cage/cage variants sub minute average potential?

[rachmaninovian]

hello world

as topic title...Does anyone believe that cage or any cage variants could have a sub 1 average potential?

Per had a 1:01.07 average 10 of 12 as posted on the UWR, and I have a 1:07.90 average (pb as of today, 10 of 12 as well). His pb is 47.24s and mine 55.96s (lucky - 54.81s).

I must say that if i cut like 7s I'd beat per....wells I do not know whether to remain skeptical or anything. sure cage has a high move count, but sub minute is still possible perhaps?

I'm developing centre control techniques and also solving more than 2 edge cubies (or dedge) for the top and bottom layer at the same time...the slowest part is often the centres anyway...

my current breakdowns are
first 2 centres - 4-5s
corners - 8-12s
finish top+bottom layers - 20-25s
finish cage - 8-12s
final centres - 15 - 25s
total ranging from 55s to 1:14

my timings right now hover over 1:10 +/- 2s most of the time..grhh i've spent 16 months with this already? haha..

please leave any comments if any..

 

[cubacca1972]

I think that sub 1 minute should be possible with the right cube and the right algorithms for each stage. I think you would need to have a killer system for everything up to the remaining centers in order to compensate for the potentially lengthy center finish phase.

I have seen a video of you solving, and think you definitely have the dexterity for it.

I tried to look up your site, but my computer hangs whenever I try to navigate your site, so I don't know your full method. It looks like you use Waterman to solve your l and r layer edges.

How do you solve your remaining centers?

I did some research into what little is out there on the net, and put my own system together with algorithms borrowed from or derived from Waterman and from Jaap's site.

You can find my method here:

http://cubacca1972.googlepages.com/home

I would be interested to hear what you think of Phase 2 and Phase 3 of my method. In particular, check out my alternate Phase 2 system.

 

[TMOY]

Your method requires up to eight algs to solve the last four centers, which is way too much. I've already described here a way to do it in only two algs, by first putting all center cubies on either the rignt side or its opposite, and theh solving both opposite pairs of centers at once; The drawback is that you have to look at all four faces to recognise the cases, but you don't lose that much time doing so.
And yes, I too think cage definitely has a sub-1 potential.

 

[cubacca1972]

Your method requires up to eight algs to solve the last four centers, which is way too much. I've already described here a way to do it in only two algs, by first putting all center cubies on either the rignt side or its opposite, and theh solving both opposite pairs of centers at once; The drawback is that you have to look at all four faces to recognise the cases, but you don't lose that much time doing so.
And yes, I too think cage definitely has a sub-1 potential.

I am having a hard time understanding the move notation, even with the superset notation glossary.

I would consider the sheer volume of algorithms listed as a drawback as well. I counted 42 algorithms for step 1, and 27 algorithms for the second step. Does this set include all orientations, or do you have to do multiple face turns to set up the patterns?

Have you memorized all of these algorithms? If you know these algorithms cold, then you're golden. I would be worried about forgetting most of them with any length of time away from the cube.

Looking at the probabilities of number of required algorithms for my system, a 3.8% chance of needing 8 algorithms seems fairly reasonable. If you are selective about which swaps you do, you can control the total number of algorithms required. For example, start with any center that can be solved in 2 or less algorithms. This automatically drops the total number of algorithms needed to 7 or less. If you take care as you solve any particular center, you can sort the cubies you are swapping out into blocks of 2 which are moved easily, or send them to their appropriate centers.

In addition, most of the algorithms are short, and easy to remember.

 

[TMOY]

The set includes only one orientation for each case, you have to do setups. Anyway I stated it was far from perfect.
And no, I haven't memorized all of them. I'm doing each step in two algs most of the time, which adds up to 4 or less algs overall and doesn't require that much algs.

 

[somerandomkidmike]

Yes I think it is possible. Just you wait... I will accomplish it some day.

 

[rachmaninovian]

Your method requires up to eight algs to solve the last four centers, which is way too much. I've already described here a way to do it in only two algs, by first putting all center cubies on either the rignt side or its opposite, and theh solving both opposite pairs of centers at once; The drawback is that you have to look at all four faces to recognise the cases, but you don't lose that much time doing so.
And yes, I too think cage definitely has a sub-1 potential.

