#### ottozing

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What I've gone ahead and done is taken every possible LS case you can get with ZZ for the FR slot & found one alternative algorithm that can be used to guarantee that you never get 0 oriented corners for LL. Not all of these are actually worthwhile, but many of them are & the recognition demands really aren't that bad once you get used to them (won't be explaining that part here)

This idea can also apply to ZBLS, and in my opinion will probably become the primary approach to LSLL for advanced CFOP solvers, with the secondary approach being ZBLS, and the tertiary approach being some mix of other stuff like VLS, true OLS, and forcing very nice OLL cases in terms of move count/look ahead into PLL/good alternative OLLCP's

Bolded = worth it

Underlined = almost worth it but needs work/unsure

No bold/no underline = not worth it

F2L 4 - R U R' & R U' R' U' R U' R'

In total, 15/20 are worth it using this system, and of the remaining 5, the only one that definitely isn't worth it in my opinion is F2L 4 aka split free pair. I'd say suck it up for this case and take H/Pi unless you can cancel nicely into the standard OLL (happens for 3 of the 6 cases), but even then it's debatable and I'm very much inclined to think you should always take H/Pi here

Reducing to F2L 4 as such isn't anywhere near as good as reducing to F2L 1, so for that reason I don't like F2L 17 with this system since it only has one way to reduce to a free pair in 3-4 moves (whereas F2L 30 at least has a 2nd way that removes the H/Pi for all but one case). I think that for the 6 cases where the standard insert gives H/Pi, you're better off taking OLL unless there's a good 11 mover (ignoring pre-AUF) for the pure OLS (ones that I found by hand: R U2' R' U' R U R' U2 R U' R' and R U R' U' R U2' R' U2 R U R')

F2L 14 is interesting to me. Even though it has two algs, the secondary alg is 3QTM worse and can't be done from home grip. That said, it's basically a sune with an extra R turn, so I'm more inclined to think it's worth it even if it's a bit weird

F2L 25 I'm just kinda sad about lol. I tried a bunch of combos of F' R U R' U' R' F R + inverse & S' R U' R' f R' F' R + inverse but couldn't get 100% with only 2 algs. To get 100% you need to use U' R' F R f' R U R' S and then you get U ZBLL from the U2 angle (or maybe there's a good BLE alg)

Lastly, for the F2L 30 OLS that always gives 4 misoriented corners using the 2 good solutions, you can either do the 7QTM one and get H (which is still nicer than Pi) do F R' F' R d' L' U' L U L' U L (which kinda sucks tbh), or do U' R U2' L U' R' U L' to get T ZBLL from the U2 angle (also kinda sucks)

All in all, using the most conservative version of this system (aka not using gross F2L algs, only 2 per case, and no fancy OLS tricks like WV), you're forced to take H/Pi for 14 out of the 540 possible OLS cases (not sure what the actual stats are on this but I know that just dividing them is incorrect because symmetry or something)

This seems pretty damn solid to me for a start considering that with 0 influence, you'd be getting H/Pi for 120/540 cases

That said, if you were only to use reduction to F2L 1 tricks (excluding F2L 34), the final number of cases where you're stuck getting H or Pi becomes 42/540. This is important because reducing to F2L 1 aka a built pair means you only need to learn one recog system, and you can also do WV on top of that for some cases. This is absolutely the place to start if you're a ZZ solver looking to up your OLS game B)

Underlined = almost worth it but needs work/unsure

No bold/no underline = not worth it

**F2L 1 - U R U' R' & U2 R U2' R'**F2L 4 - R U R' & R U' R' U' R U' R'

**F2L 5 - Reduce to F2L 1**

F2L 7 - Reduce to F2L 1

F2L 10 - U2 R U' R' U' R U R' & U' R U R' U R U R'

F2L 12 - R' U2' R2 U R2' U R & R U' R' U R U' R' U2 R U' R' (can also just reduce to F2L 1 with the 2nd or F2L 2 with the 1st)F2L 7 - Reduce to F2L 1

F2L 10 - U2 R U' R' U' R U R' & U' R U R' U R U R'

F2L 12 - R' U2' R2 U R2' U R & R U' R' U R U' R' U2 R U' R' (can also just reduce to F2L 1 with the 2nd or F2L 2 with the 1st)

