# Optimal OLL maneuvers



## Bruce MacKenzie (Jan 5, 2020)

I am working on an optimal solver which can do partial solves--solves where some cubies are solved just for orientation, just for position or with no restrictions at all. Using this I have optimally solved the 57 non-trivial OLL cases. The orientations of the flip/twist patterns are determined by how my program does the C4 symmetry reduction and in most cases are rotated about the up-down axis from that in the Wiki database here. The configurations are given as facelet permutations of the identity permutation:

UF UR UB UL DF DR DB DL FR FL BR BL UFR URB UBL ULF DRF DFL DLB DBR

So, the first pattern listed has the up-back and up-left edges flipped, the up-front-right corner twisted CW and the up-left-back corner twisted CCW.


Optimal OLL maneuvers, face turn metric

State 1: UF UR BU LU DF DR DB DL FR FL BR BL FRU URB LUB ULF DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7 8 9 10
B R' U2 R B2 L' B2 L U2 B'
F' L' U' L2 U F U' F' L' F
L U L2 B' U' B U L2 U2 L'

State 2: FU RU BU LU DF DR DB DL FR FL BR BL UFR URB LUB LFU DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7 8 9 10 11
B' R2 U' F U R U' F' R U B
B U2 B' R' F' U L' U2 L F R

State 3: UF RU UB LU DF DR DB DL FR FL BR BL UFR RBU UBL FUL DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7 8 9
F R' F' U' F U R U' F'

State 4: FU RU BU LU DF DR DB DL FR FL BR BL UFR RBU BLU LFU DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7 8 9 10 11
R L' B' L U2 L' B' R B' L R2
B L2 B2 U2 B L' B' U2 B2 L2 B'

State 5: UF UR BU LU DF DR DB DL FR FL BR BL FRU BUR BLU FUL DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7 8 9 10
F' L F L' U2 F2 R' F' R F'

State 6: UF UR BU LU DF DR DB DL FR FL BR BL UFR RBU BLU LFU DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7
B L2 F' L' F L' B'

State 7: UF UR BU LU DF DR DB DL FR FL BR BL FRU RBU BLU ULF DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7
F' L' B L' B' L2 F

State 8: FU RU BU LU DF DR DB DL FR FL BR BL UFR BUR LUB FUL DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7 8 9 10 11
B F' L B' U2 B L F' L B' F2
R B2 R2 U2 R B R' U2 R2 B2 R'
F' B2 L B' L F U2 F' L B' F

State 9: FU RU BU LU DF DR DB DL FR FL BR BL RUF RBU LUB LFU DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7 8 9 10 11
R U' R2 D' L F' L' D R2 U R'
B U L' B L B2 U' B' R B R'

State 10: UF UR BU LU DF DR DB DL FR FL BR BL UFR BUR LUB FUL DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7
L' B2 R B R' B L

State 11: UF UR BU LU DF DR DB DL FR FL BR BL RUF RBU LUB LFU DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7 8 9 10
R B' R' B U2 R2 F R F' R

State 12: UF RU UB LU DF DR DB DL FR FL BR BL RUF URB LUB FUL DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7 8 9 10
L F L' B' L U F' U' L' B
F' L' B' F U' B U F' L F

State 13: UF UR BU LU DF DR DB DL FR FL BR BL UFR RBU LUB ULF DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6
L' U' B' U B L

State 14: UF UR UB UL DF DR DB DL FR FL BR BL UFR URB LUB LFU DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7 8
B' R' B L' B' R B L
L' B' R B L B' R' B

State 15: UF UR BU LU DF DR DB DL FR FL BR BL RUF URB UBL LFU DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7 8 9 10
R' U' R F' B2 D L D' F B2
B U L2 D L' U' L D' L2 B'
R L2 D' B' D B L B' R' L

State 16: UF UR BU LU DF DR DB DL FR FL BR BL UFR URB UBL ULF DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7 8 9
L B D2 R2 U2 F R2 D2 L
R B' R B2 L' B L B2 R2
L2 B2 R B R' B2 L B' L

State 17: UF RU UB LU DF DR DB DL FR FL BR BL UFR URB BLU FUL DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7 8
L' B' U R' U' R B L

State 18: FU RU BU LU DF DR DB DL FR FL BR BL UFR URB UBL ULF DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7 8 9 10 11 12
R B U B' R' B F2 D' L' D B' F2
R2 B F' U2 L' B2 F2 R U2 B F' L2

