cage/cage variants sub minute average potential?

[rachmaninovian]

actually I have started using the fastest algorithms for each case =P except for say a few other cases like PLL parity...and if I see that a lot of centres are done, I'd use the pure algs which don't really affect centres. though the pure algs might be a bit slower, it is still worth it as you don't want to switch extra centres later on.

Right now I try to control the centres for the bottom 2 dedges for the r and l slices..and by edges I mean everything in general, including the first 8 for the opposite faces.

I do the last 4 dedges this way: for the first 2, either one at a time, or both at the same time..depends.

again, back to centre control...I do it differently for each solve, it can be during the last 2 dedges or even before that..it is so intuitive I cannot put it in words...there are many different tricks I use differently in each solve..like anyone who learns any direct solving method, he/she would have his/her own twist to it..

 

[Kirjava]

Average: 59.02
Standard Deviation: 3.08
Best Time: 51.36
Worst Time: 1:04.09
52.17, 59.30, 1:01.50, 1:02.77, 57.05, 58.06, (1:04.09), 58.67, 57.50, 59.72, 1:03.48, (51.36)

**** yeah! Mostly thanks to KLL and mocktricks.

 

[Neroflux]

wow direct solving is suddenly sub 1!

 

[somerandomkidmike]

I wish I had a meffert's

Maybe I'll sub-1 on my rubik's

 

[somerandomkidmike]

actually I have started using the fastest algorithms for each case =P except for say a few other cases like PLL parity...and if I see that a lot of centres are done, I'd use the pure algs which don't really affect centres. though the pure algs might be a bit slower, it is still worth it as you don't want to switch extra centres later on.

Right now I try to control the centres for the bottom 2 dedges for the r and l slices..and by edges I mean everything in general, including the first 8 for the opposite faces.

I do the last 4 dedges this way: for the first 2, either one at a time, or both at the same time..depends.

again, back to centre control...I do it differently for each solve, it can be during the last 2 dedges or even before that..it is so intuitive I cannot put it in words...there are many different tricks I use differently in each solve..like anyone who learns any direct solving method, he/she would have his/her own twist to it..

Like my blockbuilding twist on it! I'm getting some pretty good times on the 5x5 now!

 

[rachmaninovian]

actually I have started using the fastest algorithms for each case =P except for say a few other cases like PLL parity...and if I see that a lot of centres are done, I'd use the pure algs which don't really affect centres. though the pure algs might be a bit slower, it is still worth it as you don't want to switch extra centres later on.

Right now I try to control the centres for the bottom 2 dedges for the r and l slices..and by edges I mean everything in general, including the first 8 for the opposite faces.

I do the last 4 dedges this way: for the first 2, either one at a time, or both at the same time..depends.

again, back to centre control...I do it differently for each solve, it can be during the last 2 dedges or even before that..it is so intuitive I cannot put it in words...there are many different tricks I use differently in each solve..like anyone who learns any direct solving method, he/she would have his/her own twist to it..

Like my blockbuilding twist on it! I'm getting some pretty good times on the 5x5 now!

what kind of times? many many sub 2s? what's your pb now?

damn i can't solve a professor as fast as before...zzz if i find the inspiration i will return to the dormant professor lying at the end of my desk xD

bleah..i need to find faster algorithms for the "OLL parity" and double parity...

 

[cubacca1972]

My cube brain is failing me.

In my 4 step center solve method (work/obsession in progress), center cubies are sorted into either the center they belong to, or in the opposite center. So if the red and orange faces were solved, and the remaining centers to be solved were the blue, green, yellow and white, then:

Step 1: Get 4 green or blue center cubies in the blue center

Step 2: Get the remaining green or blue center cubies in the green center

Step 3: Solve the blue and green centers

Step 4: Solve the yellow and white centers

I have been thinking (obsessing) about the probability of needing only 3 steps instead of 4.

My proposed system would have sorting algorithms for steps 1 and 2, which only draw center cubies from adjacent faces. For example, if sorting the Blue center first, any combination of green or blue center cubies would be pulled from the white and or yellow centers and added to whatever is already sorted in the blue face. No algorithms from steps 1 and 2 will draw center cubies from the opposite face (disregard the no brainer cases where it would make sense to do so).

So, in cases where you can solve the blue face in step 1 (all 4 blue center cubies to the blue face), step 2 would solve the green face, which would lead to only needing to solve the white and yellow faces in the last step. In rare cases, you could end up with only 2 steps.

I believe that once the cage is complete, there are 63 063 000 possible permutations of the remaining 4 centers.

