# Sortega!



## Lucas Garron (Nov 8, 2010)

In case you missed the party, there's a new 2x2x2 method on the block*, thanks to qq.



qqwref said:


> 2x2 method idea:
> 0) 2x1 bar of the same color on left half of D face.
> 1) Orient remaining 6 pieces without messing up the bar.
> 2) Finish sorting by placing the other two pieces of the D color.
> ...


(NOTE: I changed the word "block" to "bar" un qq's description to match terminology conventions.)


Here are some algs.

Talking about it with qq, we came across a lot of interesting properties new to this method. I'm definitely planning to learn it and play around with it.
There are also a lot of opportunities for improvement. My guess is it'll be incorporated into fast solvers' toolsets more clearly.

By the way, my favorite property is how every 2-gen move gets you closer to solved while still being a sortega case. I call this "cascading" and it doesn't show up very much in cubing: Square-1 shapes, and as qq pointed out, some versions of Roux L6E.

*It's not actually on the block. That's supposed to be a terrible pun.

EDIT: This method is rather new and experimental. It should be pretty clear to you how it works if you're familiar with 2x2x2 speedsolving, but nevertheless, here are 5 random sample solves: 1 2 3 4 5


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## 04mucklowd (Nov 8, 2010)

I already use this method for some cases that I get
It is nice that it now has a name


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## Erik (Nov 8, 2010)

So in fact it's just Guimond with some more cases you can start from (since guimond requires this pattern of 3). The feature of 2-gen ness if you also have the same colour of the first block is nice. Only 3 possible orientation cases = yummy. Might learn it for fun one day when I have spare time (will be like.. never  )


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## qqwref (Nov 8, 2010)

As I said in the other thread, I was surprised at how nicely the orientation step worked out when restricted to 2gen only. I had a feeling some cases would end up kinda long, so Lucas's short algs are a pleasant surprise.



Erik said:


> So in fact it's just Guimond with some more cases you can start from (since guimond requires this pattern of 3).


Well, one benefit over Guimond is in the sorting step. Since there are only 2 pieces to trace, you can easily look ahead to sort during the solve. Thus you can be decently fast without actually seeing the sort step in inspection (in Guimond you would often have to look at D).


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## Erik (Nov 8, 2010)

QQ that's what I meant with 3 possible orientation cases ;-) (probably named it wrong)

EDIT: I think with Sortega it might be a bit hard to predict this orientation/separation case since, mostly in a solve where I use the XLL algs I can see everything up till the XLL case in inspection (no matter if it's Ortega/Guimond/last piece + orient/method with no name)


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## Godmil (Nov 8, 2010)

I haven't got a 2X2 yet, though I will be getting one soon. Would you recommend going head first into this method? The order of the algs makes it look like it could be learned in phases (starting with having all the bottom layer oriented then just 3 cubies oriented, before going for just 2. It seems attractive as an advanced method that gets easier to set up the more algs you learn.


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## StachuK1992 (Nov 8, 2010)

Learn Ortega first.
That should take you about 5 minutes.
Then go for this if you want, but it's an upcoming method, not very experimented yet.


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## joey (Nov 8, 2010)

Similar to SOAP.


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## masterofthebass (Nov 8, 2010)

joey said:


> Similar to SOAP.


 
hardly... there's no separation first here.


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## theace (Nov 8, 2010)

So. Many. Algs. ... O_O


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## StachuK1992 (Nov 8, 2010)

theace said:


> So. Many. Algs. ... O_O


 
Dude. They're like 5 moves long.
And only 84 or something.


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## Lucas Garron (Nov 8, 2010)

StachuK1992 said:


> Dude. They're like 5 moves long.
> And only 84 or something.


Well, 72. Not only are they shorter, you'd be silly to learn them as individual "algs." For each alg, you only have to learn a move or two to reduce it to the next (sort of like F2L).


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## Toad (Nov 8, 2010)

Do I learn this or do I learn CLL?

Which first?

EDIT:



Lucas Garron said:


> Well, 72. Not only are they shorter, you'd be silly to learn them as individual "algs." For each alg, you only have to learn a move or two to reduce it to the next (sort of like F2L).


 
Kinda like sq1 cubeshape?


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## Toad (Nov 8, 2010)

Please please do!! I really wanna learn this.


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## qqwref (Nov 8, 2010)

You don't even have to do them as algs to start. In my test runs I did the orientation part using only intuition and Ortega orientation algs.


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## FatBoyXPC (Nov 8, 2010)

This method looks fun. I was actually about to just go learn EG1, but I might look into this more. I guess this would definitely be better if I started learning PBLs from various angles. Stachu, I'm really interested in seeing the chart you're going to make!


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## Lucas Garron (Nov 8, 2010)

StachuK1992 said:


> I'm going to make a cubeshape-like progression chart for this.


Hmm, I already have picture of the cascading graph. But it might be annoying to make it usable, so go ahead. Do you want a list of optimal algs for each case, full graph data. or something?



fatboyxpc said:


> I guess this would definitely be better if I started learning PBLs from various angles.


Yeah, I've been playing with it all day, and it feels much cooler do do PBL if you always start holding the cube the same way (and much easier to do AUF/ADF variations consistently).




qqwref said:


> You don't even have to do them as algs to start. In my test runs I did the orientation part using only intuition and Ortega orientation algs.


True, but I think the cool part comes from the (previously) unintuitive tricks. Not even the regular OCLLs stay the same.


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## Lucas Garron (Nov 8, 2010)

StachuK1992 said:


> If you could send the pictures and optimal algs, that'd be appreciated.
> email


 
Was about to post something, but then my computer did its lovely crashing thing.

