Rare Occurences

[Zane_C]

Today about an hour or so ago my personal 2x2x2 best was 6.25 with a PBL skip (I use ortega).
I started doing some solves not long ago and the first several solves were amazing (for me anyway)

(4.425), 6.540, 5.808, 5.283, (12.623) Avg of 5 = 5.877

The first 4 were very lucky, infact 4 PBL skips in a row!
So my AO5 suddenly reduced below my former personal best!
(by the way, I did not deliberatly manipulate the permutation of the first layer, the orientated first side just happened to be permuted)

So what is the probability of a PBL skip anyway?

I was also wondering about some rare occurances people here have experienced.

Zane.

 

[iSpinz]

sub-5 2x2 with lbl?

 

[Zane_C]

sub-5 2x2 with lbl?

Ortega, no I wouldn't call it layer by layer.
Yeah I guess it may of been layer by layer, but it was unintented.

 

[iSpinz]

sub-5 2x2 with lbl?

Ortega, no I wouldn't call it layer by layer.
Yeah I guess it may of been layer by layer, but it was unintented.

I mean I had a sub-5 2x2 with LBL.

 

[Zane_C]

Oh, that's really good.

 

[4Chan]

3 T Perms within an average of 5.

I actually considered putting that in the accomplishment thread.

EDIT: My chances of a single T perm is around .002136752137% or so, just to give you an idea of the profundity.

 

[Thomas09]

Assembling a cube randomly and getting a PLL skip.

 

[KConny]

Thomas09: I think it's 1/(2*3*2*72) = 1/864. I'm a right?

 

[Zane_C]

Thomas09: I think it's 1/(2*3*2*72) = 1/864. I'm a right?

Yes I would say so, 1/12 assembled cases are solvable, probability of PLL skip = 1/72 = (12x72) = 1/864

 

[qqwref]

How about messing up OLL horribly, fixing it by putting F2L back together and doing OLL again... and then getting a PLL skip.

The probability isn't all that low, but it made me WTF all the same.

 

[Meep]

I've gotten a last 4 edges skip on 5x5 once =P Same with last two centers skip.

 

[Dene]

How about messing up OLL horribly, fixing it by putting F2L back together and doing OLL again... and then getting a PLL skip.

The probability isn't all that low, but it made me WTF all the same.

How about messing up OLL and then doing another OLL and getting PLL skip, just after getting a PLL skip in the previous solve... in competition

 

[Thomas09]

How about messing up OLL horribly, fixing it by putting F2L back together and doing OLL again... and then getting a PLL skip.

The probability isn't all that low, but it made me WTF all the same.

OMG I just got that only it was an OLL skip.

 

[Zane_C]

How about messing up OLL horribly, fixing it by putting F2L back together and doing OLL again... and then getting a PLL skip.

The probability isn't all that low, but it made me WTF all the same.

OMG I just got that only it was an OLL skip.

That's 1/216 x 1/216 = 1/46656. That's rare.

Also, does anyone know what the probability for a PBL skip is?

 

[kinch2002]

Also, does anyone know what the probability for a PBL skip is?

If you make the first face randomly (i.e. don't try to get permutation right on purpose) then you have a 1/6 chance of each layer being solved, so that's 1/36 for a PBL skip. If you don't want to have to AUF either it would be 1/144.

Yesterday I got a 2 move double x-cross after redution on my 4x4x4

 

[Zane_C]

Thanks kinch2002, so (1/36)^4=1/1,679,616 probability of 4 PBL skips in a row (exluding AUF).
THAT'S RARE!

 

[kinch2002]

(1/36)^4=1/1,679,616 probability of 4 PBL skips in a row (exluding AUF).
THAT'S RARE!

That is indeed very rare. One thing to consider is whether you influenced the first face at all. For example, try this scramble with white on U and green on F - R U2 F' R F R2. Now at first glance you would spot the green face with 3 pieces solved.
I think the first thing I would think of is to insert the last green piece with x2 R U R' U' R U R'.
This certainly isn't the best solution though, because x F R U' R' also solves green but without the permutation correct.
However, if you glance at white you'll see that you have a 2 move non-permuted first layer.

This is just to demonstrate how we might be influencing the permutation of the first layer without realising it - we tend to spot those connected pieces easier than ones that won't connect with the right permutation. As a result of this we often take the option of making a permuted first layer even though there are easier first layers to be made.

Still, this would only the increase the chance of making a correct first layer to maybe 1/4 at the most, which would give (1/24)^4 = 1/331,776 of 4 PBL skips - significantly greater chance than before.

Please don't take this as me accusing you of trying to influence the first layer - it's just a few thoughts I had!

 

[Owen]

Thanks kinch2002, so (1/36)^4=1/1,679,616 probability of 4 PBL skips in a row (exluding AUF).
THAT'S RARE!

 

[adimare]

Thanks kinch2002, so (1/36)^4=1/1,679,616 probability of 4 PBL skips in a row (exluding AUF).
THAT'S RARE!

That's not the probaility of getting 4 PBL skips in a row, that's the probability of doing exactly 4 solves and getting PBL skips in all of them.

 

[eastamazonantidote]

Triple multislot while scanning for the first pair with a PLL skip to finish. That one was special.

Finishing the VHF2L with a R' F R F', have the cube pop out of your hand and hit the spacebar, stopping the solve. And the cube is solved. Not even a +2. Happened yesterday during my avg. of 100. I couldn't stop laughing.

What is the probability of a LL skip with ZBF2L/ZZF2L/Petrus? For every OLL? I think I remember hearing OLL skip is 1/76. I'll search it but thought I could ask here.