**F2L 14 - U' R U' R' U R U R' & U2' R2 U R' U R U2' R2' (can also reduce to F2L 4 with the 1st)****F2L 15 - Reduce to F2L 1**__F2L 17 - Reduce to F2L 4 (could also use R U2' R' U' R U2' R' U R U2' R' as the alt instead of R U2' R' U' R U' R' U' R U' R' which has nicer U layer turns and allows some look ahead into ZBLL since it's got similar properties to R' D' R <U> R' D R)__**F2L 19 - Reduce to F2L 1**

F2L 21 - Reduce to F2L 1

F2L 23 - Reduce to F2L 1F2L 21 - Reduce to F2L 1

F2L 23 - Reduce to F2L 1

__F2L 25 - Reduce to F2L 1 (U' F' R U R' U' R' F R & S' R U' R' f R' F' R covers all but 1 case)__**F2L 27 - Reduce to F2L 1**__F2L 30 - Reduce to F2L 4 (R U R' U' R U R' & U' R U2' R' U2 R U R' covers all but 1 case, can also technically do F R' F' R into F2L 2 but it's kinda gross)__**F2L 32 - Reduce to F2L 1**

F2L 33 - Reduce to F2L 1

F2L 34 - U R' D' R U' R' D R & U R U R' U2' R U R' (can also do D R' U R to reduce to F2L 2)

F2L 38 - R U R' U' R U2 R' U' R U R' or R U' R' U' R U R' U' R U2' R' with the correct pre-AUF (or reduce to F2L 1)

F2L 39 - R U' R' U R U2' R' U R U' R' with the correct pre-AUF (or reduce to F2L 1)F2L 33 - Reduce to F2L 1

F2L 34 - U R' D' R U' R' D R & U R U R' U2' R U R' (can also do D R' U R to reduce to F2L 2)

F2L 38 - R U R' U' R U2 R' U' R U R' or R U' R' U' R U R' U' R U2' R' with the correct pre-AUF (or reduce to F2L 1)

F2L 39 - R U' R' U R U2' R' U R U' R' with the correct pre-AUF (or reduce to F2L 1)

In total, 15/20 are worth it using this system, and of the remaining 5, the only one that definitely isn't worth it in my opinion is F2L 4 aka split free pair. I'd say suck it up for this case and take H/Pi unless you can cancel nicely into the standard OLL (happens for 3 of the 6 cases), but even then it's debatable and I'm very much inclined to think you should always take H/Pi here

Reducing to F2L 4 as such isn't anywhere near as good as reducing to F2L 1, so for that reason I don't like F2L 17 with this system since it only has one way to reduce to a free pair in 3-4 moves (whereas F2L 30 at least has a 2nd way that removes the H/Pi for all but one case). I think that for the 6 cases where the standard insert gives H/Pi, you're better off taking OLL unless there's a good 11 mover (ignoring pre-AUF) for the pure OLS (ones that I found by hand: R U2' R' U' R U R' U2 R U' R' and R U R' U' R U2' R' U2 R U R')

F2L 14 is interesting to me. Even though it has two algs, the secondary alg is 3QTM worse and can't be done from home grip. That said, it's basically a sune with an extra R turn, so I'm more inclined to think it's worth it even if it's a bit weird

F2L 25 I'm just kinda sad about lol. I tried a bunch of combos of F' R U R' U' R' F R + inverse & S' R U' R' f R' F' R + inverse but couldn't get 100% with only 2 algs. To get 100% you need to use U' R' F R f' R U R' S and then you get U ZBLL from the U2 angle (or maybe there's a good BLE alg)

Lastly, for the F2L 30 OLS that always gives 4 misoriented corners using the 2 good solutions, you can either do the 7QTM one and get H (which is still nicer than Pi) do F R' F' R d' L' U' L U L' U L (which kinda sucks tbh), or do U' R U2' L U' R' U L' to get T ZBLL from the U2 angle (also kinda sucks)

All in all, using the most conservative version of this system (aka not using gross F2L algs, only 2 per case, and no fancy OLS tricks like WV), you're forced to take H/Pi for 14 out of the 540 possible OLS cases (not sure what the actual stats are on this but I know that just dividing them is incorrect because symmetry or something)

This seems pretty damn solid to me for a start considering that with 0 influence, you'd be getting H/Pi for 120/540 cases

That said, if you were only to use reduction to F2L 1 tricks (excluding F2L 34), the final number of cases where you're stuck getting H or Pi becomes 42/540. This is important because reducing to F2L 1 aka a built pair means you only need to learn one recog system, and you can also do WV on top of that for some cases. This is absolutely the place to start if you're a ZZ solver looking to up your OLS game B)