A new way of doing CFOP last slot (JPLS placeholder name)

[ottozing]

Recently I've been thinking about alternative approaches to last two pairs when you have adjacent slots already solved

I've already developed things like FRUF stuff, and PSF2L is also a very solid approach, but what if you reach last two pairs and find that one of your corners is solved but the edge of the other pair is oriented & placed with the solved corner?

Well, the obvious thing you can do is reduce to R2 U2 R2 U2 R2

A less obvious thing you can do is reduce to R2 U R2 U' R2 (or R F R2' F' R' which gives edge control)

An even less obvious thing you can do is reduce to R S' U2 S R'

Another thing you can do which I wasn't even aware of until I started genning algs was R S R2' S' R reduction

Point being, there's clearly quite a few things you can do that are quite nice, so I've decided to go ahead and generate nice solutions for all of these weird last slot cases

My reasoning for this is that this last two pair "situation" isn't particularly nice to deal with using PFS2L (though there are a few ways you can do keyhole into free pair, and for these cases they might be the best alg), and it's also not the best with FRUF stuff (though this also shows up occasionally.

Having a 3rd advanced option here feels like a nice thing to have in your tool-kit as an advanced solver. Assuming a cuber learns all if these alternate last slot algs, if you consider PSF2L as well as the fact that S <R> S' is a 3 move insert, you now have 32 possible 3-4 move inserts you could do before last slot (though most people don't do S R2 S' over R U' R2' U R, including me, but that's a discussion for another time)

Point being, if you combine this algset with an already advanced repertoire of PSF2L + the occasional FRUF stuff, you have a lot of opportunities to be really efficient with the remainder of your F2L

Going to call this JPLS for now (Jay's Pseudo Last Slot) which can also be said as "J pls" which I think is hilarious. Naming suggestions would be appreciated (I feel like Pseudo doesn't quite communicate what's going on here tbh)

Spoiler: Algs

So far I've only done one pass over the FR variant from the pairs on right angle

In the future I would like to develop algs with pairs in back, as well as the F/B mirror of this subset (so 4 total sets of algs)

Cases in bold & underline are 5 movers (generally it's nice to reduce to these if you can't do a nice solution with FRUF stuff or PSF2L)
Cases in bold are 6 movers (these cases are just very nice and already optimized IMO)

F2L 1 - U R U' R U2' R2' U2' R2
F2L 2 - F R' F' R' U2' R2 U2' R2
F2L 3 - F' U' F R2 U2' R2' U2' R2
F2L 4 - R U R U2' R2' U2' R2
F2L 5 - F' U' F R S R2' S' R
F2L 6 - R2' f R f' U R2 U2' R2' or U' R F R' F' U2 R' U' R U R'
F2L 7 - U R U' S R2' S' R or U2 R2 U R U' R' U R'
F2L 8 - R S U R' U' R' S' R
F2L 9 - U R f R' F' R2 S' R
F2L 10 - F R S R2' f' R or U D' R' U R D U2' R U R'
F2L 11 - U F D R2 D' R' F' R
F2L 12 - R U S R2' S' R or D R' U' R D' R U R'
F2L 13 - R F R' F' R' U' R U R'
F2L 14 - U2 R2 U R' U R' U2' R2 or U D R' U' R D' U2 R U' R'
F2L 15 - R U' R' U2' R2 U R2' U' R2
F2L 16 - U R F R' F' U R' U' R U R'
F2L 17 - U' D R' U R D' R U' R'
F2L 18 - u U' R U' R' D' U2 L' U L
F2L 19 - U' R U' R2' U R2 U' R2' U' R
F2L 20 - U R F R f' U S R'
F2L 21 - U' R' U R2 U' R2' U' R
F2L 22 - U' R' U R f' U f U' R' (or U' R' U R y R' F R U' F')
F2L 23 - U' R2 U2 R U2' R' U2 R'
F2L 24 - U R F U R2' U' R F' U R'
F2L 25 - U2 R S R2' S' R
F2L 26 - U' S' R S R2' S' R S
F2L 27 - U' R U R' U' R2 U R2' U' R2
F2L 28 - U S U R U' F R2 F' R' S'
F2L 29 - U R U F R f' U S R'
F2L 30 - U R U' F R2' F' R'
F2L 31 - U' R2' F R2 F' R' U' R
F2L 32 - R2 U R2' U' R2 or R F R2' F' R'
F2L 33 - U2 R S' U2 S R' or R U2' S R2' S' R
F2L 34 - D U R' S' U2 S R D'
F2L 35 - U2 R f R' f' R U R U' R' U R' or U' F' U' F R2 U R U' R' U R'
F2L 36 - R S R' S' d' R' F R or y F' r U r' F U' r U2 r' F'
F2L 37 - R U S U' R' U R' S' R
F2L 38 - R2' U2' R U' R U' R' U2 R'
F2L 39 - R U2' R U R' U R' U2' R2
F2L 40 - F' U F U' R' U R2 U' R2' U' R
F2L 41 - F' U' F R2 U2 R U2' R' U2 R'
F2L 42 - R2 U2 R2 U2 R2

Feel free to gen your own algs! So far I've only done one pass for FR slot with BR being the "special" slot, and also only from one angle. I imagine better algs can be found for the y angle in particular (for example, F2L 37 from a y angle is really nice with FRUF stuff by doing F U r U' R' U R U' r' F')

 

[ottozing]

Here's an intuitive version of this if anyone is interested (assuming BR has the "special" pair):

Instead of learning all of the algorithms, you could always do this intuitively in two steps, where the 2nd step is very easy to recognize

Step 1: Reduce the F2L situation to something solvable with R2 U2 R2 U2 R2 (the most braindead in terms of recognition), R2 U R2 U' R2/R F R2' F' R' (the only approach that gives an edge control option), R S R2' S' R (the nicest in terms of look ahead into LL and arguably the fastest to execute), and R S' U2 S R' (easily my least favorite, but it's a 4th option at least)

For the 1st, 2nd, and 4th approaches you always need to insert the F2L edge in an oriented fashion, and you just need to avoid the F2L corner being twisted in the D layer, or twisted in the U layer such that it needs to be inserted with R U R' (if it's twisted the other way you can still do R S' U2 S R', but if you also want to avoid this then I would recommend making sure the corner either gets solved or gets oriented

For the 3rd approach, you need to solve the F2L corner while making sure the F2L edge is solvable with RUgen & In the U layer. You could also choose to ignore this if you're OK with doing S' R S R2' S' R S

Unless both the edge and the corner are misoriented & stuck in the slot you're working with, you should almost always be able to set up one of these nice 5 move triggers in only 3-4 moves