Why is it so hard to solve 5x5x5 BLD fast?

[Mike Hughey]

I hope someone finds this interesting. It was just a thing I was curious about, and I thought I'd share.

One thing I have always wondered is why a 5x5x5 BLD is as hard to solve fast as it is. If you just look at the pieces required for a 5x5x5 BLD, you have to solve the following:
1. The same pieces as a 4x4x4: 24 wings, 24 X-centers, 8 corners. It is true here that the 4x4x4 may be reoriented to decrease the number of X-centers that actually need solving, but that probably saves no more than 1 or 2 commutators on average.
2. The central edges. For many methods (such as M2), these are practically the same as solving the edges of a 3x3x3, so for a good solver, they probably shouldn't take more than about a minute to solve.
3. The +-centers. These are certainly no harder than the X-centers; I actually find the commutators for these slightly easier to "see" than the commutators for the X-centers.

So if you add all of this up, it's considerably less than the amount you must solve to solve 2 4x4x4's. So why is it, then, that the records of the best people don't have 5x5x5's solved quicker than 2 4x4x4's? Chris Hardwick is the most obvious example - his record for 4x4x4 is 6:20, and his record for 5x5x5 is 17:22. Of course, it is true that the 5x5x5 record is really not that fast of a solve for him, so it's probably not fair, but if you compare his personal bests on his webpage, he has a best 4x4x4 of 5:02 and a best 5x5x5 of 12:44. So, for Chris at least, his 4x4x4 is significantly more than twice as fast as his 5x5x5.

For my one and only competition solves of 4x4x4 and 5x5x5, I had a 5x5x5 time almost exactly double that of my 4x4x4. But that is unusual for me - at home I usually have average ratios that aren't that different from Chris's best home ratios. And Rafal and Tim's times seem similar on the online competition (but I know Tim hasn't done many 5x5x5's, so that's probably not fair). (Daniel and Istvan don't seem to fit this, though, based on their competition times.)

Anyway, I wondered why this is, so I took some splits on a 4x4x4 and 5x5x5 solve. And wouldn't you know it - my 5x5x5 time was faster than double my 4x4x4 time. (And it would have been my fastest time ever on a 5x5x5 if I had gotten it right.) I had 2 central edges flipped (dratted problem with M2), but other than that I got the 5x5x5 right, and I got the 4x4x4 correct. Here were my splits:

5x5x5:
memo centrals: 96.139
memo +: 114.560
double-check centrals, +: 64.796
memo wings: 119.763
memo X: 116.592
double check everything so far: 114.576
memo corners: 34.608
solve corners: 57.827
solve X: 144.669
solve wings: 169.794
solve +: 163.356
solve centrals: 80.608


4x4x4:
memo edges: 218.949
memo centers: 66.983
double-check everything so far: 50.874
memo corners: 28.125
solve corners: 59.202
solve centers: 122.248
solve edges: 150.575

I obviously struggled to memo the edges on the 4x4x4 on this one - that's why the 4x4x4 was this slow. Note that that time also includes the time spent orienting the cube - I forgot to split that out separately.

So what were the apparent holdups on the 5x5x5?:
1. I spent a whole 2 additional minutes double-checking memo. I guess that's a big part of it.
2. I spent significantly longer on both memorizing and solving centers on the 5x5x5 (X or +, take your pick). I had fewer centers to solve on the 4x4x4, due to orienting the cube (only 15 centers to solve), so I guess this is a bigger factor than I thought it was - being able to orient the 4x4x4 really helps!
3. My central edges took almost 3 minutes to memo + solve. That seems outrageously long to me. I suspect with practice that can come way down, and come closer to matching my 3x3x3 times.

I know that my most recent drop in 5x5x5 times happened when I started forcing myself to speed up when solving + centers; I discovered that I had a bad habit of going really slow on the + centers because I was tired and close to done. So that's no longer a place where I can speed up, but I think the central edges are a good place I can make improvement, and I think I should work on the time spent double-checking memo.

