[Help Thread] Square-1 Discussion

Lid said:
Here are some numbers from my PBL project:

[TABLE="class:grid"]
[TR][TR="colspan:4"]optimal twists for all PBLs[/TR][/TR]
[TR][TD]twists[/TD][TD]no parity[/TD][TD]parity[/TD][TD]total[/TD][/TR]
[TR][TD]0[/TD][TD]1[/TD][TD][/TD][TD]1[/TD][/TR]
[TR][TD]3[/TD][TD]6[/TD][TD][/TD][TD]6[/TD][/TR]
[TR][TD]4[/TD][TD]6[/TD][TD][/TD][TD]6[/TD][/TR]
[TR][TD]5[/TD][TD]51[/TD][TD][/TD][TD]51[/TD][/TR]
[TR][TD]6[/TD][TD]178[/TD][TD][/TD][TD]178[/TD][/TR]
[TR][TD]7[/TD][TD]387[/TD][TD]6[/TD][TD]393[/TD][/TR]
[TR][TD]8[/TD][TD]283[/TD][TD]48[/TD][TD]331[/TD][/TR]
[TR][TD]9[/TD][TD]56[/TD][TD]250[/TD][TD]306[/TD][/TR]
[TR][TD]10[/TD][TD][/TD][TD]398[/TD][TD]398[/TD][/TR]
[TR][TD]11[/TD][TD][/TD][TD]224[/TD][TD]224[/TD][/TR]
[TR][TD]12[/TD][TD][/TD][TD]42[/TD][TD]42[/TD][/TR]
[TR][TD]total[/TD][TD]968[/TD][TD]968[/TD][TD]1936[/TD][/TR]
[TR][TD]avg[/TD][TD]7.068[/TD][TD]9.942[/TD][TD]8.505[/TD][/TR]
[/TABLE]
[TABLE="class:grid"]
[TR][TR="colspan:4"]optimal moves for all PBLs[/TR][/TR]
[TR][TD]moves[/TD][TD]no parity[/TD][TD]parity[/TD][TD]total[/TD][/TR]
[TR][TD]0[/TD][TD]1[/TD][TD][/TD][TD]1[/TD][/TR]
[TR][TD]7[/TD][TD]1[/TD][TD][/TD][TD]1[/TD][/TR]
[TR][TD]8[/TD][TD]1[/TD][TD][/TD][TD]1[/TD][/TR]
[TR][TD]9[/TD][TD]6[/TD][TD][/TD][TD]6[/TD][/TR]
[TR][TD]10[/TD][TD]2[/TD][TD][/TD][TD]2[/TD][/TR]
[TR][TD]11[/TD][TD]7[/TD][TD][/TD][TD]7[/TD][/TR]
[TR][TD]12[/TD][TD]3[/TD][TD][/TD][TD]3[/TD][/TR]
[TR][TD]13[/TD][TD]25[/TD][TD][/TD][TD]25[/TD][/TR]
[TR][TD]14[/TD][TD]13[/TD][TD][/TD][TD]13[/TD][/TR]
[TR][TD]15[/TD][TD]70[/TD][TD][/TD][TD]70[/TD][/TR]
[TR][TD]16[/TD][TD]47[/TD][TD][/TD][TD]47[/TD][/TR]
[TR][TD]17[/TD][TD]116[/TD][TD]4[/TD][TD]120[/TD][/TR]
[TR][TD]18[/TD][TD]172[/TD][TD][/TD][TD]172[/TD][/TR]
[TR][TD]19[/TD][TD]165[/TD][TD]29[/TD][TD]194[/TD][/TR]
[TR][TD]20[/TD][TD]90[/TD][TD]28[/TD][TD]118[/TD][/TR]
[TR][TD]21[/TD][TD]133[/TD][TD]81[/TD][TD]214[/TD][/TR]
[TR][TD]22[/TD][TD]73[/TD][TD]142[/TD][TD]215[/TD][/TR]
[TR][TD]23[/TD][TD]31[/TD][TD]190[/TD][TD]221[/TD][/TR]
[TR][TD]24[/TD][TD]8[/TD][TD]127[/TD][TD]135[/TD][/TR]
[TR][TD]25[/TD][TD]4[/TD][TD]151[/TD][TD]155[/TD][/TR]
[TR][TD]26[/TD][TD][/TD][TD]119[/TD][TD]119[/TD][/TR]
[TR][TD]27[/TD][TD][/TD][TD]68[/TD][TD]68[/TD][/TR]
[TR][TD]28[/TD][TD][/TD][TD]28[/TD][TD]28[/TD][/TR]
[TR][TD]29[/TD][TD][/TD][TD]1[/TD][TD]1[/TD][/TR]
[TR][TD]total[/TD][TD]968[/TD][TD]968[/TD][TD]1936[/TD][/TR]
[TR][TD]avg[/TD][TD]18.510[/TD][TD]23.698[/TD][TD]21.104[/TD][/TR]
[/TABLE]
And here is a small list of the really short ones:

