Sortega!

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.
 
Last edited:
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.
Click to expand...
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.
Click to expand...
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.
Click to expand...
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.
 
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.
 
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.)
Click to expand...

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™ :D

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.
 
Last edited:
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.
Click to expand...
Haha. Very nice.

DavidWoner said:
God it's irritating when people don't know how to use Guimond.
Click to expand...
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 :D
Click to expand...
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.
 
Last edited:
cuBerBruce said:
That means step 0 (color neutral) requires an average of about 0.0424 moves.
Click to expand...
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. :eek:

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.
Click to expand...
I made that change a while before your first post.
 
@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.
 
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.
 
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).
 
cuBerBruce said:
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
Click to expand...

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?
 
Last edited:
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?
Click to expand...
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?
Click to expand...
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).
 
qqwref said:
For future reference, what's your solution to a scramble like R2 D R2 D R' U' R'?
Click to expand...

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:
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.
 
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.
Click to expand...
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.
Click to expand...
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):
Legend:
+: turned clockwise
-: turned counterclockwise
/: oriented

Order: URF ULF ULB URB DRF DRB
Code: 
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
 
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?
Click to expand...

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.

Code: 
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.
 
Last edited:
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.
 
You must log in or register to reply here.
Back
Top