Thread starter
#1

This is an alternative system for completing the last layer with edges pre-oriented. Suitable for ZZ, Petrus, VH or ZBF2L users. OCELL stands for:

The system is designed to do most of the work with 2-gen algorithms. Since edge permutation and corner orientation can both be solved 2-gen, combining them also can. It does it with a surprisingly low move count, when compared to COLL (the most similar alternative). I've generated all the 2-Gen algorithms for the system and calculated the move count statistics. Doing it non 2-gen is perfectly possible but takes away the system's principal advantage. After OCELL its CPLL (corner permute last layer). ~67% of the cases are A-perm, the rest are H-perm and E-perm, with a 1 in 12 chance of CPLL skip.

Case Recognition

The main issue with this method is recognition. Initial recognition of OCLL is extremely easy, but recognition of edge permutation is a little more challenging. The method I use is:

Look at two opposite edges, are they opposite colours?

2-Gen Algorithms

All move counts are FTM.

Solved 15 - R U R' U R U2 R' U' R' U2 R U R' U R

UF/UB: 13 - (y) R U2 R2 U2 R' U2 R U2 R' U2 R2 U2 R

UF/UL: 11 - (y) R' U2 R U R' U' R U R' U R

UF/UR: 11 - R U R' U R U' R' U R U2 R'

Avg: 12.0

Solved 15 - R U R2 U' R2 U' R2 U2 R2 U' R' U R U2 R'

. . . . . 15 - R U2 R2 U' R' U R2 U' R' U' R' U2 R' U2 R

UF/UB: 13 - R U R' U' R' U2 R U R' U R2 U2 R'

UF/UL: 13 - (y) R U R' U R U2 R2 U2 R U R' U R

UB/UL: 13 - (y) R U2 R' U' R U' R2 U' R U' R' U2 R

. . . . . 13 - (y') R' U' R U' R' U2 R2 U2 R' U' R U' R'

UF/UR: 9 - R U2 R2 U' R2 U' R2 U2 R

UB/UR: 9 - R' U2 R2 U R2 U R2 U2 R'

Avg: 12.0

Solved 15 - (y) R2 U R U' R U R2 U' R2 U' R' U R' U' R2

UF/UB: 13 - R' U' R U' R' U2 R2 U R' U R U2 R'

UF/UL: 15 - R U2 R' U2 R2 U R' U R' U' R U R U2 R2

UB/UL: 13 - (y2) R U R' U R' U2 R2 U R2 U R2 U' R'

UF/UR: 15 - (y) R U' R U' R2 U2 R2 U R U' R2 U' R U2 R

UB/UR: 13 - R' U' R U' R U2 R2 U' R2 U' R2 U R

Avg: 14.0

Solved 15 - R U R' U R U2 R' U2 R' U' R U' R' U2 R

UF/UB: 13 - (y) R U2 R' U' R U' R2 U2 R U R' U R

UF/UL: 13 - R' U' R2 U R2 U R2 U2 R' U R' U R

UB/UL: 13 - R U R2 U' R2 U' R2 U2 R U' R U' R'

UF/UR: 15 - R U R' U' R2 U2 R' U R' U2 R U2 R U R2

UB/UR: 15 - R' U' R U R2 U2 R U' R U2 R' U2 R' U' R2

Avg: 14.0

Solved 15 - R U R' U R U' R' U R U' R' U R U2 R'

UF/UB: 15 - (y) R' U2 R U R' U R U2 R' U' R U' R' U2 R

UF/UL: 15 - R2 U R' U R' U2 R' U' R' U R2 U R U' R2

UB/UL: 15 - R U' R2 U R U2 R2 U R U2 R U2 R U' R2

UF/UR: 15 - (y) R U' R U' R2 U2 R2 U R U' R2 U' R U2 R

UB/UR: 15 - R U R2 U' R2 U' R U2 R U2 R' U2 R2 U2 R

Avg: 15.0

Solved 11 - R U R' U R' U' R2 U' R2 U2 R

UF/UB: 13 - (y') R U2 R2 U' R' U' R' U R U R2 U' R'

UF/UL: 7 - (y') R U2 R' U' R U' R'

UB/UL: 13 - (y') R2 U' R' U R U R' U2 R' U R2 U R2

UF/UR: 7 - (y2) R' U' R U' R' U2 R

UB/UR: 11 - (y2) R U2 R2 U2 R2 U R2 U R2 U' R'