So, If you were to always start step 1 with the blue center, there would be
17 151 750/63 063 000 (27.2%)cases where you could direct solve the blue center (no blue center cubies in the green face).

But if you were color neutral on the order of your steps, there would be cases where you couldn't direct solve the blue center, but could direct solve one of the other 3 faces.

So, how can these cases be calculated and added to the 17 151 750 cases? In other words, how often would this proposed system require 3 (or less) algorithms?

 

[qqwref]

What if you combined step 3 and 4? Since each pair of faces only has 8 possibilities, there should be about 36 algs, right? I'm assuming turns of the outer layers are allowed to set up positions.

 

[rachmaninovian]

mm doesnt TMOY have an alg list for step 3+4?

anyway i believe that a lucky cage solve can be sub 40...i had a sub 30 cage (obviously lucky, 3 moves first layer corners, sune OLL, PLL skip for corners plus 2 free dedges on yellow done) and if i had lucky centres, sub 40 should be around the corner..the solve ended up at 47.16s anyway..

 

[TMOY]

Yes, my set of algs covers step 3+4. And there are 7 possiblities for each pair of faces, not 8, hence 27 different algs (28 cases including skip).
The easiest and most helpful one: u2 M u2 M'.

 

[cubacca1972]

What if you combined step 3 and 4? Since each pair of faces only has 8 possibilities, there should be about 36 algs, right? I'm assuming turns of the outer layers are allowed to set up positions.

I kept the total number of algorithms to a minnimum to make learning the system more feasible. The more cases you need to recognize and set up with multiple face turns, the higher the risk that you will have long delays between algorithms.

I initially proposed a 3 step solve for the centers:

Step 1: Direct solve one center (1 of 39 algorithms)

Step 2: Direct solve the opposite center

Step 3: Direct solve the remaining two centers

The problem with this theoretical method would be that you would have to peek at all four centers, and potentially have to do setups on four faces for step 1, then execute the correct algorithm, and not get confused when undoing the setup moves.

So I revised the theoretical system to be a 4 step maximum in order to reduce it to a sane number of algorithms (21).

I would not include algorithms which combine steps 3 and 4 simply because it would boost the required number of algorithms too high, and be clunky because of the need to potentially peek at and set up all 4 centers as mentioned previously. That being said, if you happen to already know those algorithms, by all means, add them in.

On further reflection, I realized that there would be many ways in which the 4step center system (I think I will call it 4SCS) would need 3 steps once the cage is built:

1. One of the centers can be direct solved, because all of its center cubies are in their correct face, or in adjacent faces:

1 Direct solve the first center
2 Direct solve the opposite center
3 Direct solve the remaining 2 centers

2. One of the centers can be direct solved because all of its center cubies are in their correct face, or in the opposite face:

1 Direct solve the first center
2 Direct solve the opposite center
3 Direct solve the remaining 2 centers

3. One of the centers is already sorted:

1 Sort the opposite center
2 Direct solve one pair of opposite centers
3 Direct solve the other pair

I think those are the 3 step cases. This does not include the occasional lucky cases where doing one step causes a later step to be completed.

Two step solves:

1. One face is already solved

2. All centers sorted

One step:

two centers solved.

Granted, the two step and one step scenarios are not very probable, but my initial survey already shows at least 27% of the time, it will take 3 or less steps. I am just wondering what the exact number of cases there are out of all possible cases.

 

[rachmaninovian]

as i said...i have at most a 5 alg system, and the algs are fast..
would you rather a system with sucky and long algs? not really. this might be better than FMC than all the comms i use for centres, freestyle, but it might just not be suitable for speed.

personally i HATE setup moves with 2 faces =P they usually steal about 2-3s for each alg...say 4 algs? that is a maximum of 12s wasted..I have to admit that some comms I use DO require those redundant 2 face set up moves..thats why i'm trying to find better stuff to replace them but i'm too lazy to do that anyway =P the reason I have 4 versions of niklas is because I HATE setup moves (with 2 faces, especially.. )...they are slow for speedsolving. of course AUF is still some setup move theoretically..but they don't waste much time. at most 1s? say I use algs that only need AUF to setup, then I'd waste a total of 4s max.
Of course, freestyling would definitely produce inconsistent timings...I had a 54s solve followed by a 1:27 solve (which should really had been at least 1:19-20 but it was too slow and i gave up.)