Nevertheless, here's a CSV of the 243 cases; you can get customized images from the second column through VisualCube, and you can decide how to lay out the graph.
http://cube.garron.us/sortega/sortega.csv


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## FatBoyXPC (Nov 8, 2010)

Lucas Garron said:


> Yeah, I've been playing with it all day, and it feels much cooler do do PBL if you always start holding the cube the same way (and much easier to do AUF/ADF variations consistently).



Yeah, I've already looked at doing the PBL that's double bars in back (J perm on U and D) in the front (basically doing the inverse mirror of lefty version, I guess?) and if I were to practice it I could get it really close to as fast as I do the on in the back. So I'd need to learn how to do that same PBL with bars on R and L, and then the J/Y perm on R, L, and B as well. It would probably also help to know a J and Y perm on D so I can avoid a rotation. Ideally I should learn the Guimond separation cases from all angles too, but maybe not if I can get this Sortega method down


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## riffz (Nov 9, 2010)

Anyone know the probability of getting an unpermuted bar after a random scramble? (Step 0)

This looks really cool. Guess it's another thing I have to put on my memo list, but BLD COMES FIRST DAMMNIT.


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## vcuber13 (Nov 9, 2010)

riffz said:


> Anyone know the probability of getting an unpermuted bar after a random scramble? (Step 0)
> 
> This looks really cool. Guess it's another thing I have to put on my memo list, but BLD COMES FIRST DAMMNIT.


 
what are you learning new for blind?


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## Escher (Nov 9, 2010)

I don't know about this being a completely new idea (practically nothing ever is in 2x2 these days) but awesome job actually going ahead and making it a reality 

Might learn it, has a great potential for one (and '1.5') look solves if you traced CP in inspection.

Exciting stuff


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## riffz (Nov 9, 2010)

vcuber13 said:


> what are you learning new for blind?


 
Mostly working on solidifying my blindfold images list, as well as my speed optimal corner cycles.


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## Anthony (Nov 9, 2010)

Pretty sexy. I'll probably learn a bit (all eventually?) just to throw into my arsenal for when scrambles suck for EG.


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## qqwref (Nov 9, 2010)

Lucas: Might I suggest re-formatting your site in the following way:
- Break the table into 9 visually separated sub-tables, and provide opaque 2D views (top layer for a case, bottom layer for a case group) instead of transparent 3D views. It's just a bit hard to see what's what at a glance.
- Break the algs into two parts. Generally there is one part that's just a bunch of moves, and then one part that's R Ux R' or R' Ux R. The exceptions are R, R2 U2 R, and the triggers. I think this would push full mastery back by a few hundred solves, but actually learning the algs will be a lot quicker.


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## FatBoyXPC (Nov 9, 2010)

Thank you so much for those suggestions, qq. The one about the opaque views has been bothering me but I just let it go since I knew stachu was going to be making a chart. Then your point about the algs, there was something else that was just slightly under my skin but I couldn't place it, and I think that will fix it!


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## Lucas Garron (Nov 9, 2010)

qqwref said:


> Lucas: Might I suggest re-formatting your site in the following way:
> - Break the table into 9 visually separated sub-tables, and provide opaque 2D views (top layer for a case, bottom layer for a case group) instead of transparent 3D views. It's just a bit hard to see what's what at a glance.
> - Break the algs into two parts. Generally there is one part that's just a bunch of moves, and then one part that's R Ux R' or R' Ux R. The exceptions are R, R2 U2 R, and the triggers. I think this would push full mastery back by a few hundred solves, but actually learning the algs will be a lot quicker.



Only two-gen algs, and without trying to make them easy to understand:
http://cube.garron.us/sortega/files/sortega_1_0.pdf


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## HaraldS (Nov 9, 2010)

Sweet method  Would be fun to have algs that solve the rest in one step after the orientation step!


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## deepSubDiver (Nov 9, 2010)

Decent idea with the sorting. Fortunately I already know half of the orientation algs since I compiled a HTW set some time ago


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## FatBoyXPC (Nov 9, 2010)

I feel like a noob for posting this, but for "top view of bottom" you mean as if you can see through the top layer, NOT as if you do an x2? I'm also having issues following this since you're counting opposite colors as the same, unless I missed somewhere how that's the intention (but I really thought there wouldn't be any separation here).

Edit:
I'm doing some experimenting with the algs on my 2x2 and it appears as though the you are supposed to "see through" instead of x2. Although I'm still unsure about this separation question, as of why the opposite colors are white on the spreadsheet and all the other colors are black.

Edit 2:
I see that's why there are multiple algs now. Without brute force doing and memorizing, is there any way to logically sort out which ones separate?


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## Lucas Garron (Nov 9, 2010)

fatboyxpc said:


> I feel like a noob for posting this, but for "top view of bottom" you mean as if you can see through the top layer, NOT as if you do an x2? I'm also having issues following this since you're counting opposite colors as the same, unless I missed somewhere how that's the intention (but I really thought there wouldn't be any separation here).


I knew this would be unclear, so I just tried to use the common term ("top view" as opposed to "bottom view"). I think a few people would use this chart without thinking about it, but if not, testing a few alg inverses should make it clear.

I think this is a better way to do it because you can visualize both halves of the cube from the same side instead of using cumbersome (physical or mental) rotations. See http://cube.garron.us/sortega/sortega-split.htm.

If anyone really wants it the other way, just switch the images between rows 4<->8, 5<->7, 6<->9.



fatboyxpc said:


> Although I'm still unsure about this separation question, as of why the opposite colors are white on the spreadsheet and all the other colors are black.


I posted an alg sheet, not a tutorial, so look at the method description. After the bar, you first orient the other 6 pieces, _then_ go straight into sorting.



fatboyxpc said:


> Edit 2: I see that's why there are multiple algs now. Without brute force doing and memorizing, is there any way to logically sort out which ones separate?


Hmm? That has nothing to do with the multiple algs; those are just for mathematical completeness.

The best thing would be to look at the AUF and the first R turn, then look at the cube again and repeat.