3 twists: op/op, Na/Na, Nb/Nb, Na/Nb, Nb/Na, pN/pN
4 twists: adj/adj, J/J, J/L, L/J, L/L, pJ/pJ
7 twists parities: op/Na, Na/op, op/Nb, Nb/op, H/pN, pN/H

7 moves: Na/Na
8 moves: J/J
9 moves: op/op, J/Na, Na/J, Na/Nb, Nb/Na, pN/pN
10 moves: J/L, L/J
11 moves: adj/adj, J/Nb, L/Na, Na/L, Nb/J, Nb/Nb, pJ/pJ
12 moves: -/J, J/-, L/L

and the lonely long one:
29 moves: Ra/Q

(p=pure corner swap)

.. and move numbers may not be 100% due to that I may not have found the optimal starting alignment for all cases :P
Click to expand...

What's a Q perm?
 
Here are some alternative EPs I found for the M2 O/op & the 2xCP H/U

O+/op ODD twist
1,0/6,0/5,-1/-3,0/1,1/-3,0/-1,-1/0,1 [7|18]
O-/op ODD twist
0,-1/1,1/3,0/-1,-1/3,0/-5,1/6,0/-1,0 [7|18]

H/U+ ODD twist
1,0/2,-1/-2,1/2,-1/3,0/-3,0/-2,1/3,0/-3,0/5,0 [9|23]
H/U- ODD twist
1,0/3,0/-3,0/2,-1/3,0/-3,0/-2,1/2,-1/-2,1/5,0 [9|23]

Some PBLs:
Those can be forced to good U/U, but they save 3 twists.
1,0/-1,2/-2,-2/6,0/-1,-1/-2,1/-1,0 [6|17] Rb/Ra
0,-1/0,3/-2,-2/3,-3/-1,-1/0,3/0,1 [6|16] Ra/Rb

For Ra/Ra and Rb/Rb, you could do pureJ/pureJ + adj/adj.

Let me know if there are any other PBLs you like to get an alg for.
 
The first two are pretty much standard, but they use 1,0/5,-1/6,0 in place of one of the M2s. I've actually used this for a while as a quick way to swap E slice on algs that use M2 (H, Z, O/opp, O/O, etc).

I gotta try those H/U algs when I get home, though.
 
Thoughts on the vandenbergh method

While I think vandenbergh method is capable of sub 10 global averages, I do think it will have its limitations for times closer to sub 9. Here are some thoughts on how it could be improved. First off, the next reasonable step would be to combine two of the steps (CS, CO, EO, CP, EP) while EP and CP would probably be the best place to combine, the number of algs makes this close to impossible in my mind. The next place to combine, EO and CP would be a lot of algs, but nowhere near as many algs as PBL (I think). Next, combining CO and EO is just known as AO, and I think that is the most reasonable place to combine. While it is ~180 algs, most of the algs are very short. However, from my experience with this, it can be somewhat hard to recognize. So, I think it would be possible to do CS+AO in one look, by using something similar to what Mike Hughey did for sq1 bld, just knowing where the pieces end up and so being able to do CS,Co, and EO in one look. Back to EP and CP, one thing that I noticed I was doing intuitively was after seeing a certain PLL case so many times, you start to generally know what EP case you'll have (I'm sure all of the faster sq1 solvers already do this) Therefore, I would just finish this off and learn what PLL case yields what EP case (and the angle at which you get the PLL so that you know how to AUF/ADF) so that you can one look CP and EP. If you were able to do all of the things mentioned, you could solve the sq1 in 2 looks every time. However, I think this can still be improved. By using CS+parity, you could probably drop ~1 second on your times. However, you would have to know how 180 (plus mirrors) CS algs affect the corners and edges so you could do AO. However, even if you eliminate parity that early, there are still some PBL cases that if you just do normal CP+EP, are downright nasty (stuff like M-Ca, which I think will give you W-O for EP) Therefore, for the really nasty cases, you could learn some PBL algs for it. This would probably only be about 20 PBLs, but you could always learn more.