State 19: UF UR UB UL DF DR DB DL FR FL BR BL UFR RBU BLU LFU DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7
L' U' L U' L' U2 L
F U2 F' U' F U' F'

State 20: UF RU UB LU DF DR DB DL FR FL BR BL RUF RBU BLU FUL DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7 8 9 10
R B L' B L B' U B' U' R'
L' U' B' U B' R B R' B L

State 21: UF RU UB LU DF DR DB DL FR FL BR BL RUF BUR BLU LFU DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7 8 9 10
R' U' F' U F U' F' U F R

State 22: UF UR BU LU DF DR DB DL FR FL BR BL UFR URB BLU FUL DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6
B U L U' L' B'

State 23: UF RU UB LU DF DR DB DL FR FL BR BL UFR BUR BLU ULF DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7 8
F' U' F U F R' F' R

State 24: UF UR UB UL DF DR DB DL FR FL BR BL RUF RBU LUB LFU DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7 8 9 10 11
B U B' U B U' B' U B U2 B'
R U R2 F2 D' L2 D' L2 D2 F2 R
B2 R F2 R' B2 U2 B2 L D2 L' B2

State 25: UF UR BU LU DF DR DB DL FR FL BR BL RUF BUR UBL FUL DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7 8 9 10
R B U' L U L' U B' U' R'
B U B' L' B L U' L' B' L

State 26: UF UR UB UL DF DR DB DL FR FL BR BL UFR BUR LUB FUL DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7
B U' F' U B' U' F
R' U2 R U R' U R

State 27: UF RU UB LU DF DR DB DL FR FL BR BL UFR URB UBL ULF DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7 8 9 10
B R U R' B' F D R' D' F'
R B U' B' R' F' L' U L F

State 28: UF UR BU LU DF DR DB DL FR FL BR BL FRU RBU UBL LFU DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7 8 9 10
L' U' L B L' B' U B L B'
F' L' U B' U' B U' L U F

State 29: FU RU BU LU DF DR DB DL FR FL BR BL UFR URB BLU FUL DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7 8 9 10 11
B' R' U2 F R' F' R2 B L U2 L'
R B U B' U R' U2 R' F R F'
L' B' U R' U R B L F U2 F'
B L F U2 F' U2 F U2 F' L' B'

State 30: UF UR BU LU DF DR DB DL FR FL BR BL RUF RBU UBL ULF DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7 8 9 10
L' B' L F' L' B2 L' B' L2 F
L F' U' F2 U' F2 U2 F U' L'
L2 F2 L U' B' U B L' F2 L2

State 31: UF UR BU LU DF DR DB DL FR FL BR BL RUF URB LUB FUL DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7
R B L' B L B2 R'

State 32: FU RU BU LU DF DR DB DL FR FL BR BL RUF RBU BLU FUL DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7 8 9 10 11
B' R B U2 L' B' R B' R2 B2 L
B L' B' L U L2 F' L' F U' L'
L' U' L F R U B' R B R2 F'
R U2 L' B L U2 L' B' L U2 R'
L2 B2 R B2 L B' R2 U2 R B L

State 33: UF UR BU LU DF DR DB DL FR FL BR BL RUF BUR BLU LFU DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7 8 9 10
L' B' U' B U B' U' B U L

State 34: UF UR BU LU DF DR DB DL FR FL BR BL UFR BUR BLU ULF DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7 8 9
B F' U L U' L' B' U' F
F' U' L U F U' F' L' F

State 35: UF UR BU LU DF DR DB DL FR FL BR BL RUF RBU BLU FUL DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7 8 9
L' B L2 B' U2 B' U2 B L'

State 36: UF UR UB UL DF DR DB DL FR FL BR BL UFR URB BLU FUL DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7 8 9
B2 D' B U2 B' D B U2 B

State 37: UF UR UB UL DF DR DB DL FR FL BR BL UFR RBU UBL FUL DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7 8
L' B L F' L' B' L F
R' F' L' F R F' L F

State 38: UF UR BU LU DF DR DB DL FR FL BR BL FRU BUR LUB LFU DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7 8 9 10
B L U L' U' L U L' U' B'

State 39: UF UR BU LU DF DR DB DL FR FL BR BL RUF BUR LUB ULF DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7 8 9 10 11
R B L' B L' D L D' L B2 R'
R' F' U F R2 D L' B' L D' R'
B' R2 F' B2 L F' L' B2 F2 R2 B
L' R2 B R' B R B2 R' B R' L
F' L' U' L2 F' L' F2 U' F' U2 F
L U2 B' R2 D' F' D R2 B U' L'
R2 D L' B' L D' R' B U B' R'
F2 L2 B L2 F L F' L B' L2 F2