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## Lucas Garron (Nov 9, 2010)

deepSubDiver said:


> Decent idea with the sorting. Fortunately I already know half of the orientation algs since I compiled a HTW set some time ago


Do you mean Human Thistlethwaite? That would be an odd way to abbreviate it since the second syllable of "Thistlethwaite" doesn't begin with the "w" and HTA is a more common abbreviation.

And with "know half the algs" do you mean "know algs for half the cases" or "know good/optimal algs for half the cases"? When I started out with SS, I knew an alg for every case, but I could hardly say I knew any of SS.


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## qqwref (Nov 9, 2010)

I propose HÞÞ as an abbreviation for Human Thistlethwaite.

Any movecounts for Sortega? I don't care about step 0 but I'd like to see what a typical step 1+2 (with cancellations) would be in HTM/QTM.


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## FatBoyXPC (Nov 9, 2010)

I apologize if you feel this has already been answered, but to be clear, this method does still involve a separation step then?


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## qqwref (Nov 9, 2010)

Yes, it's right after the orientation step, but it's easier than the Guimond separation because the left half of the bottom face is already sorted.


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## FatBoyXPC (Nov 9, 2010)

Alright, thanks. It does allow for a nice separation case though, you don't have to worry about separation from various angles. It'll be quick recognition as well. I've also noticed a decent handful (I haven't counted an actual number, I just did some cases in reverse and noticed this) of these algs are also quite intuitive.


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## Lucas Garron (Nov 9, 2010)

qqwref said:


> I propose HÞÞ as an abbreviation for Human Thistlethwaite.
> 
> Any movecounts for Sortega? I don't care about step 0 but I'd like to see what a typical step 1+2 (with cancellations) would be in HTM/QTM.



Step 0, bar)
No idea, but I think the average is less than 1. This method is probably best used when this step can be skipped by finding a bar with a nice orientation case.

Step 1, orientation)
Pure 2-gen HTM, all cases are equally likely:
{1, 1, 3, 9, 21, 33, 51, 69, 49, 6}
Mean: 7.247

Step 2, separation)
Same 2-gen, HTM, all cases are equally likely:
{1, 1, 3, 2, 6, 2}
Mean: 4.133

Step 3, PBL)
However you want to do it.

Step 1+2 are 11.38 if you never try to pick any easy cases, always stay 2-gen (even when something else is really obvious), and don't cancel the last move.
In practice, there are often a few choices for starts, you can always make a cancelation decision at the end of orientatio, and there are quite a few better algs out there, so I'd expect under ten moves to PBL.

I just did 10 random scrambles with pure Sortega (from the alg sheet), not even trying too hard:
11.00, 8.00, 10.00, 10.00, (12.00), 7.00, 8.00, 10.00, 9.00, (6.00), 11.00, 10.00 > 9.40 moves to PBL




fatboyxpc said:


> I apologize if you feel this has already been answered, but to be clear, this method does still involve a separation step then?


Step 2.


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## FatBoyXPC (Nov 9, 2010)

I see that now, thanks to qqwref, but thank you as well  Curious though, how are you seeing 6 separation cases? Or is that counting AUF?


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## qqwref (Nov 9, 2010)

He must be counting AUF.

For the purposes of combining steps 1 and 2 there are only really 4 possible orientation cases: solved, R2, and the two single corner cases. (The opposite one can always be avoided.)


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## FatBoyXPC (Nov 10, 2010)

Which single corner case can always be avoided? The one that has diagonal swap on top and bars on bottom?

Edit: I kind of feel stupid now, I think you meant the one that is typically a R2 U' R2 for separation. What about the R2 U' R2 U' R2 case then, I'm guessing it's just as avoidable?

Edit 2: My question has been answered.


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## reThinking the Cube (Nov 11, 2010)

WOW. This method (Blocktega™) is fantastic.

Special THANKS to Michael Gottlieb and Lucas Garron for making this contribution.:tu

I would like to add:

1) The are TWO frames of reference for the 2x1x1 block. Cube rotation (x2 z') will create the alternative top/bottom patterns from what was the R/L faces. A better Step#1 (orienting) case is often made possible by changing to the other frame of reference. 

2) ALL the Step#1 algs end with a *R* turn, which can sometimes be substituted with a *R'* to get a better Step#2 (sorting) case. It was not mentioned specifically, but this is how the worst case can be avoided.

3) PBL and sorting skips are more likely with this method, but it is going to depend on the alg that is used for the Step#1 case. To take advantage of this, the full color patterns of the algs that will yield a Step#2 and PBL skip, must be known. Some *natural skip* cases could be shown on Lucas's Step#1 chart, by performing the alg inverse, and then placing an indicator (i.e. small black dot) on the stickers that correspond to the color of the D-face color of the 2x1x1 block. Any sticker without a dot, would be a U-face color. This way the potential *lucky* skip patterns can also be shown - without detracting from the main *two colors treated as one* patterns.


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## riffz (Nov 11, 2010)

reThinking the Cube said:


> 1) The are TWO frames of reference for the 2x1x1 block. Cube rotation (x2 z') will create the alternative top/bottom patterns from what was the R/L faces. A better Step#1 (orienting) case is often made possible by changing to the other frame of reference.


 
The 2x1x1 block doesn't have to be permuted.


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## qqwref (Nov 11, 2010)

reThinking the Cube said:


> 1) The are TWO frames of reference for the 2x1x1 block. Cube rotation (x2 z') will create the alternative top/bottom patterns from what was the R/L faces. A better Step#1 (orienting) case is often made possible by changing to the other frame of reference.


Not really, because you are just looking for a 2-piece block of one color - the other two adjacent stickers don't have to be the same. Only 1/3 of the possible blocks will remain blocks when you do that cube rotation. (However, it IS often true that scrambles will have more than one of these blocks, in which case you can indeed choose the easiest orientation.)



reThinking the Cube said:


> 3) PBL and sorting skips are more likely with this method, but it is going to depend on the alg that is used for the Step#1 case.