Avg: 10.33

Solved 11 - (y2) R' U' R U' R U R2 U R2 U2 R'

UF/UB: 13 - R U R' U R2 U R U R2 U' R' U' R2

UF/UL: 7 - R U R' U R U2 R'

UB/UL: 11 - R' U2 R2 U2 R2 U' R2 U' R2 U R

UF/UR: 7 - (y') R' U2 R U R' U R

UB/UR: 13 - R2 U' R2 U' R U R2 U' R2 U R' U R2

. . . . . 13 - (y') R2 U R U' R' U' R U2 R U' R2 U' R2

Avg: 10.33

Total cases:

Move Count

Remember this is using only 2-gen algs for OCELL. The average optimal move count will be lower without these restrictions.

Case | Moves | Prob Occurance

------+-------+----------------

H | 12 | 2/27

Pi | 12 | 4/27

Hlight| 14 | 4/27

T | 14 | 4/27

Bowtie| 15 | 4/27

A-Sune| 10.33 | 4/27

Sune | 10.33 | 4/27

Solved| 10 | 1/27

Avg moves = (6*12 + 8*14 + 4*15 + 8*10.33 + 10)/27 ~=

Case | Moves | Prob Occurance

-------+-------+---------------

A(a) | 9 | 4/12

A(b) | 9 | 4/12

E | 14 | 2/12

H | 10 | 1/12

Solved | 0 | 1/12

Avg moves = (9*4*2 + 14*2 + 10)/12 ~=

To calculate average move counts the number of EP cases was counted as follows:

Total: 4! = 24, broken dowin into:

Solved: 4/24

Opposite Swap: 4/24

Adjacent Swap: 4 * 4/24 (16/24)

**O**rient**C**orners [permute]**E**dges**L**ast**L**ayer. It could also be called OCEPLL, but that would be a bit of a mouthfullThe system is designed to do most of the work with 2-gen algorithms. Since edge permutation and corner orientation can both be solved 2-gen, combining them also can. It does it with a surprisingly low move count, when compared to COLL (the most similar alternative). I've generated all the 2-Gen algorithms for the system and calculated the move count statistics. Doing it non 2-gen is perfectly possible but takes away the system's principal advantage. After OCELL its CPLL (corner permute last layer). ~67% of the cases are A-perm, the rest are H-perm and E-perm, with a 1 in 12 chance of CPLL skip.

Case Recognition

The main issue with this method is recognition. Initial recognition of OCLL is extremely easy, but recognition of edge permutation is a little more challenging. The method I use is:

Look at two opposite edges, are they opposite colours?

- IF YES: its either SOLVED or OPPOSITE SWAP

Differentiating between solved, or opposite swap simply involves looking at any two adjacent edges. If they are positioned correctly relative to each other then its the SOLVED case, otherwise SWAP

- IF NO: Then there are 1 of 4 adjacent swap cases to choose from. First find two adjacent edges of opposite colour (the adjacent edges diagonally opposite will also have opposite colours). If your opposite coloured adjacent edges are in BL and FR then either UF/UL or UB/UR will need to be swapped, otherwise the swap will take place between either UB/UL or UF/UR.

To choose between the two options look at two opposite coloured edges of your choice, and then the non opposite coloured edge adjacent to each one. If they are correct relative to each other then its the other two which need swapped

2-Gen Algorithms

All move counts are FTM.

**H**(on side):Solved 15 - R U R' U R U2 R' U' R' U2 R U R' U R

UF/UB: 13 - (y) R U2 R2 U2 R' U2 R U2 R' U2 R2 U2 R

UF/UL: 11 - (y) R' U2 R U R' U' R U R' U R

UF/UR: 11 - R U R' U R U' R' U R U2 R'

Avg: 12.0

**Pi**Solved 15 - R U R2 U' R2 U' R2 U2 R2 U' R' U R U2 R'

. . . . . 15 - R U2 R2 U' R' U R2 U' R' U' R' U2 R' U2 R

UF/UB: 13 - R U R' U' R' U2 R U R' U R2 U2 R'

UF/UL: 13 - (y) R U R' U R U2 R2 U2 R U R' U R

UB/UL: 13 - (y) R U2 R' U' R U' R2 U' R U' R' U2 R

. . . . . 13 - (y') R' U' R U' R' U2 R2 U2 R' U' R U' R'

UF/UR: 9 - R U2 R2 U' R2 U' R2 U2 R

UB/UR: 9 - R' U2 R2 U R2 U R2 U2 R'

