- D-- R++ D-- R-- D-- R-- D--
R++ D++ R++ D++ R-- D++ R++ D-- R++ D--
R-- D-- R++ D++ R++ D-- R++ D++ R++ D++

After the first sixty moves, there was not a single unbroken pair left.

[StefanPochmann]

It is clear that the set of move sequences this new method generates is a subset of those of the old method, so the scramble length will need to be at least as much as before for an equally fair scramble.

Not necessarily. Think about the 3x3 and our usual 25 move scrambles, forbidding parts like LR'L2R. They're a subset of the set of all 25 move algorithms, but their quality is *better*.

[jaap]

It is clear that the set of move sequences this new method generates is a subset of those of the old method, so the scramble length will need to be at least as much as before for an equally fair scramble.

Not necessarily. Think about the 3x3 and our usual 25 move scrambles, forbidding parts like LR'L2R. They're a subset of the set of all 25 move algorithms, but their quality is *better*.

I see what you mean. I did indeed skip a few steps between "the set of move sequences this new method generates is a subset of those of the old method" and my conclusion "the scramble length will need to be at least as much as before", and those steps are far from watertight proof. Even so, I don't think it would be reasonable to claim that conclusion was not true.

[StefanPochmann]

Oh and Dan Harris found the z rotation hard/confusing and suggested y instead. I myself didn't have trouble with z but y does have the advantage (?) that all two consecutive moves (of the 100 moves total) turn two adjacent faces. I'd prefer 2/5 turns, though, so each line should end with either y++ or y--:

R++ D++ R-- D++ R++ D-- R++ D-- R-- D++ y++
R++ D++ R++ D-- R++ D++ R-- D-- R-- D-- y++
R++ D-- R++ D++ R++ D++ R-- D-- R-- D++ y--
...

That would also make the rotation explicit so people can't forget to do the puzzle rotation at the end of each line.

[StefanPochmann]

Ok, I described my notation/scrambler on my website and there's also a generator giving you a few new scrambles every time you visit it:

http://www.stefan-pochmann.info/spocc/other_stuff/tools/scramble_megaminx/

[Ron]

Hi Stefan,

Thanks as always for your contribution to our community.

Three questions:
1) Can WCA freely use your idea and program for competitions?
2) Can we (or will you) make some changes to the program? We need a little explanation and move notation picture on the top of the page. We also want to generate 5 scrambles by default instead of the current 10.

Thanks,

Ron

[StefanPochmann]

Three questions? You forgot one?

Yes, you can modify and use it any way you like. Competitions are what I ultimately made it for. In practice, I might stick to just my humanrandom scrambling because I'm still faster with that, unless we find out that fewer moves are sufficient.

Currently it's written in PHP and I think I remember you prefer Javascript because it runs everywhere simply in a browser. So if it shall be equivalent to the WCA scramblers, it should be translated to Javascript. The code is really simple, as there's no need to check for trivial cancelations, but I'll make it available anyway tonight.

I'll work on the scramble quality analysis, last night I realized that this fits neatly into my diploma thesis. Would be nice if someone else could do the Javascript translation and the changes you'd like.

[JohannesLaire]

Would be nice if someone else could do the Javascript translation

I can write a JavaScript version. I'll post a link when it's ready.

[JohannesLaire]

Here: http://funktio.awardspace.com/misc/mm_scrambler/.

If someone does the little explanation and move notation picture, I'll add it.
Feel free to do anything you want with it.

[Kenneth Gustavsson]

At Speedsolving.com I asked if it may be OK to use this new notation at the Cube Day?

Stefan told it's better to wait and also that questions like that is better asked here and not at Speedsolving. I was avare of that but could not remember my log in...

Now i did

So,I aks the same question again, (sligtly modified doe =)

If this new methos shows to be good as the old one before the Cube Day, is it Ok to use it there then.

the main reason for my question is that someone of us have to learn to scramble the Megaminx before the competition and then why not learn the new style right away?

But, is that compatible with the WCA rules? Arnaud told me that it probably is because the rules say one shall use a computer generated scramble of at least 60 moves bot not much more.

So?

[Ron]

Three questions? You forgot one?

Yes, the third question was whether you could make a Javascript version of it.

I tested the Megaminx scrambles a bit manually, and they feel like regular scrambles. Definitely much better than the official 5x5x5 scrambles, which I think are in general easier than manual scrambles.

I will wait for Stefan's analysis, but they way it looks now, I want to propose this scramble program for the 2008 version of the WCA regulations.

Thanks,

Ron

[Kenneth Gustavsson]

I will wait for Stefan's analysis, but they way it looks now, I want to propose this scramble program for the 2008 version of the WCA regulations.

My interpretation of that is: we shall not use this new style before 2008.

So there will be the old style at the Cube Day =)

[BryanLogan]

So is the "Y" turn always suppose to be a +- 2?

Anyways, this looks much easier to teach scramblers that aren't cubers.

[StefanPochmann]

So is the "Y" turn always suppose to be a +- 2?

Yes. Though, this is one thing I might change. Always being +/- 1 would have the advantages of being yet easier to do and of immediately (with the following R turn) breaking the CEC triple that used to be safe at the upper left for a while.

[BryanLogan]

I was just curious that it was always 2. I'm not sure if I'd go to always 1, but I suppose that would be better than fluctuating between 1's and 2's.

[perfredlund]

Hi

I know it's bad netiquette to reopen old discussion threads, but i felt i had to comment!

Why oh why use x or y for physical turns of the MM?? This seems like a VERY bad idea. The MM is not a cubical shaped puzzle. Instead one should use the face names to designate physical turns. There's a number of notations that do this on the cube(s). QR or Rc etc ... All these rotate the cube like R (and the rest of the cube turns together with the R layer. Especially since scarmblers at competitions often are not puzzlers at all i think it's quintessential to have an easy notation. I don't hold zyz as easy notation despite the fact that it can be learnt easily. By easy i mean intuitive, reducing notational tokens to a minimum

Happy scrambling !!

-Per