Wait, why?



reThinking the Cube said:


> To take advantage of this, the full color patterns of the algs that will yield a Step#2 and PBL skip, must be known. Some *natural skip* cases could be shown on Lucas's Step#1 chart, by performing the alg inverse, and then placing an indicator (i.e. small black dot) on the stickers that correspond to the color of the D-face color of the 2x1x1 block.


I suppose this could be useful, but I think the added data would end up making the algs harder to learn. I think an experienced user of this method would end up learning the skip cases on their own anyway.


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## y3k9 (Nov 11, 2010)

Make a video tutorial??? Learning through text is hard.


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## cuBerBruce (Nov 11, 2010)

My calculations for step 0 indicate there are 3518746 positions having at least 1 pair of adjacent stickers of the same color on some face. There are 154994 positions that require 1 move, and 420 positions that require 2 moves. That means step 0 (color neutral) requires an average of about 0.0424 moves.


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## DavidWoner (Nov 11, 2010)

qqwref said:


> Yes, it's right after the orientation step, but it's easier than the Guimond separation because the left half of the bottom face is already sorted.


 
God it's irritating when people don't know how to use Guimond.


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## reThinking the Cube (Nov 11, 2010)

qqwref said:


> Not really, because you are just looking for a 2-piece block of one color - the other two adjacent stickers don't have to be the same. Only 1/3 of the possible blocks will remain blocks when you do that cube rotation. (However, it IS often true that scrambles will have more than one of these blocks, in which case you can indeed choose the easiest orientation.)



All right then, Sortega! Step#0 doesn't require a block, but just 2 adjacent stickers of same/opposite colors. I was under the impression of Lucas's method description, which made it appear differently. Sorry for any misunderstanding. I have been playing around with this method (starting off by making an actual 2x1x1 permuted block) and I really like it - ALOT! To avoid confusion, from now on, I will call this true block 1st method - Blocktega™  

PBL's are quicker/and skipper with that DL block already done. And like I mentioned above, you have 2 frames of reference to get a good orientation case (if you have a 2x1x1 block as opposed to a 2x1 patch (bar) of color).

@Bruce - What % of scrambles contain 2x1x1 permuted block in 0-moves, 1-move, and 2-moves?

EDIT: I see now that Lucas has just changed his description from *block* to *bar*, and that makes a big difference in interpretation. Thanks.


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## FatBoyXPC (Nov 11, 2010)

The first post (quote by qqwref) states the block is to be the same color. It does make PBL recognition easy, though.


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## qqwref (Nov 11, 2010)

cuBerBruce said:


> My calculations for step 0 indicate there are 3518746 positions having at least 1 pair of adjacent stickers of the same color on some face. There are 154994 positions that require 1 move, and 420 positions that require 2 moves. That means step 0 (color neutral) requires an average of about *0.0424* moves.


Haha. Very nice.



DavidWoner said:


> God it's irritating when people don't know how to use Guimond.


Sorry that I'm not familiar with all the speed optimizations that the fastest 2x2 solvers use. I don't actually use that method in practice. For future reference, what's your solution to a scramble like R2 D R2 D R' U' R'?



reThinking the Cube said:


> To avoid confusion, from now on, I will call this true block 1st method - Blocktega


Go ahead and call it that, although you ought to realize that people who see that name will think "ortega with a block", not "sortega with a block", given the respective popularities of those two methods. Comparing half a face to half a layer, I observe that step 1 and 2 are unchanged and step 0 is slightly longer on average. As for PBL we have the following probabilities:
Sortega: solved 1/36, J 8/36, Y 2/36, J/J 16/36, Y/J 8/36, Y/Y 1/36.
"Blocktega": solved 1/12, J 5/12, Y 1/12, J/J 4/12, Y/J 1/12, Y/Y 0/12.

So the great cases (solved and Y/Y) occur 2/36 of the time in the normal case, but 3/36 of the time (slightly more) in your variant. However, the icky cases (pure J and pure Y) occur 10/36 of the time in the normal case, but 18/36 of the time (half!) in your variant. Personally I would prefer slightly fewer skips if it means much fewer ugly cases.


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## Lucas Garron (Nov 11, 2010)

cuBerBruce said:


> That means step 0 (color neutral) requires an average of about 0.0424 moves.


Awesome. On top of that, there are often several choices for a block, which allows you to reduce the total moves. It's as if the move count for step 0 were negative. 



reThinking the Cube said:


> EDIT: I see now that Lucas has just changed his description from *block* to *bar*, and that makes a big difference in interpretation. Thanks.


I made that change a while before your first post.


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## riffz (Nov 11, 2010)

@reThinking: I agree with QQ that it's better to use a block that actually isn't permuted correctly. In those cases the odds of getting a Y or J perm are higher, and most of the time there would be an easy first layer solution to lead up to EG or CLL anyway. In my opinion, the strength of this method is that you can use it when there is not an easy/obvious first layer solution.


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## cuBerBruce (Nov 11, 2010)

For reThinking the Cube, here are my calculations for a 1x2x2 block.

0 moves: 1589005 positions
1 move: 1776613 positions
2 moves: 308522 positions
3 moves: 20 positions
Average: 0.6515 moves

As already noted by qqwref and riffz, from my experience with using the "Ortega Corners" method, I was also thinking that it is probably better to not use a "block" than to use a "block."

I learned the "Ortega Corners" method from a booklet published in 1981. The Jelinek/Ortega web pages describing the Ortega method say it is based upon Minh Thai's book which was published in 1982. This certainly seems to suggest to me that Ortega was not the first to publish the "Ortega Corners" method, yet the speedcubing community seems to give Ortega all the credit for it.


