#### mDiPalma

##### Member

- Joined
- Jul 12, 2011

- Messages
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Welcome.

ZZ-EF (edges first) is an interesting and potentially superior approach to the only legitimate 21st century speedcubing method, ZZ. The premise of this method is to capitalize on lucky cases when they appear, and to ignore unlucky cases that other speedsolving methods would unfortunately require that you address. The variant I am about to describe is 72 times luckier than traditional ZZ, with regards to the first block. It is 4 times luckier than traditional ZZ, with regards to a particularly important F2L pair. And it is around 18 times luckier than traditional ZZ with regards to the Last Layer. Note that ZZ is already significantly luckier than other mainstream solution methods, including CFOP and CFCE. As a result of the overall luckiness of this method, speedsolve movecounts should cap, for competent users, at 50 htm. These luckiness factors may sound strange to hear at first. Give me a chance to explain the variant.

This variant is also applicable to the Petrus and Heise methods, provided appropriate measures in adaptation are taken. This variant is not compatible with different (read, "inferior") methods: CFOP, Roux, TFM, etc.

This is an advanced approach to a complicated method. Reader discretion is advised.

The steps of this variant can be summarized simply:

1. EOLine

Per the standard ZZ method, an EOLine is required. This orients the edges on the cube with respect to the front and back faces while placing edges in the DF and DB positions. From this point on, the cube can be solved with only [R,U,L] moves, without cube rotations. This is an ergonomic enhancement as well as a blockbuilding convenience towards the remainder of the solve. EOLine is an investment of less than 7 moves.

2. Lucky ZZF2L

Now, use [R,U,L] (and [D,F2]) moves to begin to create the F2L. Typically ZZF2L involves the solution of 2 cross edges (DL and DR), 4 E-slice edges (FL, FR, BL, BR), and 4 D-layer corners. For this variant, the requirements are loosened. This higher leniency provides both for a significantly reduced movecount and a significantly increased proportion of lucky cases. The requirements for ZZ-EF F2L are as follows:

a) 2 cross edges solved

b) 4 E-slice edges solved

c) 1 D-layer corner solved

d) 3 remaining D-layer corners placed in the D-layer with an overall permutation and corner orientation that can be solved exactly without affecting another piece on the cube. In other words, these 3 corners are to be exactly 1 commutator from solved.

It is also a feature of this variant that the final corner-edge "pair" (it may not in fact be a pair at all, but rather the correct F2L edge attached to some random corner in a predefined orientation) be inserted with a Speed-Heise algorithm. I will explain "Speed-Heise" later.

2 i. So, via the traditional ZZ blockbuilding approach, users will first create an F2L square (2x2x1). This F2L square will include the correct D-layer edge, the correct E-layer edge, and a random D layer corner in any orientation. Because any of 4 random corners is permitted in any of 3 random orientations, instead of 1 particular corner in a specified orientation (per standard ZZ), we note that this F2L square can be 12 times luckier than traditional ZZ.

2 ii. Expand the F2L square to an F2L block (3x2x1 rectangle) (or create another F2L square on the other side of the cube). This time, the specific corner involved is specified to be 1 of 2 potential corners per the rules below, but the orientation of this corner is not yet required, making this step 6 times luckier than traditional ZZ.

2 ii. a) if your first D-layer corner was placed in the correct spot, but misoriented, the corner of the second "pair" must also be placed in the correct spot in any orientation.

2 ii. b) if your first D-layer corner was NOT placed in the correct spot (preferred) and not oriented, then the edge and corner of the second "pair" must NOT have the exact colors of the first "pair" that you placed. For example, if you first placed the Green-Red corner with the Blue-Red edge. It is not permitted for the Green-Red edge to be paired with the Blue-Red corner for the remainder of the solve. You must use some other corner. In other words, you may not have an isolated two-swap of corners on the D layer at any time. It must be a 3-cycle.

