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Introducing Twisted ZZ-CT: A faster, more ergonomic alternative to normal ZZ-CT


Jul 24, 2019
Background and motivation:
ZZ-CT is a great method in theory. It splits LSLL into two nearly equal steps, resulting in a 2-look LSLL method with only 197 algs. There's just one huge problem:
TTLL algorithms suck.
Despite huge efforts in the ZZ discord server to optimize TTLL, the majority of these algorithms still have either weird ergonomics, high movecount, or both.
In early 2020, Jayden McNeill proposed the concept of twisted TTLL, which solves LSLL from the R' D' R U* R' D R CLS case. In 2021, OreKehStrah and I generated the algs for this set, and they're significantly better than normal TTLL despite the algset being much less developed, which suggests that twisted TTLL is just an inherently better algset than normal TTLL. So now the question remains: Is there a good way to set up to twisted TTLL? After some experimentation, I have finally discovered a practical way to do so.

The Method:
1. Get to EO + F2L missing the FR slot. You can do this with ZZ, but there are other good ways to do this. For example, Nautilus-LSLL is another great option, especially because it guarantees that your last slot will be in FR.
2. Mentally twist the corner that belongs in DFR counterclockwise. (Equivalently, you could also just pretend that the R facelet of the DFR corner is the U/D color.)
3. Recognize the case based on the locations of the U/D colors on the corners (remembering to take the mental twist into account) and the location of the F2L edge.
4. Execute the Twisted TSLE algorithm for that case (104 algorithms).
5. You now either have a PLL (21 algorithms) or a Twisted TTLL (72 algorithms). Recognition is fairly straightforward.

The Algs:
Twisted ZZ-CT algsheet
Twisted TSLE is 104 algs and averages 9.04 moves in mostly <RU>.
Twisted TTLL is 72 algs and averages 14.39 moves in mostly <RUF> and <RUD>.
Together with PLL (21 algs), a total of 197 algs are needed for the full method, the same as normal ZZ-CT.

Example Solves:
Example using ZZ
Example using Nautilus
Example using CFOP + edge control

The TTLL algorithm quality was the main drawback preventing ZZ-CT from being viable. Twisted ZZ-CT fixes this drawback without any major sacrifices. At worst, twisted TSLE recognition becomes a little bit harder since you have to mentally twist the DFR corner, but with practice this should become instant.


Jun 5, 2018
Downtown Swagistan
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I really want to implement this alongside regular CT. OS based on TSLE vs TSLE+. But I feel I would run into issues with recogging both TSLE and TSLE+ at once without immense practice. Maybe I entirely switch to CT+?

Either way, this is a very exciting development and i'm looking forward to looking further into it in the coming days.
Great job, Trangium!