Of course the bad thing with freestyling is that it is MORE intuitive in some ways...finding the most efficient way to solve the centres AND without lag...but definitely it can produce the fastest results.

well well well...I have to return to the topic of centre control. right now I seem to be sacrificing some time building a cage with more centres solved, by solving the dedges differently. sure, I waste 3-4s doing so, but I save myself 2 or more slow comms, so it is still worth it in a way; over time it should get better...

yesterday while experimenting with a simulated 4x2x2 on my 4x4x4, I found a new way to control centres..=D =D

wells anyway that sub 1 average was because of a cubing high..my average average nowadays should be sub 1:05 though more like 1:02 or 1:03ish..setup moves cost me a lot of my supposed sub 1 solves..after that average i can sub 1 many many many times...by achieving a sub 1 average I believe that I am pushing my system to the very limits already...sure, lookahead and tps can improve, since i'm not even sub 20 for 3x3 =P more like 23s for 3x3..i'd stop at a 55s average at most..

speaking of which I should learn full CLL...it has been producing good times since I know 7 CLL xD fine I just get PLL skips for the corners...whee. but again...its almost a 20% chance of a skip anyway...ALMOST..I need to get better at corners anyway...its still at 10-12s which is super inefficient and slow..maybe something like 7s would be better?and my first 2 centres are inconsistent..I should improve these 2 thingies and I should almost be sub 1 consistently excluding the lousy cases i get =P

I've been experimenting, optimizing, and using this system since august 2007...but again I might be missing some points here and there.

Of course I'd continue to learn the most useful comms...and use them freestyle of course. maybe i should steal (i mean learn...) more comms from the BC bld people. or ask from per...lol

I must agree that I cannot prevent bad centres...thats why I'm still learning the most simple techniques like switching the entire F and U centres, and also the B and D centres. wasting one alg? yes. but at least that should prevent all the sup 1:20 times..I've never used these techniques (fine...algs) properly in a speedsolve somehow BECAUSE when i encounter them i panic, and I forget the simplest algs. funny, ain't it? I once forgot how to do niklas =P

[/end rant]
whee.

 

[cubacca1972]

as i said...i have at most a 5 alg system, and the algs are fast..

would you rather a system with sucky and long algs? not really. this might be better than FMC than all the comms i use for centres, freestyle, but it might just not be suitable for speed.

Based on your current progress using your algorithms, you should stick with what you know, as it is working well.

I do not have a complete system built yet.

Regarding algorithm length and the need for setup moves: This will only be worthwhile if the algorithm gets lots done. Otherwise, thepayoff is not justified. Generating fastest algorithms won't happen until I can get access to ksolve or some such program to really refine things. In my system, you would have to do a maximum of 3 setup moves for steps 1 and 2, as the opposite face isn't involved (unless direct solving between opposite faces only, which would have only one setup move), and a maximum o f 1 setup move for steps 3 and 4.

Why am I still pursuing (obsessing over) this system? I did a series of solves and stopped at the cage to record how often a 3 step or less scenario came up. Out of 10 solves, 8 could be done in 3 or less. I had done a set prior to this 10 with similar results, but didn't record them, so I didn't include them.

Granted, 10 is too small a sample size, but I think I can say that the centers can be solved with 3 or less steps well over half of the time.

 

[rachmaninovian]

haha, alrighty.
I did an average of 60, I got something like 4.1 (2 s.f.)
speedcubing is not about how many steps you take, but how fast you execute stuff =P
at the end of the day, it is how fast you can do stuff, not how efficient you are with the number of algs =P after all, each alg has probably high move count? so...it cancels out really =P
3 cycling between 3 colors really help =P speaking of which I just got a 59s solve, and guess what? 2 of those comms. 50s cage because I solved my corners wrongly...and I controlled some of the centres for a better finish as such.

 

[somerandomkidmike]

What if you combined step 3 and 4? Since each pair of faces only has 8 possibilities, there should be about 36 algs, right? I'm assuming turns of the outer layers are allowed to set up positions.

I kept the total number of algorithms to a minnimum to make learning the system more feasible. The more cases you need to recognize and set up with multiple face turns, the higher the risk that you will have long delays between algorithms.

I initially proposed a 3 step solve for the centers:

Step 1: Direct solve one center (1 of 39 algorithms)

Step 2: Direct solve the opposite center

Step 3: Direct solve the remaining two centers

The problem with this theoretical method would be that you would have to peek at all four centers, and potentially have to do setups on four faces for step 1, then execute the correct algorithm, and not get confused when undoing the setup moves.

So I revised the theoretical system to be a 4 step maximum in order to reduce it to a sane number of algorithms (21).