2 iii. Create another F2L square (or expand one of previous squares, if you made a square in step 2 ii.). The edges must be placed correctly as usual. But this time, the corner's orientation and permutation are defined. The corner that you use must complete the 3 cycle on the D-layer. For example, if the first random "pair" that you placed was the Green-Red corner in any orientation with the Blue-Red edge, and the second "pair" was the Blue-Red corner with the Blue-Orange edge, then you must insert the Blue-Orange corner with the Green-Red slot. This will complete the 3 cycle. But in order to assure that a commutator is possible, the orientation of this corner must also be defined. Of all the mismatched D-layer corners, the orientations must add up to a multiple of 3. For a corner with the D-color facing down, the number is 0. For a corner with the D-color rotated clockwise from down, the number is 1. For a corner with the D-color rotated anticlockwise from down, the number is 2. You must insert the final mismatched D-layer corner such that its number, when added to the numbers of the other mismatched D-layer corners is a multiple of 3. This may take some time to get used to. But it is certainly not difficult. Now that the exact corner and the orientation of the corner is specified, you may insert this pair.

2 iv. Although I've written this substep as the fourth substep of step 2, it may happen at ANY point during step 2. In this step, you solve a regular F2L pair, regularly. That means the colors of the corner and edge match, and the corner is to be inserted with the D-color facing down. This is a normal pair, just as in CFOP, Petrus, ZZ, or any other method. The advantage here is that because you can choose this as either your first, second, third, or fourth F2L pair, you get 4 chances for an easy case! No more bursting into tears because your F2L pairs are so hard and long to solve! This variant gives you 4 times the chances for a 3-move insert.

2 v. And although I've written this as the fifth substep, it actually applies to whichever "pair" (or pair) that you do last. You must insert the last F2L pair such that 1 U-layer corner, and all the U-layer edges are correctly solved after the pair is inserted. That means that only 3 U-layer corners will be out of place, after this step is complete. This, an idea adapted partially from the Heise method, may seem quite daunting at first. However, it can be accomplished completely intuitively via the approach described in Step 3 of Ryan Heise's site (given that you are solving the F2L pair). Another, perhaps simpler approach is to use the ergonomic algorithms that I generated here, known as Speed-Heise. These algorithms (designed for an F2L insert at FR, but can be mirrored and translated to apply to other F2L slots) place the F2L pair, while solving the LL edges, while solving whichever corner is already at DFR. Right now, these 24 algorithms are only designed for a DFR corner which is oriented down, but I will soon generate 48 more algorithms for the other orientations of the DFR corner. To identify which alg to use, place the F2L "pair" (or pair) over the slot. Then identify which LPELL case that you have. Then, drop the leading R (ie. "R LB" becomes "LB", etc.). Then, look at the destination of the DFR corner, relative to the edge piece at UF. If the corner belongs at the back right of the U-layer, the letter pair is "BR". Then combine the two letter pairs and apply the corresponding algorithm, per the list.

3. Use 2 commutators to solve the cube. 1 in the U layer, and 1 in the D layer. Commutators are described here. 1/27 of the time, you will not have a commutator to apply in the U-layer. It will have automatically solved itself, after the speed-Heise alg.

Example Walkthrough Solve:

[video]www.youtube.com/watch?v=jBlt8lmSlNQ[/video]

Spoiler

Good luck! I will post a few example solves and will translate and expand the Speed-Heise description tomorrow. (I didn't post it to the English forum because I wanted to make sure all the algs were good first, and I wanted to iron out any kinks. After learning the first 24 algs, it seems very promising, albeit against the fundamental algorithm-less principle of Heise)

Please let me know what you think!

ZZ-EF (edges first) is an interesting and potentially superior approach to the only legitimate 21st century speedcubing method, ZZ. The premise of this method is to capitalize on lucky cases when they appear, and to ignore unlucky cases that other speedsolving methods would unfortunately require that you address. The variant I am about to describe is 72 times luckier than traditional ZZ, with regards to the first block. It is 4 times luckier than traditional ZZ, with regards to a particularly important F2L pair. And it is around 18 times luckier than traditional ZZ with regards to the Last Layer. Note that ZZ is already significantly luckier than other mainstream solution methods, including CFOP and CFCE. As a result of the overall luckiness of this method, speedsolve movecounts should cap, for competent users, at 50 htm. These luckiness factors may sound strange to hear at first. Give me a chance to explain the variant.

