# PLL skip? No problem, but...



## Neuromancer (May 19, 2009)

... did anyone of you get two PLL skips back-to-back? 

This just happened to me a few minutes ago. 

Greets


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## cmhardw (May 19, 2009)

(1/72)^2 = 1/5184 probability of that on a 3x3x3 cube. I think that is rare yes, but not unheard of.

Chris


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## OOOH (May 19, 2009)

Ive never had it, thats quite lucky. The chance is only: (1/72)^2 = 0.02%

EDIT: Chris was a bit faster


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## Neuromancer (May 19, 2009)

Thx for the replies.

But...
Are you sure, this can be calculated this way (1/72 x 1/72) ? 

Thinking: 
If someone's exercising 100 solves a day, this should happen nearly every 50 days. That's a period not too big, so this should happen to every cuber who's training in a normal way. Even if someone's training just 50 times a day, this should happen every 100 days, so this would be three times a year. 

Did I overlook a fault? 

Greets


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## Stefan (May 19, 2009)

In other words, if just 100 cubers do just 50 solves a day, you can expect this to happen once a day. So nothing worth mentioning.


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## qazefth (May 19, 2009)

I once got 3 PLL skip in a row, but too bad I did time it. And I dont think this as lucky or something, because hand scrambled it, but I got different OLL each time.


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## AvGalen (May 19, 2009)

qazefth: you don't consider 3 PLL skips in a row lucky????


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## qazefth (May 19, 2009)

yeah maybe, coz it was hand scramble, hmm, one second tought, maybe it is lucky, hehe


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## blah (May 19, 2009)

AvGalen said:


> qazefth: you don't consider 3 PLL skips in a row lucky????



Technically, that's as lucky as getting 3 H perms in a row, or any combination of 3 H perms or PLL skips in a row


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## AvGalen (May 19, 2009)

blah said:


> AvGalen said:
> 
> 
> > qazefth: you don't consider 3 PLL skips in a row lucky????
> ...


No, technically it is just as probable. Lucky is not a technical term.

Let's say that the chances of winning the lotery and chances of getting hit by lightning are both 1/72. I would consider winning the lotery once lucky and winning it 3 times in a row really really really lucky.
I wouldn't consider getting hit by lightning lucky.....
And everyone that calls getting hit by lightning 3 times in a row really really really *lucky* must be .... the devil


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## DAE_JA_VOO (May 19, 2009)

qazefth said:


> I once got 3 PLL skip in a row, but too bad I did time it.



Yeah I'm pretty sure I've had three PLL skips in a row too. I was driving one day and i remember thinking "Man, how many PLL skips am I going to get? or something to that effect. Like I said though, i'm pretty sure, but not 100%. I've definitely had two PLL skips in a row though.


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## MTGjumper (May 19, 2009)

I've had 3 OLL skips in a row. That's (1/216)^3 = 1/10077696. Yeah, that's pretty rare, although I did get two OLL skips in a row on Saturday too


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## ThatGuy (May 19, 2009)

my first entire LL skip was on a 4x4 with no AUF.


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## Cride5 (May 19, 2009)

Entire LL skips on ZZ solves seem to be quite common, I've had 3 so far - none timed unfortunately 

I'm guessing the chances of a LL skip with edges pre-oriented would be 1/#ZBLL cases = 1/494 = ~0.2%, I may be wrong tho.


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## Johannes91 (May 19, 2009)

Cride5 said:


> I'm guessing the chances of a LL skip with edges pre-oriented would be 1/#ZBLL cases = 1/494 = ~0.2%, I may be wrong tho.


This is a common mistake cubers make. Ignoring AUF, there are actually 27*72=1944 different ZBLL positions, but some are similar, like T-perm, y T-perm, y2 T-perm, and y' T-perm, which can all be solved with the same alg. So the probability to skip ZBLL is 1/1944 ≈ 0.05%.

Some cases are symmetric, like H-perm and N-perm, so they have only 1 or 2 different rotations, which is why the total number is a bit less than 4*494=1976.


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## Swordsman Kirby (May 19, 2009)

Johannes91 said:


> Cride5 said:
> 
> 
> > I'm guessing the chances of a LL skip with edges pre-oriented would be 1/#ZBLL cases = 1/494 = ~0.2%, I may be wrong tho.
> ...



I expected there to be more than just 32 symmetric positions...


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## SimonWestlund (May 19, 2009)

I've had 3 PLL skips in a row in an average of 12.. the rest of the average sucked though..

I've also had OLL skip, PLL skip, OLL skip


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## Cride5 (May 19, 2009)

Johannes91 said:


> Cride5 said:
> 
> 
> > I'm guessing the chances of a LL skip with edges pre-oriented would be 1/#ZBLL cases = 1/494 = ~0.2%, I may be wrong tho.
> ...



Are you counting a solved LL requiring AUF as an LL-skip as well? Ie. would the probability of an LL-skip, including cases requiring U, U' and U2 still be 1/1944, or would it be 4/1944??


