trangium
Regular
I don't think you can always cancel into making the V though. For example, scramble the cube with F2 U' F2 U' F2 R. No matter which direction of R you choose to solve CO, you won't have a V.
2x2 Statistics and Method Comparison | HD-G Now Competitive!!
- Thread starter Silky
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Yes, it can happen although very rarely. If it does happen then you'll have to throw in a U/U' R2 , F2/B2, or finish with regular Guimond. For this scramble it would be R' F2. Another could be R' D R2 U R' U2 R'. Color neutrality helps obviously
PiKeeper
Veteran
Your statistics for EG faces seem to be wrong. Mathematically, the average number of moves for a CLL or EG-2 face should be the same because they are fully symmetric. And the average face movecount for full EG should be lower than the average fact movecount for EG-1 if you assume that you choose a solution based on the easiest face. A face for full EG should always average less moves than the face movecount for EG-1.
See this.
Edit: Okay, I see what you're saying. On the note of full EG, are you choosing the best solution based on first face or on the entire solution? And the best solution doesn't always mean lowest movecount. Averaging the stats for CLL/EG-1/EG-2 does seem not to be the best approach. But again I don't really know of to account for option selecting. This is obviously why I evaluated all three separately.
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If you are only solving seperately (CLL 100 solves, EG-1 100 solves), you would probably look for the easiest face. When you're using full EG and you are very good at tracking pieces (Zayn Khanani can plan 5+ moves into the solve during inspection), you would not choose the easiest layer, but you would choose the best solution in terms of fingertricks and shortness. You would also choose a solution where finishing the face flows nicely into the CLL/EG-1 alg, like having cancellations. People also usually try to force the EG bar in the back, so that will cost additional moves.
For example, here is a 2x2 solve by Zayn on the 2x2 Example solves thread.
Scramble: F2 U' F' U R2 U' R F2 U'
y' x' // inspection
U' R2 U R' U (R U R') // Face
(R U' R2') F R2 U' R' // EG-1
Notice how he chose an 8 move face, but because it cancels 6 moves, the final solution is only 10 moves.
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Case recognition are based off of this. So the picture column refers to the FU stickers and the RU stickers respectively. Other columns refer to the LD and BD stickers.
A couple of comments:
1. During 2x2 solves with full EG, 4 in 6 solves will have EG-1 faces, 1 in 6 will have CLL and 1 in 6 will have EG-2. This means generally 2/3rd or 66% of solves will use EG-1 if you are only looking at the easiest face
2. The movecount for Full-EG cannot be calculated mathematically. This is because top 2x2 solvers are able to one look between 2 and 4 solutions all in 15 seconds (which BLOWS my mind), and in so doing, they choose the shortest one, or in some cases not quite the shortest but the most ergonomic. I can't see any possible way that this could be mathematically modeled since you don't know which solutions are the ones they will look into, all you can say is the average movecount for full EG is less than the theoretical. I talked to a top 2x2 solver and said his average movecount was 12.8 including AUF over 100 solves, while 1-looking several solves per 15-second inspection
1. During 2x2 solves with full EG, 4 in 6 solves will have EG-1 faces, 1 in 6 will have CLL and 1 in 6 will have EG-2. This means generally 2/3rd or 66% of solves will use EG-1 if you are only looking at the easiest face
2. The movecount for Full-EG cannot be calculated mathematically. This is because top 2x2 solvers are able to one look between 2 and 4 solutions all in 15 seconds (which BLOWS my mind), and in so doing, they choose the shortest one, or in some cases not quite the shortest but the most ergonomic. I can't see any possible way that this could be mathematically modeled since you don't know which solutions are the ones they will look into, all you can say is the average movecount for full EG is less than the theoretical. I talked to a top 2x2 solver and said his average movecount was 12.8 including AUF over 100 solves, while 1-looking several solves per 15-second inspection
OreKehStrah
Veteran
In theory, you could model this by using a fixed set of algs for the CLL part. Then for each scramble look at every single optimal solution for an EG layer for every single color. Then check that solution for cancellations into the CLL alg. Then take whatever is the lowest movecount. This assumes a solver takes the lowest move count solution they find.