In conclusion, I think the best vandenbergh variant would be CS+parity and AO in one look, and then CP+EP or PBL. However, this would also be quite a lot of algs and you would have to put a massive amount of time and effort just to be able to learn all the algs/cases for this method. I think the alg count would be somewhere around 260 algs, plus figuring out how 180 CS cases effect your pieces. On top of that, you'd have to learn how to tell if you have parity during CS, but I don't think that is too bad.(I would ask Jabari if he'd be willing to learn all these algs, but he already told me that he hates Sq1 :P) I think this is doable, though because if you learned one alg or CS case a day, which is very doable, you would learn this full method in about 16 months. Also, a lot of you probably know lots of non-parity EPs already, and so you could reduce the alg count greatly.
 
TMarshall said:
Thoughts on the vandenbergh method

While I think vandenbergh method is capable of sub 10 global averages, I do think it will have its limitations for times closer to sub 9. Here are some thoughts on how it could be improved. First off, the next reasonable step would be to combine two of the steps (CS, CO, EO, CP, EP) while EP and CP would probably be the best place to combine, the number of algs makes this close to impossible in my mind. The next place to combine, EO and CP would be a lot of algs, but nowhere near as many algs as PBL (I think). Next, combining CO and EO is just known as AO, and I think that is the most reasonable place to combine. While it is ~180 algs, most of the algs are very short. However, from my experience with this, it can be somewhat hard to recognize. So, I think it would be possible to do CS+AO in one look, by using something similar to what Mike Hughey did for sq1 bld, just knowing where the pieces end up and so being able to do CS,Co, and EO in one look. Back to EP and CP, one thing that I noticed I was doing intuitively was after seeing a certain PLL case so many times, you start to generally know what EP case you'll have (I'm sure all of the faster sq1 solvers already do this) Therefore, I would just finish this off and learn what PLL case yields what EP case (and the angle at which you get the PLL so that you know how to AUF/ADF) so that you can one look CP and EP. If you were able to do all of the things mentioned, you could solve the sq1 in 2 looks every time. However, I think this can still be improved. By using CS+parity, you could probably drop ~1 second on your times. However, you would have to know how 180 (plus mirrors) CS algs affect the corners and edges so you could do AO. However, even if you eliminate parity that early, there are still some PBL cases that if you just do normal CP+EP, are downright nasty (stuff like M-Ca, which I think will give you W-O for EP) Therefore, for the really nasty cases, you could learn some PBL algs for it. This would probably only be about 20 PBLs, but you could always learn more.

In conclusion, I think the best vandenbergh variant would be CS+parity and AO in one look, and then CP+EP or PBL. However, this would also be quite a lot of algs and you would have to put a massive amount of time and effort just to be able to learn all the algs/cases for this method. I think the alg count would be somewhere around 260 algs, plus figuring out how 180 CS cases effect your pieces. On top of that, you'd have to learn how to tell if you have parity during CS, but I don't think that is too bad.(I would ask Jabari if he'd be willing to learn all these algs, but he already told me that he hates Sq1 :P) I think this is doable, though because if you learned one alg or CS case a day, which is very doable, you would learn this full method in about 16 months. Also, a lot of you probably know lots of non-parity EPs already, and so you could reduce the alg count greatly.
Click to expand...

a lot of what you have stated has already been done. CO+EO = OBL. EO+CP = PBL etc. There are a lot of people who have contributed and thought of these things before, but it's great that you're thinking about possible adjustments.
 
Raptor56 said:
a lot of what you have stated has already been done. CO+EO = OBL. EO+CP = PBL etc. There are a lot of people who have contributed and thought of these things before, but it's great that you're thinking about possible adjustments.
Click to expand...