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## qqwref (Nov 11, 2010)

We're certainly not the first community to name things after someone who wasn't the first to discover it - many mathematical theorems are named this way. I think the problem is that it is difficult to determine who really thought of something first (and this is especially difficult in cubing history because of the number of unpublished discoveries plus the difficulties of actually getting books/pamphlets from that era). Of course, once you do, you would still have to change years of the habit of calling a method a particular thing (and years of websites/videos/posts cannot be changed easily).


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## StachuK1992 (Nov 11, 2010)

qqwref said:


> We're certainly not the first community to name things after someone who wasn't the first to discover it.


 *coughnewtonsmethod*


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## reThinking the Cube (Nov 12, 2010)

cuBerBruce said:


> For reThinking the Cube, here are my calculations for a 1x2x2 block.
> 
> 0 moves: 1589005 positions
> 1 move: 1776613 positions
> ...



Thanks Bruce. How many contain a 1x1x2 block that can be created for the position (and hypothetically rotated to DL) that would also at the same time put the remaining 6 corners in a 2-gen <U,R> solvable state? 

@qqwref - What are the PBL case probabilities that will result from BLOCKTEGA™ solving 2-gen <U,R> cubes like the ones above? 

@Woner - Guimond [R2 D R2 D R' U' R'] reference?


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## qqwref (Nov 12, 2010)

reThinking the Cube said:


> Thanks Bruce. How many contain a 1x1x2 block that can be created for the position (and hypothetically rotated to DL) that would also at the same time put the remaining 6 corners in a 2-gen <U,R> solvable state?


This doesn't completely answer your question, but when you randomly solve a block on a random cube, you have a 1/6 chance that the rest can be solved 2-gen. It might be interesting to look at how many moves on average it takes to bring the cube to a 2-gen solvable state (i.e. a block with the remaining corners permuted in the proper way). This could be considered a very advanced Sortega variation, but I'm not sure it's feasible, as you'd have to either check an average of 6 block solutions (takes a while) or be able to modify a block solution to make the rest 2genable (seems hard). Of course, whichever you do, you'd then have to lookahead enough to at least see step 1 in inspection, or else you'd end up with a slow time. It would be pretty neat to have a (nearly) entirely 2gen solve.



reThinking the Cube said:


> @qqwref - What are the PBL case probabilities that will result from BLOCKTEGA solving 2-gen <U,R> cubes like the ones above?


A Sortega solve which results in a complete 2-gen solution has only two possible PBLs: solved and N/J (with the J on the right side). Each has a probability of 1/2. You can always avoid N/J during the separation step (by just putting in the two D layer pieces in differently).


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## DavidWoner (Nov 12, 2010)

qqwref said:


> For future reference, what's your solution to a scramble like R2 D R2 D R' U' R'?



R U L x' U' R2 U' R2

I find that a diagonally permuted bar > adjacent > permuted. R2F2R2 and the one bar cases with the bar on top are the best PBLs, which are worth the risk of getting Y on bottom. Adjacent will always force the D-layer bar to be at DF or DB which means you shouldn't need to rotate for 2bars. Though you will never get any skips, you will also not get Yperms ever. Permuted of course has the decent possibility of getting a skip, especially if you force the layer, but the other possible PBLs are not the best.

Some more example solves:


Spoiler



R2 F' U2 R F' U F' U' F
x2 y U' R U' R' U' F2 (2bar)

U2 R U' F' R2 U F2 R' U'
x2 y R U2 R' U R D R2 (2bar)

F U2 F U' R F2 R2 U'
z y' R' U2 R U' R' (2bar) hurrrr

R U F' U' F' R2 U F2 R'
z y F' U2 L' U L' U L2 (J)

F U2 R' F U2 R' F' U' F' 
z' y U R' U' R U2 R2 (2bar)

U' R F U2 R2 U' F' R2 F2
y' R U R' U' R U2 R (1bar)
 
F' R F' U' F U2 R2 F' U2
y R U' R' U' R U' R' (U2 + y') R2 (2bar)

R U R2 F' U F' U2 F U2
R' U R' U' R2 U' R2' (J) or U' R' U2 R' U' R U' R' (J) depending on if you like R2s

U F2 R2 U R2 U F' U2
y x2 U2 R U' R2 U' F2 R2 U'

U2 F R' F R F2 U2 R' F
z F' U R U R' (J)



Just the first 10 scrambles I got.


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## deepSubDiver (Nov 13, 2010)

Lucas Garron said:


> Do you mean Human Thistlethwaite? That would be an odd way to abbreviate it since the second syllable of "Thistlethwaite" doesn't begin with the "w" and HTA is a more common abbreviation.


I will refer to HTA in the future, thanks.



Lucas Garron said:


> And with "know half the algs" do you mean "know algs for half the cases" or "know good/optimal algs for half the cases"? When I started out with SS, I knew an alg for every case, but I could hardly say I knew any of SS.


This means I compiled a complete set for orienting the Corners for the appropriate substep in HTA and learned a few of them. Thus, Sortega orientation is a subset of that HTA set.

