Hey guys, so I notice a lot of people spending most of their learning on the LL, which in my opinion has very little improvement to be had after learning OLL/PLL (like 2% improvement to average time). Stuff like COLL, ZBLL, VLS, HLS, MGLS, WV (somewhat useful), etc... Either way, my opinion is that improving the last layer comes from things like PLL 2-side recognition, etc.
Where I really see all the improvement to be had is in the F2L (and to an extent performing the extended cross)... And from what I've been able to find, the resources really suck. People like Cyo make advanced F2L videos, and they don't help me at all, since there's absolutely no organization to the algorithms he spits out you. He is talking about algorithms that are parts of huge 200-800 algorithm sets without any structure, nobody can reasonably learn like this. Almost all cubing videos about F2L techniques follow this type of format, and it's just not useful for me.
So, one website that kind of does what I ask is cubeloop.com, however my issue here is from what I can see is they go out of their way to not do any double layer turns, or any M,E,S turns, which I think hurts the efficiency of those algorithms quite a bit. I myself still don't know how to find algs with double layer turns, as Cube Explorer doesn't support it.
Empty Slot F2L Set
The way I see it is that there are 42 standard F2L algs (one of those solved), and then for each one of those cases there's an algorithm for slot to the left open, slot to the right open, and back slot open (assuming you're holding the cube such that the slot you're trying to solve is in front of you, ie normal grip, then turning cube 45 degrees CW). Then there is all the combinations of those, left + right, left + back, right + back, and also all slots open.
So in total we have 42*8 ESF2L algorithms = 336 (8 of those solved cases). Out of those, I think as a starting point, I think you want to deal with single-empty slot algorithms first, which would narrow down the algorithm count to 42*4 - 42 (the ones we already know) = 126 1ESF2L. Then there's some obvious stuff like the 4 easy F2L cases will always be the same, so that's 12 less algorithms there, and bam, down to 114 empty slot algorithms. Furthermore, I would expect... Say only 50%~ of those 114 algorithms to be actually superior to doing the regular algorithm. For example, I think to switch to a ESF2L algorithm, I would require it to be 2 moves shorter if fairly fingertrick friendly (relative to the standard F2L alg), or 3 moves shorter if kind of awkward to do. But either way, there'd be a really nice structure to it, and some 50-60 new algorithms to learn. To me this seems like the obvious choice forward after learning Full CFOP, but it seems like that's not where most people go, and because of that, I'm having trouble finding some resources. And then we have the other set of algs which I find to be very useful:
Stuck Pieces F2L Set
Now this is really just an extension of classic F2L, and if we consider every single case, I think we would have somewhere in the mid thousands (an edge can be in any of the 8 spots in any orientation, and a corner can be in any of the 8 spots in any orientation, versus 5 spots for the other.) As a first order approximation, I'd estimate there to be roughly: 8/5 = 1.6, so (336^1.6)/2... 5,500 cases. 336 because the number of EOF2L cases, divided by 2 to roughly account for not having all slots available for all the cases (like classic F2L), and to the power of 1.6, because generally speaking, I've seen a bit of a trend where something of double complexity in a rubik's cube requires x^2 cases to perform.
However if we isolate our problem to only dealing with pieces stuck in one other slot, plus the one we're trying to solve (we wont have a corner stuck in the FL and edge stuck in the BL if we're trying to solve the FR slot) there's way fewer cases. It's not natural to try and solve a block that has both pieces stuck in different slots, I don't have some mathematical proof, but I believe the percentage chance that you have 0 F2L pairs that cannot be done this way (or the normal F2L way) IF you did an extended cross is 0%. If you didn't do an extended cross, I suppose there are some odd and extremely rare F2L setups where this can happen (such as a FR slot having a piece in FL and BR, BL slot having a piece in FL and BR as well, FL having a pieces in FR and BL, and BL having pieces in FR and BL as well)... But the number of cases here can quite literally be counted on one hand.
The advantage here is that you'll never need to do a "2 look" for an F2L pair, where you have to pop it out, and then inspect what to do. Sure, there's some cases you can do intuitively, but again, it's the difference between algorithmic and intuitive F2L, where imo algorithmic is superior in the speed department as there's no thinking involved.
In total I count 90 algorithms (30 of those are mirrors though), 30 algorithms each for of the left slot relative to the one you're solving, the right slot, and the back/diagonal slot. (http://cubeloop.com/?page_id=366 is a complete set for the left slot, however not using any double layer or middle layer turns). Some of these might not save many moves, but surely some are worth learning if optimized. Many of my solves I find myself not having any pairs to solve at the start of my F2L, and having to do a RUR' or R'U'R to pop some pieces out, then having to inspect what to do. So 90 algorithms in the 1SPF2L subset.