This variant is also applicable to the Petrus and Heise methods, provided appropriate measures in adaptation are taken. This variant is not compatible with different (read, "inferior") methods: CFOP, Roux, TFM, etc.

This is an advanced approach to a complicated method. Reader discretion is advised.

The steps of this variant can be summarized simply:

1. EOLine

Per the standard ZZ method, an EOLine is required. This orients the edges on the cube with respect to the front and back faces while placing edges in the DF and DB positions. From this point on, the cube can be solved with only [R,U,L] moves, without cube rotations. This is an ergonomic enhancement as well as a blockbuilding convenience towards the remainder of the solve. EOLine is an investment of less than 7 moves.

2. Lucky ZZF2L

Now, use [R,U,L] (and [D,F2]) moves to begin to create the F2L. Typically ZZF2L involves the solution of 2 cross edges (DL and DR), 4 E-slice edges (FL, FR, BL, BR), and 4 D-layer corners. For this variant, the requirements are loosened. This higher leniency provides both for a significantly reduced movecount and a significantly increased proportion of lucky cases. The requirements for ZZ-EF F2L are as follows:

a) 2 cross edges solved

b) 4 E-slice edges solved

c) 1 D-layer corner solved

d) 3 remaining D-layer corners placed in the D-layer with an overall permutation and corner orientation that can be solved exactly without affecting another piece on the cube. In other words, these 3 corners are to be exactly 1 commutator from solved.

It is also a feature of this variant that the final corner-edge "pair" (it may not in fact be a pair at all, but rather the correct F2L edge attached to some random corner in a predefined orientation) be inserted with a Speed-Heise algorithm. I will explain "Speed-Heise" later.

2 i. So, via the traditional ZZ blockbuilding approach, users will first create an F2L square (2x2x1). This F2L square will include the correct D-layer edge, the correct E-layer edge, and a random D layer corner in any orientation. Because any of 4 random corners is permitted in any of 3 random orientations, instead of 1 particular corner in a specified orientation (per standard ZZ), we note that this F2L square can be 12 times luckier than traditional ZZ.

2 ii. Expand the F2L square to an F2L block (3x2x1 rectangle) (or create another F2L square on the other side of the cube). This time, the specific corner involved is specified to be 1 of 2 potential corners per the rules below, but the orientation of this corner is not yet required, making this step 6 times luckier than traditional ZZ.

2 ii. a) if your first D-layer corner was placed in the correct spot, but misoriented, the corner of the second "pair" must also be placed in the correct spot in any orientation.

2 ii. b) if your first D-layer corner was NOT placed in the correct spot (preferred) and not oriented, then the edge and corner of the second "pair" must NOT have the exact colors of the first "pair" that you placed. For example, if you first placed the Green-Red corner with the Blue-Red edge. It is not permitted for the Green-Red edge to be paired with the Blue-Red corner for the remainder of the solve. You must use some other corner. In other words, you may not have an isolated two-swap of corners on the D layer at any time. It must be a 3-cycle.

2 iii. Create another F2L square (or expand one of previous squares, if you made a square in step 2 ii.). The edges must be placed correctly as usual. But this time, the corner's orientation and permutation are defined. The corner that you use must complete the 3 cycle on the D-layer. For example, if the first random "pair" that you placed was the Green-Red corner in any orientation with the Blue-Red edge, and the second "pair" was the Blue-Red corner with the Blue-Orange edge, then you must insert the Blue-Orange corner with the Green-Red slot. This will complete the 3 cycle. But in order to assure that a commutator is possible, the orientation of this corner must also be defined. Of all the mismatched D-layer corners, the orientations must add up to a multiple of 3. For a corner with the D-color facing down, the number is 0. For a corner with the D-color rotated clockwise from down, the number is 1. For a corner with the D-color rotated anticlockwise from down, the number is 2. You must insert the final mismatched D-layer corner such that its number, when added to the numbers of the other mismatched D-layer corners is a multiple of 3. This may take some time to get used to. But it is certainly not difficult. Now that the exact corner and the orientation of the corner is specified, you may insert this pair.