lol, too many algs =D my centres average is around 20 now...and I think that your method for centres has potential, but it'll take too long to master everything..and I think I use 4-5 algs to finish centres on average...one alg takes at most 3-4s? which corresponds to my centres timings...I believe lookahead is what really attracts me still to the way I do the centres..I can do 12s final sometimes or less if i'm lucky or I see the shortest number of algs needed to commute the pieces..xD

cubacca1972 - yes, I use advanced waterman I guess...I know around 50 algs for the middle edges. waterman has 16+5 at most =P
your method and mine is quite similar, the only difference being the middle edges, and that I solve most of the time one dedge at time without pairing up edges manually...the max number of moves of such an alg is 7 and the average should be around 5 moves..maybe 6 at most?
to be honest and frank with you, I never really liked the alternate solution =D
you have more optimal algs then me for the last dedge of the first 2 faces, but with my algs I can plan my moves more =)
for centres I do about the same as you but I have an optimal one for adjacent whole centres =D and I use 3cycling of 3 different colored cubies as well (though not most of the time), so I save about 1 alg =D and I think I use more algs than you...so probably my average number of algs is 5.5 or something along that line.

maybe IF i can solve corners faster and pause less (look at per's 70s vid..almost no pauses!!!!) sub 1 should be around the corner...all I want is a 59s pb average =) and perhaps sub 50 single?

well right now I use a mefferts black which I like...but I think it gets loose easily =(

 

[Neroflux]

why do i get less and less motivated?

 

[cubacca1972]

Your method requires up to eight algs to solve the last four centers, which is way too much. I've already described here a way to do it in only two algs, by first putting all center cubies on either the rignt side or its opposite, and theh solving both opposite pairs of centers at once; The drawback is that you have to look at all four faces to recognise the cases, but you don't lose that much time doing so.
And yes, I too think cage definitely has a sub-1 potential.

lol, too many algs =D my centres average is around 20 now...and I think that your method for centres has potential, but it'll take too long to master everything..and I think I use 4-5 algs to finish centres on average...one alg takes at most 3-4s? which corresponds to my centres timings...I believe lookahead is what really attracts me still to the way I do the centres..I can do 12s final sometimes or less if i'm lucky or I see the shortest number of algs needed to commute the pieces..xD

cubacca1972 - yes, I use advanced waterman I guess...I know around 50 algs for the middle edges. waterman has 16+5 at most =P
your method and mine is quite similar, the only difference being the middle edges, and that I solve most of the time one dedge at time without pairing up edges manually...the max number of moves of such an alg is 7 and the average should be around 5 moves..maybe 6 at most?
to be honest and frank with you, I never really liked the alternate solution =D
you have more optimal algs then me for the last dedge of the first 2 faces, but with my algs I can plan my moves more =)
for centres I do about the same as you but I have an optimal one for adjacent whole centres =D and I use 3cycling of 3 different colored cubies as well (though not most of the time), so I save about 1 alg =D and I think I use more algs than you...so probably my average number of algs is 5.5 or something along that line.

maybe IF i can solve corners faster and pause less (look at per's 70s vid..almost no pauses!!!!) sub 1 should be around the corner...all I want is a 59s pb average =) and perhaps sub 50 single?

well right now I use a mefferts black which I like...but I think it gets loose easily =(

Man, I need to get to a computer that doesn't hang when I try to browse your site. I am very curious about your center solves ,especially adjacent center whole soves. Mine is just two back to back 2 adjacent pair swaps.

As for my alternate method for middle edges, recognition for part one is pretty harsh for a while. Part two is fairly easy.

 

[rachmaninovian]

d M2 d' L2 B2 u' M2 u M2 B2 R2 x2 [alg by Rainer aus dem Spring] I changed some stuff obviously =P

as I said for centres I do anything that I see at the moment.

I rarely use that alg but still I do use it sometimes...that case is rare...

and anyway I pretty much use the same algs as you for the 4x4 centres..maybe different angles and less setup moves required for some =P

and again...with some centre control you will purposely get luckier centres =P so your middle edges method wouldn't very much control centres..

 

[AvGalen]

hello world

as topic title...Does anyone believe that cage or any cage variants could have a sub 1 average potential?

Per had a 1:01.07 average 10 of 12 as posted on the UWR, and I have a 1:07.90 average (pb as of today, 10 of 12 as well). His pb is 47.24s and mine 55.96s (lucky - 54.81s).

I have a very high respect for Pers techniques and understanding of the cube, but I don't believe those times on the UWR. If you look at his official results you can see that the difference between his official and unofficial times are just to big to rationalise by "nerves", "lack of practice" or anything else.

http://www.worldcubeassociation.org/results/p.php?i=2004FRED02
Between 2004 and 2008 his 4x4x4 times have hardly dropped and with a PB of 1:21.33 and average of 1:49.11 I believe you already have bypassed Per in speed

I do believe that caging can go sub 60 on average, but if you are developing a new method for speed (not fun or research) shouldn't you be aiming for sub 50?

 

[rachmaninovian]

lol I had my doubts with that anyway..

well sub 50? I believe that there isn't any direct solving method yet that has reached that level...so right now I'm aiming sub 60 first. long way to go..and almost impossible.