F2L Case #1-#4 From All Positions
Pretty basic, but obviously case #1 to #4 in F2L are way easier than any other case, and because of that, you'll do these cases first... Which means you'll be doing them a lot more than any of the other F2L cases. Which makes it fairly useful I think to be able to solve them from any orientation. up face orientation, and any angle slot insertion in the most efficient way possible. Fairly intuitive, but I would appreciate having an algorithm sheet for these, so I can minimize my cube rotations and do the most fingertrick friendly move every time.
I suppose that there's 16 cases for each of the F2L cases (4 up face orientations, and 4 different locations where the slot you're trying to insert into)... So in total, 64 different cases with algorithms, but again, these are all going to be 3-5 move insertions, so not that bad - and heck, they're all very intuitive anyway.
Outside of that
I agree with Badmephisto where he says that multislotting is quite a difficult thing to do, requires a lot of on the spot thinking and computation, and unless you're someone super super dedicated and talented, the identification time to save a couple of moves isn't worth it. Partial edge control imo is not really worth it, as the dot OLL's really aren't hard compared to the others imo. Full edge control without ZBLL is also useless imo. VLS+HLS.... meeeh I think it's useless. You're saving a 3 more insert which you already were in the flow for, you're not saving any looks whatsoever... For what? The average VLS is as long as an OLL, but you're saving that insert. HLS is about the same. Saving those 3 very finger trick friendly moves versus recalling 400+ or 800+ algorithms? Not worth. Using it for some very easy cases... Meeeeeeh. Okay, I guess. But that inspection time you're spending when you might get a case you don't even do, overall, I'm just not a fan.
The only other F2L method that imo can compete with what I'm proposing would be a method that does full edge control with the 2nd and 3rd pair, and then WV for the last pair, but even that I'm not so sure about. Summer variation requires 9.4 HTM, which is roughly the same as OLL... So once again, all you're saving is that 3 move insert... However, you're likely losing those moves anyway while adding a couple extra moves to get that full edge control in your previous pairs.
Anyway, so that's what I'm looking for, the 64 algorithms for every insertion of the #1-#4 F2L cases, optimized algorithms for the 90 cases of 1SPF2L, and the 336 algorithms of ESF2L, of which I'd like to take some of the best ones in the 1ESF2L subset. Do they exist? Please and thank you.
edit: Oh, I should have mentioned, my only goal is to solve a 3x3x3 in as little time as possible, minimizing moves or whatever isn't my objective. That hopefully was clear in the post though.
Where I really see all the improvement to be had is in the F2L (and to an extent performing the extended cross)... And from what I've been able to find, the resources really suck. People like Cyo make advanced F2L videos, and they don't help me at all, since there's absolutely no organization to the algorithms he spits out you. He is talking about algorithms that are parts of huge 200-800 algorithm sets without any structure, nobody can reasonably learn like this. Almost all cubing videos about F2L techniques follow this type of format, and it's just not useful for me.
So, one website that kind of does what I ask is cubeloop.com, however my issue here is from what I can see is they go out of their way to not do any double layer turns, or any M,E,S turns, which I think hurts the efficiency of those algorithms quite a bit. I myself still don't know how to find algs with double layer turns, as Cube Explorer doesn't support it.
Empty Slot F2L Set
The way I see it is that there are 42 standard F2L algs (one of those solved), and then for each one of those cases there's an algorithm for slot to the left open, slot to the right open, and back slot open (assuming you're holding the cube such that the slot you're trying to solve is in front of you, ie normal grip, then turning cube 45 degrees CW). Then there is all the combinations of those, left + right, left + back, right + back, and also all slots open.
So in total we have 42*8 ESF2L algorithms = 336 (8 of those solved cases). Out of those, I think as a starting point, I think you want to deal with single-empty slot algorithms first, which would narrow down the algorithm count to 42*4 - 42 (the ones we already know) = 126 1ESF2L. Then there's some obvious stuff like the 4 easy F2L cases will always be the same, so that's 12 less algorithms there, and bam, down to 114 empty slot algorithms. Furthermore, I would expect... Say only 50%~ of those 114 algorithms to be actually superior to doing the regular algorithm. For example, I think to switch to a ESF2L algorithm, I would require it to be 2 moves shorter if fairly fingertrick friendly (relative to the standard F2L alg), or 3 moves shorter if kind of awkward to do. But either way, there'd be a really nice structure to it, and some 50-60 new algorithms to learn. To me this seems like the obvious choice forward after learning Full CFOP, but it seems like that's not where most people go, and because of that, I'm having trouble finding some resources. And then we have the other set of algs which I find to be very useful:
Stuck Pieces F2L Set
Now this is really just an extension of classic F2L, and if we consider every single case, I think we would have somewhere in the mid thousands (an edge can be in any of the 8 spots in any orientation, and a corner can be in any of the 8 spots in any orientation, versus 5 spots for the other.) As a first order approximation, I'd estimate there to be roughly: 8/5 = 1.6, so (336^1.6)/2... 5,500 cases. 336 because the number of EOF2L cases, divided by 2 to roughly account for not having all slots available for all the cases (like classic F2L), and to the power of 1.6, because generally speaking, I've seen a bit of a trend where something of double complexity in a rubik's cube requires x^2 cases to perform.