2 iv. Although I've written this substep as the fourth substep of step 2, it may happen at ANY point during step 2. In this step, you solve a regular F2L pair, regularly. That means the colors of the corner and edge match, and the corner is to be inserted with the D-color facing down. This is a normal pair, just as in CFOP, Petrus, ZZ, or any other method. The advantage here is that because you can choose this as either your first, second, third, or fourth F2L pair, you get 4 chances for an easy case! No more bursting into tears because your F2L pairs are so hard and long to solve! This variant gives you 4 times the chances for a 3-move insert.

2 v. And although I've written this as the fifth substep, it actually applies to whichever "pair" (or pair) that you do last. You must insert the last F2L pair such that 1 U-layer corner, and all the U-layer edges are correctly solved after the pair is inserted. That means that only 3 U-layer corners will be out of place, after this step is complete. This, an idea adapted partially from the Heise method, may seem quite daunting at first. However, it can be accomplished completely intuitively via the approach described in Step 3 of Ryan Heise's site (given that you are solving the F2L pair). Another, perhaps simpler approach is to use the ergonomic algorithms that I generated here, known as Speed-Heise. These algorithms (designed for an F2L insert at FR, but can be mirrored and translated to apply to other F2L slots) place the F2L pair, while solving the LL edges, while solving whichever corner is already at DFR. Right now, these 24 algorithms are only designed for a DFR corner which is oriented down, but I will soon generate 48 more algorithms for the other orientations of the DFR corner. To identify which alg to use, place the F2L "pair" (or pair) over the slot. Then identify which LPELL case that you have. Then, drop the leading R (ie. "R LB" becomes "LB", etc.). Then, look at the destination of the DFR corner, relative to the edge piece at UF. If the corner belongs at the back right of the U-layer, the letter pair is "BR". Then combine the two letter pairs and apply the corresponding algorithm, per the list.

3. Use 2 commutators to solve the cube. 1 in the U layer, and 1 in the D layer. Commutators are described here. 1/27 of the time, you will not have a commutator to apply in the U-layer. It will have automatically solved itself, after the speed-Heise alg.

Example Walkthrough Solve:

[video]www.youtube.com/watch?v=jBlt8lmSlNQ[/video]

R2 U2 F2 D L2 B2 U F2 D2 F2 R2 B' R' D U' F2 D2 L' B2 R B'

L B' F D' F' L2 D' // eoline (7)

U2 L R2 U2 L // real pair (5)

R2 U2 L // fake pair (3)

U' R U2 R2 U' R // fake pair (6)

U R U R' // set up speed-heise (4)

L U' R U L' U R' U' // speed heise RB/FR (8)

L2 D' L U2 L' D L U2 L // commutator 1 (9)

x2 R2 B2 R F R' B2 R F' R // commutator 2 (9)

=51 htm

L B' F D' F' L2 D' // eoline (7)

U2 L R2 U2 L // real pair (5)

R2 U2 L // fake pair (3)

U' R U2 R2 U' R // fake pair (6)

U R U R' // set up speed-heise (4)

L U' R U L' U R' U' // speed heise RB/FR (8)

L2 D' L U2 L' D L U2 L // commutator 1 (9)

x2 R2 B2 R F R' B2 R F' R // commutator 2 (9)

=51 htm

Good luck! I will post a few example solves and will translate and expand the Speed-Heise description tomorrow. (I didn't post it to the English forum because I wanted to make sure all the algs were good first, and I wanted to iron out any kinks. After learning the first 24 algs, it seems very promising, albeit against the fundamental algorithm-less principle of Heise)

Please let me know what you think!

Last edited: Jan 1, 2015