You could also modify this to examine the percentage of the solution that is RU moves vs non-RU to weigh in ergonomic considerations into this model.
You could even take the average between the two versions to use as well.
Yeah we'd need to run through 1000+ solves/ reconstructions to get the best idea of the actual movecount. And a broader question is if it's even fair to evaluate all 3 as a singular method. Option selecting is difficult in that sense. Evaluating CFOP runs into this problem as well. On one hand, top solvers are option selecting so this really can be ignored analysis wise, one the other hand, it can be misleading relative to the method. If you're looking for a true average movecount you mudy consider best case and worse case scenarios. This is something that will happen in cube solving master, where Petrus averages 35-38 moves because it often sets up into a EPLL skip. You need to find a balance, as well as consider the audience you are making this for. If you're looking for the 'peak potential' of a method you're going to always choose the best solutions which is unrealistic for the average cuber. It's a bit too common that people look to the top cubers to base what methods they will use. Sure top cubers are using psuedo and edge control and ZBLL, etc, but for most cubers they aren't going to be using the majority of this.
Most of what I said above but only looking at the best/optimal solutions, especially for intuitive steps is sus. Kinda like using HARCs to calculate average movecount.
D
Deleted member 36445
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good method for 2x2 linear fmc lol
Updates:
(1) I updated the Full EG stats to match theh 2/3 - 1/3 option select distribution
(2) I updated the average movecount/MCC of HD-G using trangium's algs as they are currently the best algs
(a) HD-G is now slightly less efficient than EG-1 going from 14.04 to 14.25 and is less ergonomic going from 17.75 to 19.09 but still maintains the lowest MCC
(b) Thanks to trangium's NLL algs being <RUF> the MCC score should be more accurate relative to the EG stats. Because now most of the algs between methods are <RUF> MCC should have a similar bias in evaluating them. MCC still should be taken with a grain of salt but now it should be a bit more accurate.
(3) I updated my original alg sheet with some better algs
(4) Came out with public algsheet so you guys can add/update it as you find better algs. I'm not too great at picking the best 2x2 algs so I'm going to leave it to y'all.
(5) Also ran through 30 HD-G solves and got an average movecount of 13.83
Also, would anyone like me to add OFOTA, SS, SOAP stats as well? Any other method you want added? Let me know
(1) I updated the Full EG stats to match theh 2/3 - 1/3 option select distribution
(2) I updated the average movecount/MCC of HD-G using trangium's algs as they are currently the best algs
(a) HD-G is now slightly less efficient than EG-1 going from 14.04 to 14.25 and is less ergonomic going from 17.75 to 19.09 but still maintains the lowest MCC
(b) Thanks to trangium's NLL algs being <RUF> the MCC score should be more accurate relative to the EG stats. Because now most of the algs between methods are <RUF> MCC should have a similar bias in evaluating them. MCC still should be taken with a grain of salt but now it should be a bit more accurate.
(3) I updated my original alg sheet with some better algs
(4) Came out with public algsheet so you guys can add/update it as you find better algs. I'm not too great at picking the best 2x2 algs so I'm going to leave it to y'all.
(5) Also ran through 30 HD-G solves and got an average movecount of 13.83
Also, would anyone like me to add OFOTA, SS, SOAP stats as well? Any other method you want added? Let me know
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Neuro
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Oh this is awesome! For those who don’t know, I helped make the HD method and NLL stands for Neuro Last Layer. It seems it’s more competitive than we creators thought. However, there is a major issue inherent to the method:
Difficulty 1-looking.
Reducing the cube to a state required for NLL involves two major steps: Guimond Layer and CO+V. Now, a Guimond layer is very easy to do, but one must also know what CO case they’ll get and how to make a V once it’s been executed. Then they have to predict NLL.
This is, in my experience, much more difficult than 1-looking with CLL+EG1+EG2. That alone makes this method unviable in my opinion, as I think a good 2x2 method should be one-look-able and have good movecounts/algs. HD-G only has the latter trait.