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## Yes We Can! (May 19, 2009)

Rama Temmink got two in a row:


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## irontwig (May 19, 2009)

Cride5 said:


> Johannes91 said:
> 
> 
> > Cride5 said:
> ...



1/1944.


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## cookingfat (May 19, 2009)

I once got 2 PLL skips in a row, it certainly felt lucky. And I once got a LL skip but wasn't timing it.


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## amostay2004 (May 19, 2009)

Actually the title of the thread seems to imply that there's a problem with having 2 PLL skips in a row..

Anyway, I'm sure every cuber will happen to have 2 or more PLL skips in a row in their cubing lifetime...if they cube long enough...


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## (X) (May 19, 2009)

Most things have a very low probability


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## Dene (May 19, 2009)

I got two in a row... in competition.


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## Johannes91 (May 19, 2009)

Cride5 said:


> Are you counting a solved LL requiring AUF as an LL-skip as well? Ie. would the probability of an LL-skip, including cases requiring U, U' and U2 still be 1/1944, or would it be 4/1944??


I ignored AUF, i.e., counted all groups of 4 positions a U-move away from each other as 1 position. Counting them separately, there are 16 T-perms, the number is 3^3 * 4! * 4! / 2 = 7776 = 4 * 1944, and the probability is 4/7776 = 1/1944.



amostay2004 said:


> Anyway, I'm sure every cuber will happen to have 2 or more PLL skips in a row in their cubing lifetime...if they cube long enough...


... and because everybody uses a method that ends with PLL.

Edit: Also, I'm 100% sure I will have over 9000 F3L skips in a row, _if I cube long enough_.


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## Cride5 (May 20, 2009)

Johannes91 said:


> Cride5 said:
> 
> 
> > Are you counting a solved LL requiring AUF as an LL-skip as well? Ie. would the probability of an LL-skip, including cases requiring U, U' and U2 still be 1/1944, or would it be 4/1944??
> ...



Aah, right. I get what you're saying! I like your example. There are four possible T perms, and for each one, there are four ways it can be rotated on the U face, giving 16 distinct cases for T-perm.

Just to make sure I'm getting the theory>

There are 4 corners, each with 3 possible orientations, combined that's 3*3*3*3 = 3^4 possibilities, but because only a third of corner orientations are reachable, that's (3^4)/3 = 3^3.
There are 4! ways to arrange (permute) the four corner pieces, and 4! ways to permute the edge pieces which gives 4!*4! ways to permute them independently. However, since only an even number swaps is possible only the even permutations are valid, giving (4!*4!)/2.
Thus the total number of cases is (3^3) * (4!*4!)/2 = 7776, since one of these cases involves the LL solved, and three more involve the LL solved, but rotated, the chances of a ZBLL skip = 4/7776 = 1/1944

... sorry for the repetition, just had to be sure


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## Johannes91 (May 20, 2009)

Yep, that's it. One nitpick: it's better to use "ZBLL" instead of "LL", the latter usually includes cases where EO isn't solved (adds a factor of 2^3).


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## Hadley4000 (May 20, 2009)

Not too long ago(few days I think) I got H, PLL skip, N. Same odds.


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## royzabeast (May 20, 2009)

Does it actually matter how many moves are made in a scramble? When I give it to somebody for a scramble and they don't know much about the cube, they always try to make it as scrambled as possible, they try to have it so that the same color is never 3 in a row. But does that actually make a difference between a quick 10 move hand scramble? More chance of a skip or easier F2L?


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## Cride5 (May 20, 2009)

Johannes91 said:


> Yep, that's it. One nitpick: it's better to use "ZBLL" instead of "LL", the latter usually includes cases where EO isn't solved (adds a factor of 2^3).



Fixed, cheers


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## Anthony (May 20, 2009)

Dene said:


> I got two in a row... in competition.



Did you really?! 
That's awesome.

I don't know if that was meant to be a joke, but if it wasn't.. Here's my guess as to which two solves it was.. 13.75, 13.92, your last two solves during the first round of Discovery Science Center. Only guessing those because they were much faster then your other solves at that competition and it helped you break your AuR.


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## ManasijV (May 20, 2009)

Rama Temmink even got it on tape once.


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## Dene (May 20, 2009)

ManasijV said:


> Rama Temmink even got it on tape once.



Did you even bother to read any of the posts in this thread?


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## jcuber (May 20, 2009)

Dene said:


> ManasijV said:
> 
> 
> > Rama Temmink even got it on tape once.
> ...



Do you even have to ask this question? j/k


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## ManasijV (May 28, 2009)

jcuber said:


> Dene said:
> 
> 
> > ManasijV said:
> ...



are you so pathetic to interpret that? i missed that page that was my fault. there's no need for u to reply in such a manner for that.


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## soccerking813 (May 28, 2009)

I got 3 of the same N-perms in a row. Same odds, only the worst things possible, because I have forgotten the algs.


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## Kian (May 28, 2009)

my brother got two no parity plls skips on 4x4 in competition. that was pretty nuts.


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