Ya i was sure others had thought of this, but I'm fairly certain PBL and OBL/AO have not been developed in full. The point of my post was to just put everything together into an "ultimate" method
 
TMarshall said:
Ya i was sure others had thought of this, but I'm fairly certain PBL and OBL/AO have not been developed in full. The point of my post was to just put everything together into an "ultimate" method
Click to expand...

when it comes to PBL, all the cases have been done as seen here: http://www.cubezone.be/square1eocp.txt

If you look on some of the older threads you can find a lot of good information on these topics.
 
TMarshall said:
Thanks for the list! Do you know if full AO/OBl is done? All I could find is AO for the 1 slice CO cases.
Click to expand...

Here is a link to Andrew Nelson's Page on OBL.

http://andrewknelson.com/sq1ao.html

I can't confirm that all the cases have been done, but his page has a lot of the nice cases. You would have to talk it over with him to know if all the cases have been done.
His page is a great place to start learning OBL / AO, so I highly recommend using it if you want to learn more about it.
 
Last edited:
Raptor56 said:
Here is a link to Andrew Nelson's Page on OBL.

http://andrewknelson.com/sq1ao.html

I can't confirm that all the cases have been done, but his page has a lot of the nice cases. You would have to talk it over with him to know if all the cases have been done.
His page is a great place to start learning OBL / AO, so I highly recommend using it if you want to learn more about it.
Click to expand...

Thank you! I'll definitely be learning those. Also, what should my splits be for sub 13? (I don't do any fancy stuff, just standard CS, CO, EO, CP, EP). I know splits are kinda hard to give on sq1 because of parity and stuff, but I need to figure out where my weak points are.
 
TMarshall said:
Thank you! I'll definitely be learning those. Also, what should my splits be for sub 13? (I don't do any fancy stuff, just standard CS, CO, EO, CP, EP). I know splits are kinda hard to give on sq1 because of parity and stuff, but I need to figure out where my weak points are.
Click to expand...


I can't actually give any advice until you tell me what your splits are currently. Everyone is different when it comes to solving.
 
Last edited:
TMarshall said:
CS: 2-3
CO:1-2
EO:2-3
CP:1-2
EP:4-6
Click to expand...

Your Cubeshape, Corner Orientation, Edge Orientation, and Corner Permutation all seem fine to me. EP is usually the barrier when it comes to getting sub 13 averages. How many EP cases do you know involving parity?
 
Raptor56 said:
Your Cubeshape, Corner Orientation, Edge Orientation, and Corner Permutation all seem fine to me. EP is usually the barrier when it comes to getting sub 13 averages. How many EP cases do you know involving parity?
Click to expand...

I think I know around 50 or so. However, I think my fingertricks for some of the cases aren't that great, so I'll just drill the ones I already know and learn some more ones for annoying cases. Thanks for the advice!
 
TMarshall said:
I think I know around 50 or so. However, I think my fingertricks for some of the cases aren't that great, so I'll just drill the ones I already know and learn some more ones for annoying cases. Thanks for the advice!
Click to expand...

Seems solid to me. I suppose you can just follow your own advice for that. Practice makes perfect ^^.
 
TMarshall said:
Ya i was sure others had thought of this, but I'm fairly certain PBL and OBL/AO have not been developed in full. The point of my post was to just put everything together into an "ultimate" method
Click to expand...

Sorry to contradict, but OBL has indeed been developed in full :) Here's an OBL tree (like the cubeshape tree on Jaap's page): http://www.its.caltech.edu/~skuroyam/obl_data_numstates_1110.pdf

That being said, I don't think anyone in the world quite uses it 100% - my girlfriend was the one who made that tree, and although I know nearly all of it, I don't always use it (there are some kinda messy 4s and 5s I don't always do it for, although I think it's worth it to learn all 4s). I don't know any of the messier opp/opp corner cases (but that's only 4/74 cases).

Regarding the rest of your main post, 'tho, I do think that CS+P has some merit. I definitely think that inspection is heavily underused still, and although I've been starting to do CS+CO (only for prediction, since I normally do OBL now), doing CS+OBL in inspection is probably doable. I'm not sure if CS+P+OBL is doable in inspection, but that's mostly because I don't know CS+P very well, so I can't comment on its sub-15 ability. But I think my role as someone who solves the puzzle fast is quickly waning, since I simply can't keep up with the tps of you young whippersnappers. Happy to turn into an Old Wise Man and talk theory with y'all :)
 
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