If anyone out there would care to comment on my splits with ideas of what I should work on, I'd appreciate it, but I mainly just wanted to share what I found.

 

[Pedro]

I've only tried it once, but I know I can do much faster

my memo was kinda slow because I've never done it before, so the +centers were kinda new to me...I wasn't sure about which way to go with them, but used my edges' images...and the solving part was also slow...I mean...more than 16 minutes? Chris can memorise and solve in that time

the 5x5 is probably slower because you have more data to memorise and/or check, and more stuff to do while solving, leading to more thinking time and time lost with execution mistakes, lockups, whatever

 

[masterofthebass]

I don't think it's all about the memorization. I've done timings if sighted executions, and my 4x4 is around 3:xx and my 5x5 is around 7-8. Obviously for me, the memorization on the 5x5 would be much harder, because my memo sucks. I really think that the memorization time is what really kills the 5x5 comparison.

 

[Nghia]

Hey Mike and Pedro, and Dan,

Nice to see a topic about 5x5 BLD, I'm also preparing myself for an attempt soon. Everything went good so far, I'm still trying another method to solve the central edges, since I haven't found any 3-cycle algorithm for this

Oh and btw, does anybody know a program like Cube Explorer for big cubes ?

I still haven't got the patience to make my letter pairs list, so I guess I'll be attempting this with words on the fly

The split idea was very nice and wow, nice memorization time !

 

[Mike Hughey]

I still haven't got the patience to make my letter pairs list, so I guess I'll be attempting this with words on the fly

The split idea was very nice and wow, nice memorization time !

I used the words on the fly for about 5 months before I started working on a letter pair list. Of course, I was much slower before the list, but it worked just fine - it was just slow. The list slashed 3 or 4 minutes off the memo time for me on the 4x4x4 almost instantly. Good luck on your first 5x5x5 attempt - I hope you get it!

Dan, it really seems like the difference in centers is a pretty big deal. I've also noticed that my 4x4x4 times fluctuate more than do my 5x5x5 times. That's probably largely a difference between lucky and unlucky centers. Lucky centers are pretty rare on a 5x5x5, but common on a 4x4x4.

 

[masterofthebass]

Nghia, there's easy MU versions of the U perm.

M2' U M U2 M' U M2' and
M2' U' M U2 M' U' M2'

There's other variations, like if you make the M and M' and vice versa, it does the other 2 U perms.

 

[Nghia]

Thanks Mike and Dan,

I'm in this period where I have to work for my exams here, so I think I'll leave the list for this summer Right now I'm focusing on 3x3 BLD, where I just got a new PB : 2:09 !!


As for the 3-cycle algorithms, I meant one that would only affect the central edges, not the whole wing. I'm thinking of using Orient then Permute with commutators, or just simply freestyle commutators, but I'd have to work on that ! But thanks anyway Dan

I'm also practicing speed 4x4 and 5x5, and damn, i'm at 3 minutes for 4x4 and 7 for 5x5 !! Looks like I'll need some advices from you Dan

 

[masterofthebass]

nghia, that algorithm works... the M moves would be the inner layer only. not the 3 inner layers like you would use for a 3x3 alg. any MU alg works for the central edges only.

 

[Lucas Garron]

I try to approach 5x5x5 in this optimistic way, but it doesn't seem to work.
A dew fast comments:

1) There is more time / are more cycles to make memo mistakes, and more colors don't really make memo easier.
2) 5x5x5's are kinda annoying to turn well. I broke an X-center on my Rubik's, and my Eastsheen is getting too loose, so I'm clamoring for a white one or a VC now. But care definitely comes in.
3) Trying to keep more in your head should be quadratic-ishly hard, right? Shouldn't be too much, though.
4) More nasty parity stuff, which slows the first few attempts significantly.

I wanna see what happens once my 5x5x5 attempts become more disposable (4x4x4 is getting there).

 

[Mike Hughey]

You make some interesting points here.