I would not include algorithms which combine steps 3 and 4 simply because it would boost the required number of algorithms too high, and be clunky because of the need to potentially peek at and set up all 4 centers as mentioned previously. That being said, if you happen to already know those algorithms, by all means, add them in.

On further reflection, I realized that there would be many ways in which the 4step center system (I think I will call it 4SCS) would need 3 steps once the cage is built:

1. One of the centers can be direct solved, because all of its center cubies are in their correct face, or in adjacent faces:

1 Direct solve the first center
2 Direct solve the opposite center
3 Direct solve the remaining 2 centers

2. One of the centers can be direct solved because all of its center cubies are in their correct face, or in the opposite face:

1 Direct solve the first center
2 Direct solve the opposite center
3 Direct solve the remaining 2 centers

3. One of the centers is already sorted:

1 Sort the opposite center
2 Direct solve one pair of opposite centers
3 Direct solve the other pair

I think those are the 3 step cases. This does not include the occasional lucky cases where doing one step causes a later step to be completed.

Two step solves:

1. One face is already solved

2. All centers sorted

One step:

two centers solved.

Granted, the two step and one step scenarios are not very probable, but my initial survey already shows at least 27% of the time, it will take 3 or less steps. I am just wondering what the exact number of cases there are out of all possible cases.

I like this approach to it. With Center control you can almost always have one set of centers done anyway. That gives you 2 steps. It doesn't necissarily have to be lots of long algorithms if you use a few tricks.

 

[rachmaninovian]

this is what I usually do:
1. find the fastest alg that I can do for the moment, usually M2 u2 M2 u2. or the entire opposite centre. or maybe just a niklas =D the purpose of this is to not waste time looking for stuff and instead do this and inspect stuff at the same time. at least you get something solved. inefficient step but at least you don't waste time doing nothing - you might even set up nice cases..who knows.
2. solve a single centre using 2 or less algs.
3. finish off the rest with a max of 3 algs.

i emphasized at usually...sometimes i completely go freestyle.
the max for this system is 6 algs..and my statistics point towards an average of 4.1 algs per solve, 1 alg for step 1, 1.5 for step 2, 1.5 for step 3, or somewhere along that line.

 

[cubacca1972]

speedcubing is not about how many steps you take, but how fast you execute stuff =P

I have to disagree here to some extent. It is how fast you execute stuff and how many steps you take.

Teach a new cuber a layer by layer method with an easy 4 look last layer. Let him practice for a year with this method.

Next get another new cuber and teach him Fridrich. Get them to go head to head after a month. Layer by layer guy will probably win, with his 13 month head start in practice. But what about the next month? How about after 6 months?

You must combine steps to improve your move count, and you must find the algorithms which maintain excellent turns per second. The natural result of this is relatively few steps with relatively high numbers of algorithms per step.

There simply isn't a world class cube solving system for any sized cube which has lots of steps with few algorithms per step.

each alg has probably high move count? so...it cancels out really =P

If an algorithm gets more done (vs 2 or more algorithms to get the same thing done), and does it with fewer moves than doing the substeps, and maintains a tolerable turns per second, then it would perform better than just cancelling out.

So, your current method will be the fastest one you can use at this time, because there is no other system available (other than TMOY's mega list).

If I can flesh out my system, including optimal searches for each algorithm, then at least you would have something tangible to test drive. The nice thing is that all of your current algorithms would be usable within the system.

 

[rachmaninovian]

once again i'm skeptical on how finger trickable the algs can be...wells we'll see =P
whee..

I like this approach to it. With Center control you can almost always have one set of centers done anyway. That gives you 2 steps. It doesn't necissarily have to be lots of long algorithms if you use a few tricks.

nah...its difficult to do so FAST. =P no, it's not easy to do at all. I just try to solve at least 2 cubies on a centre IF possible. anything more than that is not always possible to do fast..and you might have to cheat with niklas =P

 

[rachmaninovian]

some minor update: i've seen the potential of cll as it produced quite some sub 55 solves already.
hence I will learn 2x2 CLL =P even before I try to learn all of 3x3 OLL...this is stupid..

 

[cubacca1972]

some minor update: i've seen the potential of cll as it produced quite some sub 55 solves already.
hence I will learn 2x2 CLL =P even before I try to learn all of 3x3 OLL...this is stupid..

Nice. Consider Roux for 3x3x3. That way, you can simply bypass the rest of the OLL cases.

Another alg:

r2 U r' u2 r U' r2 u2