Still, I could just be an idiot with poor look ahead, and there is value in novelty methods. I’d love to see HD/HD-G brought to its full potential.
Difficulty 1-looking.
Reducing the cube to a state required for NLL involves two major steps: Guimond Layer and CO+V. Now, a Guimond layer is very easy to do, but one must also know what CO case they’ll get and how to make a V once it’s been executed. Then they have to predict NLL.
This is, in my experience, much more difficult than 1-looking with CLL+EG1+EG2. That alone makes this method unviable in my opinion, as I think a good 2x2 method should be one-look-able and have good movecounts/algs. HD-G only has the latter trait.
Still, I could just be an idiot with poor look ahead, and there is value in novelty methods. I’d love to see HD/HD-G brought to its full potential.
This is actually so interesting because I feel exactly the opposite. For me, HD-G ( I can't really speak to HD because I am less familiar ) seems like its far easier to 1-look. Firstly is because you can pre-memorize how the Guimond CO alg will effect permutation. Given the fact that the average distance to a Guimond 3/4 face is 0.16 this becomes very easy. The second reason is due to the fact that HD-G orients first. This means when you're tracking the rest of the pieces for the rest of the solution you only have to worry about permutation, not both permutation and orientation as in EG. Lastly, as mentioned before, very very often you're only required to modify the Guimond alg by doing a R instead of a R' ( and vise versa ) to solve the V. The other nice solution is that if the R/R' doesn't form the V you can just work through several solutions which will produce that V.
Example:
Scramble: F' R' F' R2 U R' U' F2 U
So here we can look to 3 solutions:
(1) z2 // Here we have the Red/Orange V and immediately l see that the stickers are arranged in a opposite pattern ( no 2 stickers are set adjacent to one another). This is a bad situation because we produce 2 bad situations (a) where a Red sticker will be placed in DFR meaning we will have to add an additional move to create the V and (b) where an Orange sticker will be placed there which would set the V an D2 away.. not great. So I'd just avoid this.
(2) x2 z // Here the you have 2 adjacent blue sticker which is much better but still not great. The best Guimond face is going to be 2 matching stickers on L ot R. Luckily the way to solve this case is y' U2 R2 U R' U2 R' which places the bar on L. Here ( after the y' ) UFL > DRF > DBR. Since the alg is 2 gen the DFL and DBL are untouched. Good but I got one better.
(3) x' L' // Here we are 1 move off from a Guimond face that produces a 3 move case which is the easiest to track. Here I'd actually do y2 U2 R' U R instead of U2 L' U L as it sets up the V correctly. the alg doesn't effect the rest of the V and we only have to track 3 remaining pieces in the U layer.
8/15 Guimond algs are 3 moves. Another is 4 moves but is sneakily just F into a previous case. Since all but 1 alg is 2 gen the DFL DBL pieces always stay the same.
This is probably longer than it needs to be but here you go.
tldr; Tracking orientation and permutation is harder than just tracking permutation. Easier to track pieces through an alg as it always has the same effect and you don't need to do it on the fly.
Also an honor to have your input!! Very fond of this method
Hope we can see it grow!! I think it has good potential and it seem some other people do as well. Would be awesome to get some reactions/input of top level 2x2 solvers.Added stats for DFR algs and the summation of both DFR and DBR algsets. DFR algs are a notably more efficient. When I get a chance I'll change recognition of DFR algs to match F/B reflection.
Also going to go through 100 example solves to get a better idea of the natural movecount per method. After I'm finished I'll open up the sheet to the public so we can get better solutions as my EG solutions aren't looking too hot comparatively. Would like to get all of this wrapped up by the end of the year. Another note this that several of the HD-G solves I've been going through are move optimal since HD-G is solved in the same manor as computer solves.
Also going to go through 100 example solves to get a better idea of the natural movecount per method. After I'm finished I'll open up the sheet to the public so we can get better solutions as my EG solutions aren't looking too hot comparatively. Would like to get all of this wrapped up by the end of the year. Another note this that several of the HD-G solves I've been going through are move optimal since HD-G is solved in the same manor as computer solves.
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