State 40: UF RU UB LU DF DR DB DL FR FL BR BL UFR URB LUB LFU DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7 8 9 10
B U B' U' L' B' R B R' L
L2 B2 R B' D' B D R' B2 L2

State 41: UF UR BU LU DF DR DB DL FR FL BR BL FRU RBU LUB FUL DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7 8 9
B R' U2 R U2 R B2 R' B

State 42: UF UR BU LU DF DR DB DL FR FL BR BL FRU URB UBL FUL DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7 8 9 10
B' R U R2 U R2 U2 R' U B
B L B' R B L2 B L B2 R'
B2 R2 B' U L U' L' B R2 B2

State 43: UF RU UB LU DF DR DB DL FR FL BR BL FRU URB BLU LFU DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7 8 9 10
B' R B U B' R' B R U' R'
L' B' U' B2 U B' L B U' B'
R' U' F' U2 F U' R B U' B'

State 44: UF RU UB LU DF DR DB DL FR FL BR BL RUF URB BLU ULF DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7 8 9
B' R B U B' U' R' U B

State 45: UF RU UB LU DF DR DB DL FR FL BR BL RUF RBU LUB LFU DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7 8 9 10 11
B L F L' B2 L U F' U' L' B

State 46: UF RU UB LU DF DR DB DL FR FL BR BL UFR RBU LUB ULF DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6
R' F' U' F U R

State 47: UF RU UB LU DF DR DB DL FR FL BR BL UFR BUR LUB FUL DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7 8 9 10
R U B U2 B' U' B U B' R'
L F U F2 U' F L' F' U F
F R' F' U' F R F' R' U R

State 48: UF UR UB UL DF DR DB DL FR FL BR BL RUF RBU BLU FUL DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7 8 9
R U2 R2 U' R2 U' R2 U2 R

State 49: UF RU UB LU DF DR DB DL FR FL BR BL UFR RBU BLU LFU DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7 8 9 10
B L B' F U F' U' B L' B'
L' B' L F L' U' B U L F'

State 50: UF UR BU LU DF DR DB DL FR FL BR BL FRU URB BLU LFU DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7 8 9 10 11
R B U B2 R B R2 U R U2 R'
B L2 F2 D2 F D2 L' F L2 B' L
B' U2 L F2 D R D' F2 L' U B
F' L' B L' B D' B' D B' L2 F
F R U' R' F2 D' B L B' D F
L F2 R L2 B' R B R2 L2 F2 L'
R2 B2 L' B2 R' B' R B' L B2 R2
F2 D' B L B' D F L' U' L F

State 51: UF RU UB LU DF DR DB DL FR FL BR BL FRU BUR BLU FUL DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7 8 9 10 11
R D' R2 U F' U2 F U' R2 D R'

State 52: FU RU BU LU DF DR DB DL FR FL BR BL UFR RBU UBL FUL DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7 8 9 10 11
L' B' R' U2 R U' B L F U2 F'
R B' R' B U2 B U' L U' L' B'
L F U2 F2 U' L' U L F U2 L'

State 53: UF UR BU LU DF DR DB DL FR FL BR BL RUF URB BLU ULF DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7 8 9 10
R B U B2 U' R' U R B R'
L' B L2 B' L2 F U2 F' U2 L
B' U' B2 L U L' U' B2 U2 B

State 54: UF UR BU LU DF DR DB DL FR FL BR BL UFR BUR UBL LFU DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7 8 9
R U2 R2 F R F' R U2 R'

State 55: UF UR BU LU DF DR DB DL FR FL BR BL FRU BUR UBL ULF DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7 8 9 10
L' U' B2 D' B U B' D B2 L
F' B2 D L D' L' B' L B' F
F U F' R L2 D' B' D R' L2

State 56: UF UR BU LU DF DR DB DL FR FL BR BL UFR RBU UBL FUL DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7 8
L' B L B' U' B' U B

State 57: UF UR BU LU DF DR DB DL FR FL BR BL UFR URB LUB LFU DRF DFL DLB DBR
Target Depth: 1 2 3 4 5 6 7 8 9
R L' U' B' U B L U R'


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## Bruce MacKenzie (Jan 5, 2020)

Question: In the listing of the OLL maneuvers in the Wiki database here, which faces are visible in the graphic--the Up,Left,Front faces or the Up,Front,Right faces?