In case anyone is interested, here is my compilation (2-Gen, HTM, DLF/DLB oriented):


Spoiler



Legend:
+: turned clockwise
-: turned counterclockwise
/: oriented

Order: URF ULF ULB URB DRF DRB

```
Building transition table: 0[1], 1[1], 2[3], 3[9], 4[21], 5[33], 6[51], 7[69], 8[49], 9[6], nodes: 243, excluding symmetrical cases: 72

HASH || STATE  --> SOLUTION
---------------------------
1368 || ++++-/ --> RU2RU'RU2R, RU2RU'RU2R',
1365 || ++++++ --> RUR2UR, RUR2UR', R'UR2UR, R'UR2UR',
1362 || ++++/- --> R2UR'U'RU2R, R2UR'U'RU2R', R2U2RU2RU'R, R2U2RU2RU'R', R2U2R'U2RU'R, R2U2R'U2RU'R',
2649 || +--+-+ --> R2U2R'UR2U2R, R2U2R'UR2U2R', R2U2R'U'R2U2R, R2U2R'U'R2U2R', R2U'RU'RU'R, R2U'RU'RU'R',
1353 || ++/+-+ --> RU2R2U'RU2R, RU2R2U'RU2R', R2U2R'U'RU2R, R2U2R'U'RU2R', R2U'RU2RU'R, R2U'RU2RU'R', R2U'R'U2RU'R, R2U'R'U2RU'R', R'UR2U'R'U2R, R'UR2U'R'U2R',R'UR'UR2U'R, R'UR'UR2U'R', R'U2RU'R2UR, R'U2RU'R2UR', R'U2R2URU2R, R'U2R2URU2R',
2730 || ------ --> RU'R2U'R, RU'R2U'R', R'U'R2U'R, R'U'R2U'R',
1350 || +++/+- --> R'UR2U'RU2R, R'UR2U'RU2R',
2136 || -/++-/ --> R2UR, R2UR',
2640 || ++--// --> RUR'UR2U2R, RUR'UR2U2R', RUR'U'R2U2R, RUR'U'R2U2R', RU2RU'RU'R, RU2RU'RU'R', R'U2R'UR'UR, R'U2R'UR'UR', R'U'RUR2U2R, R'U'RUR2U2R', R'U'RU'R2U2R, R'U'RU'R2U2R',
1344 || +++/// --> R2UR'UR, R2UR'UR',
2328 || /+-+-/ --> RU'RU'RU2R, RU'RU'RU2R',
2721 || ----/+ --> R'U2R'UR'U2R, R'U2R'UR'U2R',
2370 || +/-+/- --> RU'R2U'RU'R, RU'R2U'RU'R', R2UR2U'R2UR, R2UR2U'R2UR', R2UR'URU2R, R2UR'URU2R', R2U'R2U'R2UR, R2U'R2U'R2UR', R2U'R'URU2R, R2U'R'URU2R', R'URU'R'UR, R'URU'R'UR', R'UR2URU'R, R'UR2URU'R',
2322 || /+-+/- --> R'U2R, R'U2R',
2712 || +----/ --> RU2R'UR2U2R, RU2R'UR2U2R', RU2R'U'R2U2R, RU2R'U'R2U2R', RU'RU'RU'R, RU'RU'RU'R',
2709 || ---+++ --> RU'RU'R, RU'RU'R',
2313 || /-+/-+ --> R2UR2U2R, R2UR2U2R', R2U'R2U2R, R2U'R2U2R',
2706 || --+-/- --> R'UR'U2R, R'UR'U2R',
2310 || -+//+- --> R2U2R'U2R, R2U2R'U2R',
2112 || -/+/// --> R2U'RU2R'U2R, R2U'RU2R'U2R',
2304 || -+//// --> R'U2R'U2R, R'U2R'U2R',
2697 || -/---+ --> RU2R2U'R'U2R, RU2R2U'R'U2R', RU2R'UR2U'R, RU2R'UR2U'R', RU'RU'R2UR, RU'RU'R2UR', RU'R2URU2R, RU'R2URU2R', R2URU2R'UR, R2URU2R'UR', R2UR'U2R'UR, R2UR'U2R'UR', R2U2RUR'U2R, R2U2RUR'U2R', R'U2R2UR'U2R, R'U2R2UR'U2R',
2694 || ---/+- --> R2U'R'UR'U2R, R2U'R'UR'U2R', R'UR2U'RU'R, R'UR2U'RU'R',
2688 || /---// --> R2U'RU'R, R2U'RU'R',
1098 || +/+/-- --> RU'R'U2R, RU'R'U2R', R2UR2U'R, R2UR2U'R',
1290 || /++/-- --> R'UR'U'RU2R, R'UR'U'RU2R', R'U2RU2RU'R, R'U2RU2RU'R', R'U2R'U2RU'R, R'U2R'U2RU'R',
1092 || +/+/+/ --> RUR, RUR',
1089 || /+/+/+ --> RU2RU'RU'RU2R, RU2RU'RU'RU2R', R2UR2U'R2UR'UR, R2UR2U'R2UR'UR', R2UR'URU'RU2R, R2UR'URU'RU2R', R2U'RU'R'U2RU2R, R2U'RU'R'U2RU2R', R2U'R2UR2U'R'UR, R2U'R2UR2U'R'UR', R2U'R2UR'URU'R, R2U'R2UR'URU'R', R'URU'RU2R'U2R, R'URU'RU2R'U2R', R'U2R'UR'U2RU2R, R'U2R'UR'U2RU2R',
2073 || /+-/-+ --> RU2R'UR'UR, RU2R'UR'UR', RU'RUR2U2R, RU'RUR2U2R', RU'RU'R2U2R, RU'RU'R2U2R', R'UR'UR2U2R, R'UR'UR2U2R', R'UR'U'R2U2R, R'UR'U'R2U2R', R'U2RU'RU'R, R'U2RU'RU'R',
1284 || +//++/ --> RU'R'U2RU2R, RU'R'U2RU2R', R2UR2U'R'UR, R2UR2U'R'UR', R2UR'URU'R, R2UR'URU'R',