I try to approach 5x5x5 in this optimistic way, but it doesn't seem to work.
A dew fast comments:
1) There is more time / are more cycles to make memo mistakes, and more colors don't really make memo easier.

For me, the biggest deal is keeping track of where the centers are. I like the fact that the 5x5x5 has that nice piece in the center to tell where each color is supposed to go. For 4x4x4's, I pretty much always have to have at least one red center in the front (that's how I hold it), or else I start messing up my wing tracing. So I think the colors part of this is better on 5x5x5 than 4x4x4, for me. But I will agree there's more to make mistakes on; I'm not surprised 5x5x5 has worse accuracy - I'm just surprised it's slower.

2) 5x5x5's are kinda annoying to turn well. I broke an X-center on my Rubik's, and my Eastsheen is getting too loose, so I'm clamoring for a white one or a VC now. But care definitely comes in.

I'm lucky here - all 3 of my Eastsheens are still pretty nice, thanks to Kenneth's mod/fix (if you have a loose Eastsheen, you should REALLY try it - it will make a big difference!). I will admit that I think being careful probably adds 15 to 30 seconds per phase on solving centers (and maybe a little on edges too).

3) Trying to keep more in your head should be quadratic-ishly hard, right? Shouldn't be too much, though.

I've found that with multiBLD, once you get past 4 or 5 cubes, it doesn't seem to get that much harder - it just takes longer (and about the same amount longer per cube you add, too - the time per cube no longer seems to increase much). Several other people who do multiBLD have made the same comment.

4) More nasty parity stuff, which slows the first few attempts significantly.

I wanna see what happens once my 5x5x5 attempts become more disposable (4x4x4 is getting there).

I'll agree with the parity thing, but I'm thinking about once you're past that. I've already gotten to the point where I think of my 5x5x5 attempts as disposable (I threw away a pretty good effort on this one - I wouldn't have counted it if I got it right because I had my eyes open - I was solving under the table and watching the timer to make sure I did the splits right).

 

[cmhardw]

I can answer at least why it's harder to solve 5x5BLD in competition, in my opinion, and that is that the format (best of 1) is very intimidating for me.

I once analyzed how I have to solve based on the various formats for 3x3x3 BLD assuming I want to ensure I have the best possible chance to always achieve a solve in competition.

I want the probability that I solve a cube in competition to be as close to 100% as possible.

Let's assume 3x3x3 is best of 3 and that I solve the cube, in that particular competition, with a probability of success of p. The odds that I solve at least one cube is 1-(1-p)^3

If I want to ensure I solve a cube in that competition, I will accept no less than a 99% chance that I get a solve that round.

1-(1-p)^3 >= 0.99
p^3-3p^2+3p-0.99 >= 0
p >= 0.785

And so you must solve with a greater than 78% accuracy rate on each solve (I mentally think 80%) in order to nearly guarantee you walk away from that competition with a successful solve. Obviously if you get a solve successfully before your 3rd solve, then this is your "safety" and you can solve as fast as you want after that.

For 2 solves you can do the same thing. I will assume that for this particular competition I solve with a probability of success of p. I will accept no less than a 99% chance that I get at least 1 solve.

1-(1-p)^2 >= 0.99
-p^2+2p-0.99 >= 0
p >= 0.9

so you must solve with a 90% accuracy rate on both solves to ensure you walk away from that competition with a success. Obviously if you get the first solve then that is your "safety" so go as fast as you please on the second solve.

For best of 1 format I treat it the same way. Nothing has changed in that I still will accept no less than a 99% chance that I walk away from that competition with a success. So you must solve with a 99% accuracy rate for that solve, or really just try as best you can to get the solve successfully.

I train that way at home too, because I don't see any point in going for super fast solves and making that my habit. This makes me afraid of falling into those same habits in competition. Yes I may miss out on getting a fast time in competition, but I will get a solve successfully (hopefully). My experience in the 5x5x5 BLD event at Worlds '07 stung quite a bit to DNF the one solve, and I don't want to experience that feeling again. So now I train for 100% success on that cube.