However if we isolate our problem to only dealing with pieces stuck in one other slot, plus the one we're trying to solve (we wont have a corner stuck in the FL and edge stuck in the BL if we're trying to solve the FR slot) there's way fewer cases. It's not natural to try and solve a block that has both pieces stuck in different slots, I don't have some mathematical proof, but I believe the percentage chance that you have 0 F2L pairs that cannot be done this way (or the normal F2L way) IF you did an extended cross is 0%. If you didn't do an extended cross, I suppose there are some odd and extremely rare F2L setups where this can happen (such as a FR slot having a piece in FL and BR, BL slot having a piece in FL and BR as well, FL having a pieces in FR and BL, and BL having pieces in FR and BL as well)... But the number of cases here can quite literally be counted on one hand.
The advantage here is that you'll never need to do a "2 look" for an F2L pair, where you have to pop it out, and then inspect what to do. Sure, there's some cases you can do intuitively, but again, it's the difference between algorithmic and intuitive F2L, where imo algorithmic is superior in the speed department as there's no thinking involved.
In total I count 90 algorithms (30 of those are mirrors though), 30 algorithms each for of the left slot relative to the one you're solving, the right slot, and the back/diagonal slot. (http://cubeloop.com/?page_id=366 is a complete set for the left slot, however not using any double layer or middle layer turns). Some of these might not save many moves, but surely some are worth learning if optimized. Many of my solves I find myself not having any pairs to solve at the start of my F2L, and having to do a RUR' or R'U'R to pop some pieces out, then having to inspect what to do. So 90 algorithms in the 1SPF2L subset.
F2L Case #1-#4 From All Positions
Pretty basic, but obviously case #1 to #4 in F2L are way easier than any other case, and because of that, you'll do these cases first... Which means you'll be doing them a lot more than any of the other F2L cases. Which makes it fairly useful I think to be able to solve them from any orientation. up face orientation, and any angle slot insertion in the most efficient way possible. Fairly intuitive, but I would appreciate having an algorithm sheet for these, so I can minimize my cube rotations and do the most fingertrick friendly move every time.
I suppose that there's 16 cases for each of the F2L cases (4 up face orientations, and 4 different locations where the slot you're trying to insert into)... So in total, 64 different cases with algorithms, but again, these are all going to be 3-5 move insertions, so not that bad - and heck, they're all very intuitive anyway.
Outside of that
I agree with Badmephisto where he says that multislotting is quite a difficult thing to do, requires a lot of on the spot thinking and computation, and unless you're someone super super dedicated and talented, the identification time to save a couple of moves isn't worth it. Partial edge control imo is not really worth it, as the dot OLL's really aren't hard compared to the others imo. Full edge control without ZBLL is also useless imo. VLS+HLS.... meeeh I think it's useless. You're saving a 3 more insert which you already were in the flow for, you're not saving any looks whatsoever... For what? The average VLS is as long as an OLL, but you're saving that insert. HLS is about the same. Saving those 3 very finger trick friendly moves versus recalling 400+ or 800+ algorithms? Not worth. Using it for some very easy cases... Meeeeeeh. Okay, I guess. But that inspection time you're spending when you might get a case you don't even do, overall, I'm just not a fan.
The only other F2L method that imo can compete with what I'm proposing would be a method that does full edge control with the 2nd and 3rd pair, and then WV for the last pair, but even that I'm not so sure about. Summer variation requires 9.4 HTM, which is roughly the same as OLL... So once again, all you're saving is that 3 move insert... However, you're likely losing those moves anyway while adding a couple extra moves to get that full edge control in your previous pairs.
Anyway, so that's what I'm looking for, the 64 algorithms for every insertion of the #1-#4 F2L cases, optimized algorithms for the 90 cases of 1SPF2L, and the 336 algorithms of ESF2L, of which I'd like to take some of the best ones in the 1ESF2L subset. Do they exist? Please and thank you.
edit: Oh, I should have mentioned, my only goal is to solve a 3x3x3 in as little time as possible, minimizing moves or whatever isn't my objective. That hopefully was clear in the post though.