2580 || -/+-+/ --> RU2R2U'R'UR, RU2R2U'R'UR', RU2R'URU'R, RU2R'URU'R', R'U2R2UR'UR, R'U2R2UR'UR',
2070 || -//++- --> R, R',
1281 || //++/+ --> R'UR, R'UR',
2064 || -//+// --> RU2R'U2RU2R, RU2R'U2RU2R', R'U2RU2R'U2R, R'U2RU2R'U2R',
2457 || -+-+-+ --> RU2R2UR, RU2R2UR', R'U2R2U'R, R'U2R2U'R',
2454 || +-+-+- --> RU'R'UR'UR'U2R, RU'R'UR'UR'U2R', R2UR2U2R'UR2U2R, R2UR2U2R'UR2U2R', R2UR2U2R'U'R2U2R, R2UR2U2R'U'R2U2R', R2UR2U'RU'RU'R, R2UR2U'RU'RU'R', R2U'R2UR'UR'UR, R2U'R2UR'UR'UR', R2U'R2U2RUR2U2R, R2U'R2U2RUR2U2R', R2U'R2U2RU'R2U2R, R2U'R2U2RU'R2U2R', R'URU'RU'RU2R, R'URU'RU'RU2R',
2058 || ///--- --> RU'R'UR, RU'R'UR', R2URU'R, R2URU'R',
2373 || +/-+++ --> RU2RU'R, RU2RU'R', R'U2RU'R, R'U2RU'R',
2448 || -+-+// --> R2U2R, R2U2R',
2052 || //-/+/ --> R'U2RU2R, R'U2RU2R',
2049 || -////+ --> RU'RU'R'UR, RU'RU'R'UR', RU'R2URU'R, RU'R2URU'R', R2URU2R'U2R, R2URU2R'U2R',
2442 || -+-/-- --> R2UR'UR'U2R, R2UR'UR'U2R',
2634 || --+/-- --> RUR'U2R, RUR'U2R',
2436 || -+-/+/ --> RU2R, RU2R',
2433 || -+-//+ --> R'UR'UR'U2R, R'UR'UR'U2R',
2628 || -+/-+/ --> RU'R2U'R'UR, RU'R2U'R'UR', RU'R'URU'R, RU'R'URU'R', R2URU'R'U2R, R2URU'R'U2R', R2UR2UR2U'R, R2UR2UR2U'R', R2U'RU'R'U2R, R2U'RU'R'U2R', R2U'R2UR2U'R, R2U'R2UR2U'R', R'UR2UR'UR, R'UR2UR'UR',
2625 || --+//+ --> R2UR'U2R, R2UR'U2R',
2646 || ++--+- --> RU2R2U'R, RU2R2U'R', R'U2R2UR, R'U2R2UR',
2724 || ----+/ --> R2U2RU2R'UR, R2U2RU2R'UR', R2U2R'U2R'UR, R2U2R'U2R'UR', R2U'RUR'U2R, R2U'RUR'U2R',
1032 || ///+-/ --> R2U'R'U2RU2R, R2U'R'U2RU2R', R'UR2U'R'UR, R'UR2U'R'UR', R'UR'URU'R, R'UR'URU'R',
1029 || +///++ --> R2U'R'UR, R2U'R'UR', R'URU'R, R'URU'R',
1026 || /+///- --> RU2R'U2R, RU2R'U2R',
2325 || /+-+++ --> R2U'RU'RU2R, R2U'RU'RU2R',
2133 || /++-++ --> R'U2RU'RU2R, R'U2RU'RU2R',
2130 || +-/+/- --> RU2R2U'RU'R, RU2R2U'RU'R', R'U2RU'R'UR, R'U2RU'R'UR', R'U2R2URU'R, R'U2R2URU'R',
2394 || +-++-- --> RUR2U2R, RUR2U2R', RU'R2U2R, RU'R2U2R',
2586 || +--/-- --> RU2R'UR'U2R, RU2R'UR'U2R',
2388 || +-+++/ --> RU'RU2R, RU'RU2R',
2121 || -/+/-+ --> R2U'R'U2R, R2U'R'U2R', R'UR2U'R, R'UR2U'R',
2385 || +++-/+ --> R'UR'UR'UR, R'UR'UR'UR', R'U2RUR2U2R, R'U2RUR2U2R', R'U2RU'R2U2R, R'U2RU'R2U2R',
2118 || -/+/+- --> RU'RU2R'U2R, RU'RU2R'U2R',
2184 || -/-/-/ --> RU2RU'RU2R'U2R, RU2RU'RU2R'U2R', RU'R'UR'U2RU2R, RU'R'UR'U2RU2R', R2UR2U'RU'R'UR, R2UR2U'RU'R'UR', R2UR2U'R2URU'R, R2UR2U'R2URU'R', R2UR'URU2R'U2R, R2UR'URU2R'U2R', R2U'RU'R'UR'U2R, R2U'RU'R'UR'U2R', R2U'R2UR2U'RU'R, R2U'R2UR2U'RU'R', R'U2R'UR'UR'U2R, R'U2R'UR'UR'U2R',
2577 || --/+/+ --> R2U'R, R2U'R',
2181 || /-/-++ --> R2U'R2UR, R2U'R2UR', R'URU2R, R'URU2R',
2376 || /-++-/ --> R2U'RU2R, R2U'RU2R',
2178 || /-/-/- --> R'U'R, R'U'R',
   9 || ////-+ --> R2UR'U2R'U2R, R2UR'U2R'U2R', R2U'RU2RU2R, R2U'RU2RU2R',
2568 || --//-/ --> RU'R, RU'R',
   6 || ////+- --> RU2RU2R'U2R, RU2RU2R'U2R', R'U2R'U2RU2R, R'U2R'U2RU2R',
2565 || --//++ --> RU2RU'R'UR, RU2RU'R'UR', RU2R2URU'R, RU2R2URU'R', R'U2R2U'RU'R, R'U2R2U'RU'R',
2562 || /--//- --> RU'R'UR'U2R, RU'R'UR'U2R', R2UR2U'RU'R, R2UR2U'RU'R',
   0 || ////// --> ,
Took 3,461 s
```