Avg: 12.0

**Headlights**Solved 15 - (y) R2 U R U' R U R2 U' R2 U' R' U R' U' R2

UF/UB: 13 - R' U' R U' R' U2 R2 U R' U R U2 R'

UF/UL: 15 - R U2 R' U2 R2 U R' U R' U' R U R U2 R2

UB/UL: 13 - (y2) R U R' U R' U2 R2 U R2 U R2 U' R'

UF/UR: 15 - (y) R U' R U' R2 U2 R2 U R U' R2 U' R U2 R

UB/UR: 13 - R' U' R U' R U2 R2 U' R2 U' R2 U R

Avg: 14.0

**T**Solved 15 - R U R' U R U2 R' U2 R' U' R U' R' U2 R

UF/UB: 13 - (y) R U2 R' U' R U' R2 U2 R U R' U R

UF/UL: 13 - R' U' R2 U R2 U R2 U2 R' U R' U R

UB/UL: 13 - R U R2 U' R2 U' R2 U2 R U' R U' R'

UF/UR: 15 - R U R' U' R2 U2 R' U R' U2 R U2 R U R2

UB/UR: 15 - R' U' R U R2 U2 R U' R U2 R' U2 R' U' R2

Avg: 14.0

**Bowtie**Solved 15 - R U R' U R U' R' U R U' R' U R U2 R'

UF/UB: 15 - (y) R' U2 R U R' U R U2 R' U' R U' R' U2 R

UF/UL: 15 - R2 U R' U R' U2 R' U' R' U R2 U R U' R2

UB/UL: 15 - R U' R2 U R U2 R2 U R U2 R U2 R U' R2

UF/UR: 15 - (y) R U' R U' R2 U2 R2 U R U' R2 U' R U2 R

UB/UR: 15 - R U R2 U' R2 U' R U2 R U2 R' U2 R2 U2 R

Avg: 15.0

**Anti-Sune**Solved 11 - R U R' U R' U' R2 U' R2 U2 R

UF/UB: 13 - (y') R U2 R2 U' R' U' R' U R U R2 U' R'

UF/UL: 7 - (y') R U2 R' U' R U' R'

UB/UL: 13 - (y') R2 U' R' U R U R' U2 R' U R2 U R2

UF/UR: 7 - (y2) R' U' R U' R' U2 R

UB/UR: 11 - (y2) R U2 R2 U2 R2 U R2 U R2 U' R'

Avg: 10.33

**Sune**Solved 11 - (y2) R' U' R U' R U R2 U R2 U2 R'

UF/UB: 13 - R U R' U R2 U R U R2 U' R' U' R2

UF/UL: 7 - R U R' U R U2 R'

UB/UL: 11 - R' U2 R2 U2 R2 U' R2 U' R2 U R

UF/UR: 7 - (y') R' U2 R U R' U R

UB/UR: 13 - R2 U' R2 U' R U R2 U' R2 U R' U R2

. . . . . 13 - (y') R2 U R U' R' U' R U2 R U' R2 U' R2

Avg: 10.33

Total cases:

**40**Move Count

Remember this is using only 2-gen algs for OCELL. The average optimal move count will be lower without these restrictions.

**OCELL**:Case | Moves | Prob Occurance

------+-------+----------------

H | 12 | 2/27

Pi | 12 | 4/27

Hlight| 14 | 4/27

T | 14 | 4/27

Bowtie| 15 | 4/27

A-Sune| 10.33 | 4/27

Sune | 10.33 | 4/27

Solved| 10 | 1/27

Avg moves = (6*12 + 8*14 + 4*15 + 8*10.33 + 10)/27 ~=

**12.47****CPLL**:Case | Moves | Prob Occurance

-------+-------+---------------

A(a) | 9 | 4/12

A(b) | 9 | 4/12

E | 14 | 2/12

H | 10 | 1/12

Solved | 0 | 1/12

Avg moves = (9*4*2 + 14*2 + 10)/12 ~=

**9.17**To calculate average move counts the number of EP cases was counted as follows:

Total: 4! = 24, broken dowin into:

Solved: 4/24

Opposite Swap: 4/24

Adjacent Swap: 4 * 4/24 (16/24)

**Total moves for OCELL**= (6*12 + 8*14 + 4*15 + 8*10.33 + 10)/27 + (9*4*2 + 14*2 + 10)/12 + 0.75 ~=**22.38**
Last edited: Aug 10, 2010

Likes:
Pyjam