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## ProStar (Jan 5, 2020)

If you're trying to find the optimal solution for the OLLs, then you probably shouldn't. Just because an alg is short doesn't mean it's better. Take, for example, two U-Perms. Here are two algs, both solving the Ua-Perm:

R U' R U R U R U' R' U' R2
F2 U L R' F2 L' R U F2

The latter is shorter, but it will take much longer. This is because things like F2 and B2 cause you to change your grip on the cube, while during R and U sequences you can stay in the same grip, making it faster. Whenever you try a new alg, make sure you can do it quickly, with as little regrips as possible.


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## Etotheipi (Jan 5, 2020)

ProStar said:


> If you're trying to find the optimal solution for the OLLs, then you probably shouldn't. Just because an alg is short doesn't mean it's better. Take, for example, two U-Perms. Here are two algs, both solving the Ua-Perm:
> 
> R U' R U R U R U' R' U' R2
> F2 U L R' F2 L' R U F2
> ...


But if your doing FMC its very useful to have optimal algs. They never said this was for speed.


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## BenChristman1 (Jan 5, 2020)

ProStar said:


> If you're trying to find the optimal solution for the OLLs, then you probably shouldn't. Just because an alg is short doesn't mean it's better. Take, for example, two U-Perms. Here are two algs, both solving the Ua-Perm:
> 
> R U' R U R U R U' R' U' R2
> F2 U L R' F2 L' R U F2
> ...





Etotheipi said:


> But if your doing FMC its very useful to have optimal algs. They never said this was for speed.


Yes, it's better to have fast algs for speedsolving, using your example @ProStar, I use the U perm that involves M moves. But, @Etotheipi is also right in that you need shorter algs for FMC, it doesn't matter how easy they are to execute. It all just depends on what you are using it for. Out of curiosity, what are you using it for @Bruce MacKenzie?


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## Bruce MacKenzie (Jan 5, 2020)

ProStar said:


> If you're trying to find the optimal solution for the OLLs, then you probably shouldn't. Just because an alg is short doesn't mean it's better. Take, for example, two U-Perms. Here are two algs, both solving the Ua-Perm:
> 
> R U' R U R U R U' R' U' R2
> F2 U L R' F2 L' R U F2
> ...


I understand. I'm not a speed solver. My interest is in the mathematics and computer cubing. In fact I don't even have a physical cube any more. A partial solver grabbed my interest as an intriguing computer problem. I put the results up here. You speed solvers can do with it what you please.



Etotheipi said:


> But if your doing FMC its very useful to have optimal algs. They never said this was for speed.


What is "FMC"?


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## ProStar (Jan 5, 2020)

Bruce MacKenzie said:


> What is "FMC"?



"Fewest Moves Challenge". You have 1 hour to come up with the most efficient solve possible.


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## WoowyBaby (Jan 5, 2020)

Just saying, nobody ever uses OLL for FMC. Lmao. It’s pretty inefficient, and in fact, a good FMCer rarely ever uses any pre-made algorithms like ZBLL and such. If an FMCer gets an easy F2L so now is at last layer, they wouldn’t do OLL, they’d do an AUF to get 3c3e or something like that remaining and do insertions for those cycles. I’m not trying to be mean or anything, I’m only saying that algs aren’t used in FM.


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## Mike Hughey (Jan 5, 2020)

WoowyBaby said:


> Just saying, nobody ever uses OLL for FMC. Lmao. It’s pretty inefficient, and in fact, a good FMCer rarely ever uses any pre-made algorithms like ZBLL and such. If an FMCer gets an easy F2L so now is at last layer, they wouldn’t do OLL, they’d do an AUF to get 3c3e or something like that remaining and do insertions for those cycles. I’m not trying to be mean or anything, I’m only saying that algs aren’t used in FM.


True, but for our new event speed FMC on the weekly forum competition, OLL can be pretty useful for average level FMCers like me, so it's certainly useful there!


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## Etotheipi (Jan 5, 2020)

WoowyBaby said:


> Just saying, nobody ever uses OLL for FMC. Lmao. It’s pretty inefficient, and in fact, a good FMCer rarely ever uses any pre-made algorithms like ZBLL and such. If an FMCer gets an easy F2L so now is at last layer, they wouldn’t do OLL, they’d do an AUF to get 3c3e or something like that remaining and do insertions for those cycles. I’m not trying to be mean or anything, I’m only saying that algs aren’t used in FM.


I am aware of that lol, but as Mike said, for low level FMCers it can be useful.


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