On the other hand, I am running out of ideas on optimizing the method; the last optimization I had done was the concept of centre control using different algs for the last 2 dedges to finish the cage...of course I can very much use TMOY's centres method but I am rather skeptical about how fast it can really be...69 algs is a hefty load, and I wouldn't very much be able to use it for the 5x5. So right now commutators ftw..

any suggestions? bleah.

 

[masterofthebass]

k4 is almost sub60 at this point. With some more LL alg generation, I can see it getting sub50.

 

[cubacca1972]

lol I had my doubts with that anyway..

well sub 50? I believe that there isn't any direct solving method yet that has reached that level...so right now I'm aiming sub 60 first. long way to go..and almost impossible.

On the other hand, I am running out of ideas on optimizing the method; the last optimization I had done was the concept of centre control using different algs for the last 2 dedges to finish the cage...of course I can very much use TMOY's centres method but I am rather skeptical about how fast it can really be...69 algs is a hefty load, and I wouldn't very much be able to use it for the 5x5. So right now commutators ftw..

any suggestions? bleah.

The best I can think of would be this:

Corners-Solve 4 D corners, then orient/permute U corners in 1 algorithm. This would likely be the best/fastest way to solve them.

Edges for L and R layer-Not much to say here, other than concentrating on improving look aheads.

l and r edges-nail them down with whichever method works best for you. I think that doing a close analysis of total number of moves required for each method would help here. Do an average of 12 for each method available (yours, both of mine, pure Waterman, whatever else is out there), and give serious consideration to adopting the method with the lowest move average. I have no idea which is the best as far as number of moves goes.

Centers-I think that a good search program is needed here. I would propose the following solve system:

Solve 1 entire center in 1 algorithm.

Solve the opposite center in 1 algorithm

Solve the last two centers in one algorithm

I have no idea how many algorithms would be required for each step here, but if the algorithm sets could be found, it would take care of the fiddly single center cubie swaps.

 

[Robert-Y]

Thank god I'm not the only one who doubts Per's abilities. No offense or anything but I cannot find any evidence to suggest that he can actually do the 4x4 using the cage method in about a minute, therefore I can't believe that he can do this. Although I was in a similar situation, I had some sort of proof (replays) that I didn't lie about my times on the computer cubes. What I find weird is that I think Per doesn't really have any reason to lie though, he's a good guy (at least I think so).

 

[blade740]

I could see cage getting ridiculous lucky times if the centers were paired up. If you know how to cycle blocks of two centers, you can get a bunch of skips if things pan out correctly (read: very luckily).

 

[rachmaninovian]

I purposely pair up blocks of centres while swapping single cubies =)

well I do agree that there isn't much proof of per having minute solves...but well, however different my cage is I have done sub 1 on tape before though it was really lucky...anyway, I just had a 1:05 average with 3 1:00s, 1 1:01 and a 57s. and also a 1:44 xD but again this is with a lot of warmup..and some luck.

I did another break down of a good solve(approx)
4s 1st 2 centres
8s corners (without inspection and bad recognition called for lousy times like this always -.-)
22s finish R and L faces
8s finish cage
15s centres
total abt 57?

my centres are barely sub 20 now...and considering how efficient reduction centres can be it is really bad..

I think I can improve my cage to the sub 45 region or possibly sub 40 in the future, but everything would come down to the centres. Either I find a more efficient way of solving centres, or I just practise like nuts.

cubacca1972:

1. corners - you do know that recognition stinks xD ortega recognition is faster...especially on a messy cube.
2. middle edges - I use a mixture or waterman, my own stuff, some of kenneth's and francois' algs. I would say I average 10s or below; the first method that you proposed of the edges was what I was doing for a long time until I decided that it was too slow...and my method allows centre control =P and its getting faster and faster...though I think the limit is an 8s average, without inspection of course.
3. centres - WAYYYYYYY too many algs for the first centre...wells I have most of the algs to solve 2 opposite centres at one go..I can think of 6 algs for that..1. M2 u2 M2 u2, 2. u2 r2 u2 r2, 3. r2 U' l2 U r2 U' l2 U, 4. U2 D' M' u2 M U2 D M' u2 M, 5. U (rl') u2 (r'l) U' D' (rl') u2 (r'l) D and 6. l2 U r2 U' l2 U2 l2 U' r2 U l2 U2
for the first centre maybe find the best centre and do 2 looks max? =D then all we are left to find is the solve that opposite centre..i had some algs but i forgot them all..

 

[masterofthebass]

I just got a 1:03 average for K4. I will get a sub-1 avg before Thom.

 

[Kirjava]

I just got a 1:03 average for K4. I will get a sub-1 avg before Thom.

No you won't.