For 4x4x4 since it's almost always a format best of 2 in competition in the US, then I shoot for 90% accuracy rate (because I want to ensure I still have a 99% chance to get a solve). Obviously that isn't much riskier than 99% accuracy rate, but it does still allow for more risks, trying to go faster, etc..

Just my opinions on this issue. I do think that the 5x5x5 BLD is much more of a challenge than 4x4x4 BLD, and 6x6x6 BLD was much more of a challenge than 5x5x5 BLD. I think I can sub-30 the 6x6x6 with lots more practice, so my time of 1 hour 45 minutes is just ridiculously slow in my opinion, but I was shooting for 99.999999999999% success rate on that solve lol.

That is the reason why my particular times are much slower for 5x5x5 than my 4x4x4, but I think that the mental effort required and time used will increase either exponentially or as a power function as the cube size increases.

Chris

 

[Mike Hughey]

Wow, Chris - a 99% accuracy on 5x5x5 BLD in competition is a pretty tall order. I go pretty hard for accuracy in general, and yet I am only now starting to approach a 50% accuracy on 5x5x5 BLD at home. Until you can manage that at whatever speed, obviously you're just stuck with your "really just try as best you can to get the solve successfully." So I guess that's what I'm stuck with.

About the only things I ever do that seriously decrease my accuracy with a BLD solve are:
1. to start solving before I have it adequately memorized - sometimes a single pass simply isn't good enough; I usually know when this is true, though, and this rarely happens;
2. to try to move too quickly or think too hard about the next pieces, losing my place in my moves; this happens too often to me for my tastes - probably about 10% of my solves.
The rest of my failures are just simple errors - usually I cycle the wrong piece, or sometimes I cycle the wrong direction, or occasionally I forget to undo a setup move or else I undo a setup move twice (I did the latter yesterday).

I really need to try hard for a successful 5x5x5 next time; even a really slow one for me now would still be 15 minutes faster than the one I got in Virginia. But I honestly thought I had that one in Atlanta - I was so sure of it; pity it was completely scrambled.

Thank you for your computational analysis of this - I think those numbers will be very useful to me!

 

[cmhardw]

Wow, Chris - a 99% accuracy on 5x5x5 BLD in competition is a pretty tall order. I go pretty hard for accuracy in general, and yet I am only now starting to approach a 50% accuracy on 5x5x5 BLD at home. Until you can manage that at whatever speed, obviously you're just stuck with your "really just try as best you can to get the solve successfully." So I guess that's what I'm stuck with.

Hey Mike,

For the record I think 99% for 5x5x5 is also a tall order, and I agree with you to just try as best as possible for a success.

About the only things I ever do that seriously decrease my accuracy with a BLD solve are:
1. to start solving before I have it adequately memorized - sometimes a single pass simply isn't good enough; I usually know when this is true, though, and this rarely happens;
2. to try to move too quickly or think too hard about the next pieces, losing my place in my moves; this happens too often to me for my tastes - probably about 10% of my solves.
The rest of my failures are just simple errors - usually I cycle the wrong piece, or sometimes I cycle the wrong direction, or occasionally I forget to undo a setup move or else I undo a setup move twice (I did the latter yesterday).

I've noticed that my errors tend to be cycling to the wrong pieces, or just dumb things like twisting an x-center mid-algorithm and not knowing where I am. Sometimes when executing a BAB'A' commutator I do the B part of a commutator 3 times. The first B, the later B' then a final B after the A' for good measure ;-)

Also, Daniel Beyer and I noticed that when we cycle to the wrong piece (this is freaky) we nearly every single time replaced a hard cycle in our, correct, memo with a much easier and faster cycle using a piece close to the real one. I find this fascinating, it's like subconsciously wanting a fast time your brain replaces hard cycles with easy ones. Seriously, this has happened to Daniel and I often enough (when our error is cycling to a wrong piece) to be freaky, and suggests to me something neat is going on subconsciously with BLD cubers' brains.