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## cuBerBruce (Nov 14, 2010)

reThinking the Cube said:


> Thanks Bruce. How many contain a 1x1x2 block that can be created for the position (and hypothetically rotated to DL) that would also at the same time put the remaining 6 corners in a 2-gen <U,R> solvable state?



I have previously calculated there are 316699 positions that are 2-gen solveable (can be solved using <U,R> after possibly rotating the cube).

The number of positions a given distance from this set of positions is given below.


```
distance positions
    0     316699
    1     779487
    2    2022790
    3     552640
    4       2544
```
This means that from any position, a 2-gen position can be reached using no more than 4 moves, and over 99.9% of positions require no more than 3 moves.

@reThinking the Cube: I don't know if this answers your question. If not, can you explain some more exactly what you would like to have calculated.


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## oll+phase+sync (Nov 19, 2010)

I use Guimond (Step1 is RU also) as a lucky case addon to Ortega, but my transition between Orientation and Separation definity is not perfect, and would greatly benefit from a bar. 
ive 
Is there someone who can foretell the exact seperation step of Guimond within inspection time?

Are there movecount statistics for Guimond?

I currently still feel like I preferr to break the sortega bar in favour of an 3 move Orientation. Will count the number of cases.


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## TK 421 (Nov 19, 2010)

So, this is an alg for speeding up ORTEGA

wow, 2-layer orientation

nice job  i'll start learning when my ortega is perfect


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## oll+phase+sync (Nov 19, 2010)

TK 421 said:


> i'll start learning when my ortega is perfect



Don't wait so long, this one should get go faster than pure Ortega.


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## Kirjava (Nov 20, 2010)

reThinking the Cube said:


> Blocktega™


 
You make me cringe.


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## Baian Liu (Nov 20, 2010)

Very interesting method.

I tried combining BRASS and Sortega! by doing this:

Reduce to 2-gen
Orient the remaining six pieces
Permute the remaining six pieces

Some examples:

Scramble: R2 U' F' U2 R F2 R U2
Reduce to 2G: y
Orient: R' U' R U2 R'
Permute: U2 R2 U R2 U' R2 U2

Scramble: F2 R' U R2 U2 R' U2 R' F2 U' 
Reduce to 2G: x' F
Orient: U R' U2 R' U2 R
Permute: U R2 U R2 U2

Scramble: U F U R U R2 U F2 U2 
Reduce to 2G: y F' U' F' U' F
Orient: U2 R' U R U' R
Permute: U' R2 U' R2

Scramble: F R' U R F' R2 F U2 F2
Reduce to 2G: x2 y' F2 U' F' U' F
Orient: R U' R' U2 R'
Permute: U' R2 U R2 U' R2 U'


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## cubacca1972 (Nov 20, 2010)

Just a thought on naming the method.

To my eye, this method is distinct enough from other methods to be named after its creators. Something like GGCF?


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## Lucas Garron (Nov 20, 2010)

Baian Liu said:


> I tried combining BRASS and Sortega! by doing this:


I actually looked a little into making this two-gen based on my solution to Roux's riddle, but didn't get very far. Maybe I should look at phasing again.



cubacca1972 said:


> To my eye, this method is distinct enough from other methods to be named after its creators. Something like GGCF?


Nah. In the beginning, I joked about calling it "GG" in analogy to "SS," but then qq suggested "Sortega," which just fits. It's not like either of us *need* the validation from having our name in a new method, and besides, the real credit goes to qq (I just tried to drum up attention).


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## cubacca1972 (Nov 20, 2010)

Lucas Garron said:


> Nah. In the beginning, I joked about calling it "GG" in analogy to "SS," but then qq suggested "Sortega," which just fits. It's not like either of us *need* the validation from having our name in a new method, ...



I don't see it so much as validation, in the sense of placating a fragile ego. Its more about accurately pointing out who the creators/developers of the method are.



Lucas Garron said:


> and besides, the real credit goes to qq (I just tried to drum up attention).



That's why qq gets the first G in GG.


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## Vishal (Nov 20, 2010)

This seems like an ok method but I personally think full eg is better


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## riffz (Nov 21, 2010)

Vishal said:


> This seems like an ok method but I personally think full eg is better


 
>_>


Can we get an alg list going with solutions that aren't all 2-gen, such as using F moves or doing a rotation? Before I bother learning this I want to make sure that I'm learning the fastest solutions for each case, not just the <R,U> ones.


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## Lucas Garron (Nov 21, 2010)

riffz said:


> >_>
> 
> 
> Can we get an alg list going with solutions that aren't all 2-gen, such as using F moves or doing a rotation? Before I bother learning this I want to make sure that I'm learning the fastest solutions for each case, not just the <R,U> ones.


Yeah, this should be easy in ACube. Interesting to note: The two corners of the bar can switch.


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## riffz (Nov 21, 2010)

Lucas Garron said:


> Yeah, this should be easy in ACube. Interesting to note: The two corners of the bar can switch.


 
Ah, cool, but I think unless the alg is considerably better, I'd rather use ones that preserve the bar permutation, since it would be easier to predict or at least narrow down the PBL case.


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## userman (Dec 14, 2010)

StachuK1992 said:


> Learn Ortega first.
> That should take you about 5 minutes.
> Then go for this if you want, but it's an upcoming method, not very experimented yet.


5 min? I used days.


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## pi.cubed (Dec 18, 2010)

How much potential do you guys think Sortega has? Sub 4 is definitely possible, and it looks like faz got a 3.14 a12 with it. 



> Cool method bro
> 
> 2.65, 3.16, 2.65, 2.36, 3.15, 4.91, 2.77, 3.83, 3.58, 1.34, 3.80, 3.40 = 3.14



Do you guys think sub-3 is possible?


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## qqwref (Dec 18, 2010)

Sub 3 is definitely possible. I doubt Faz was fully used to the method when he did that average - there are plenty of optimal situations to learn, and to develop lookahead in.


----------