 

[cubacca1972]

cubacca1972:

1. corners - you do know that recognition stinks xD ortega recognition is faster...especially on a messy cube.
2. middle edges - I use a mixture or waterman, my own stuff, some of kenneth's and francois' algs. I would say I average 10s or below; the first method that you proposed of the edges was what I was doing for a long time until I decided that it was too slow...and my method allows centre control =P and its getting faster and faster...though I think the limit is an 8s average, without inspection of course.
3. centres - WAYYYYYYY too many algs for the first centre...wells I have most of the algs to solve 2 opposite centres at one go..I can think of 6 algs for that..1. M2 u2 M2 u2, 2. u2 r2 u2 r2, 3. r2 U' l2 U r2 U' l2 U, 4. U2 D' M' u2 M U2 D M' u2 M, 5. U (rl') u2 (r'l) U' D' (rl') u2 (r'l) D and 6. l2 U r2 U' l2 U2 l2 U' r2 U l2 U2
for the first centre maybe find the best centre and do 2 looks max? =D then all we are left to find is the solve that opposite centre..i had some algs but i forgot them all..

As I have mentioned before, I am not going for any world record myself. If I was though, this is the way I would go about it.

First, I would make sure I had the best 4x4x4 available on the market. I have no idea what that would be, though I hear good things about the V cubes.

Regarding corners:

Whichever system works the fastest is the way to go. I would consider any method used by the top 10 2x2x2 solvers. If the system I end up using is one in use by one of the top 5 2x2x2 solvers, then I would be confident in sticking with it. If my system is not in use by the top 10, then I would have to strongly consider switching, no matter how much I was in love with my system. That's why I gave up Guimond.

Regarding the l and r edges:

I still think that the system which requires the fewest total moves is the best choice.

Regarding the centers, I think that the method I propose may be worth exploring, mainly because of the sheer brute force potential here. Brute force has worked very well for 2 look Last Layer solves on the 3x3x3.

If you were to use setup moves, you would need a whole lot of algorithms for the first center, but still a finite number.

Assuming that you are trying to solve the entire U center in one algorithm, and L and R centers are solved:

3 center cubies solved-
single center cubie on adjacent face
single center on opposite face

2 adjacent solved-
single on adjacent, single on opposite
single on adjacent, single on other adjacent
2 adjacent cubies on adjacent face
2 adjacent cubies on opposite face
2 diagonal cubies on adjacent face
2 diagonal cubies on opposite face

2 diagonal solved-
single on adjacent, single on opposite
single on adjacent, single on other adjacent
2 adjacent cubies on adjacent face
2 adjacent cubies on opposite face
2 diagonal cubies on adjacent face
2 diagonal cubies on opposite face

1 center cubie solved-
3 on adjacent face
3 on opposite face
2 adjacent on adjacent face, one on opposite face
2 adjacent on adjacent face, one on other adjacent face
2 adjacent on opposite face, one on adjacent face
2 diagonal on adjacent face, one on opposite face
2 diagonal on adjacent face, one on other adjacent face
2 diagonal on opposite face, one on adjacent face
one center cubie on each of the other 3 faces

0 center cubies solved
All 4 on adjacent face
All 4 on opposite face
2 adjacent on adjacent face, 2 on opposite face
2 adjacent on one adjacent face, 2 adjacent on the other adjacent face
2 diagonal on one adjacent face, 2 diagonal on opposite face
2 diagonal on one adjacent face, 2 diagonal on other adjacent face
2 adjacent on adjacent face, 2 diagonal on opposite face
2 adjacent on adjacent face, 2 diagonal on other adjacent face
2 diagonal on adjacent face, 2 adjacent on opposite face
3 on adjacent, 1 on opposite
3 on adjacent, 1 on other adjacent
3 on opposite, 1 on adjacent
2 adjacent on adjacent face, one on each remaining face
2 adjacent on opposite face, one on each remaining face
2 diagonal on adjacent face, one on each remaining face
2 diagonal on opposite face, one on each remaining face

39 algorithms, if I haven't missed any cases, and am counting correctly. We already use several of them. The only thing I would ensure while finding all the algorithms is that the opposite centers don't get disturbed during a direct center solve (so that you can use a subset of the 39 algorithms to solve the opposite face centers without messing up the first solved center).

Before giving up on this idea, consider how many algorithms an F2L solver must learn to do a 2 look last layer, or even the number of algorithms that you use for your l and r edges.

If you were to disregard center control while finishing the cage, and knew these 39 algorithms cold, you could save brain space on the l and r edge portion of the solve, and concentrate on crushing the centers in 3 algorithms.

That being said, I don't see how the best 39 algorithms can be found without a search program, so this proposed method will likely exist as a theoretical method only. I certainly don't have the time or patience to find them manually.