I really need to try hard for a successful 5x5x5 next time; even a really slow one for me now would still be 15 minutes faster than the one I got in Virginia. But I honestly thought I had that one in Atlanta - I was so sure of it; pity it was completely scrambled.

Thank you for your computational analysis of this - I think those numbers will be very useful to me!

I felt the same way about my solve at worlds, my heart was pounding in my chest as I did the final moves, and opened my eyes to quite a few pieces unsolved :-(

Also glad the analysis helps you. For the record I *have* DNF'd all solves in a 3x3 BLD competition round using this strategy, at Chattahoochee 2007. I've been using this strategy pretty much since I started official BLD cubing in 2004 and that is the only time I've ever DNF'd all solves in a competition round of 3x3x3 BLD.

Chris

 

[Nghia]

nghia, that algorithm works... the M moves would be the inner layer only. not the 3 inner layers like you would use for a 3x3 alg. any MU alg works for the central edges only.

Oh....silly me, sorry Dan.....Thank you very much indeed !

How come I haven't thought of that !!!

 

[Mike Hughey]

I've noticed that my errors tend to be cycling to the wrong pieces, or just dumb things like twisting an x-center mid-algorithm and not knowing where I am. Sometimes when executing a BAB'A' commutator I do the B part of a commutator 3 times. The first B, the later B' then a final B after the A' for good measure ;-)

I just got lost in a commutator mid-algorithm on my first 5x5x5 for this week's competition, and I'm pretty sure that accounted for all the mistakes. I think I was psyched out reading your comments about 99% accuracy - I was trying too hard to get it right, and it threw off my rhythm. Maybe I'd better forget what you said...

Also, Daniel Beyer and I noticed that when we cycle to the wrong piece (this is freaky) we nearly every single time replaced a hard cycle in our, correct, memo with a much easier and faster cycle using a piece close to the real one. I find this fascinating, it's like subconsciously wanting a fast time your brain replaces hard cycles with easy ones. Seriously, this has happened to Daniel and I often enough (when our error is cycling to a wrong piece) to be freaky, and suggests to me something neat is going on subconsciously with BLD cubers' brains.

I have certainly done that some, but I'm not sure if it's something I regularly do. I've never really thought about it that way before. I'll start watching for it and see if it's true for me. For the record, that 5x5x5 I just messed up - I switched to an easier cycle, then I realized I had done it and tried to backtrack; apparently I messed up backtracking. (I either forgot an r2 or did an extra one.) So it fit your hypothesis.

 

[Pedro]

I've done that too! lol

the brain just follows the easier way, tricking us

and, Chris, I was thinking about your 100% accuracy thing...(or getting at least one correct)

I will sure go for accuracy on my first 4x4 bld try (or until I get one)...but...why don't you go for speed? I mean...you already have quite a few successful solves, you have the WR...if I were you, I'd rather try to beat my WR than to get all successful solves

oh, well...that's just me...but I'd really do that

 

[ROOT]

i dont know if any of yall had this problem, but when i did my first attempt i had trouble on the middle edges. I forgot to orient them at first so i had to backtrack. as well i couldnt use my normal algorithm which also made me kinda overcautious.

 

[joey]

Don't orient them then, simple as.

 

[mrCage]

Well, i'm simpy going to answer the topic title, not commenting on the first post itself. The bigger the cube the harder to BLD solve - simply due to the increased number of cubies with increased size. There is more pieces/cubiesto memorize. And harder to avoid making mistakes because far more algorithms is required. Also keeping track of what is done and what remains to be solved becomes harder with increased cube size. The same reasoning is valid for larger puzzles (more layers, not physical size) of all kinds. Pyraminx, megaminx, square-1 etc etc ...

-Per

 

[alexc]

@Per

I think your arguement has some valid points, but I have one problem with it. I don't think there are "far" more algs to solve 5x5 blind. In fact, I did a sighted 5x5 blind on gabasoft and all the algs I needed I already knew because of 3x3/4x4 blind. So I don't think having "far" more algs is a reason.