Probability Thread

[advincubing]

I apologize if this has already been asked (I didn't see it in a quick search): If 4x4 OLL parity probability is 50% and 4x4 PLL parity probability is 50%, is it accurate to say that there is a 25% chance of having no parity (and 25% of having both parities)? Asked differently, are the two parities independent or somehow dependent?

 

[cmhardw]

I apologize if this has already been asked (I didn't see it in a quick search): If 4x4 OLL parity probability is 50% and 4x4 PLL parity probability is 50%, is it accurate to say that there is a 25% chance of having no parity (and 25% of having both parities)? Asked differently, are the two parities independent or somehow dependent?

Your thoughts are correct. The parities are independent of each other in reduction solving.

 

[TheCasualPerson]

I was dumbfounded 2 minutes ago when I got a scramble with correct edge orientation and a completed, correctly positioned line!?! My question is what are the chances of skipping the EOline stage from a scramble???

 

[Renslay]

I was dumbfounded 2 minutes ago when I got a scramble with correct edge orientation and a completed, correctly positioned line!?! My question is what are the chances of skipping the EOline stage from a scramble???

All edges oriented: 1/2^11 = 1 / 2048
DF and DB are in place: 1/12 * 1/11 = 1 / 132
Overall: 1 / 270336

 

[TheCasualPerson]

All edges oriented: 1/2^11 = 1 / 2048
DF and DB are in place: 1/12 * 1/11 = 1 / 132
Overall: 1 / 270336

Wow that is incredible! So basically I will never get a scramble like that again? ^_^

 

[Renslay]

Wow that is incredible! So basically I will never get a scramble like that again? ^_^

Well, there is always a chance to get it again.

 

[Jaycee]

If you knew that the first layer permutation would be solved then you can't really call it a PBL skip. In which case, it's just a LL skip which is 1/162

I was trying to figure what this probability was on my own during my study hall today because the person I've been teaching to solve some puzzles (he's got Pyraminx down so I'm teaching him 2x2) asked me. In my head, it came out to be 1/648. I knew that couldn't be right so I told him I'd tell him tomorrow. Can somebody explain to me why the probability of a LL skip on 2x2 is 1/162? I know it has to do with the possible orientations and permutations of the pieces, I just clearly went about my calculation the wrong way.

Oh and by the way I'm completely disregarding that Daniel's post was responding to something to do with Ortega and PBL

 

[Christopher Mowla]

I was trying to figure what this probability was on my own during my study hall today because the person I've been teaching to solve some puzzles (he's got Pyraminx down so I'm teaching him 2x2) asked me. In my head, it came out to be 1/648. I knew that couldn't be right so I told him I'd tell him tomorrow. Can somebody explain to me why the probability of a LL skip on 2x2 is 1/162? I know it has to do with the possible orientations and permutations of the pieces, I just clearly went about my calculation the wrong way.

Oh and by the way I'm completely disregarding that Daniel's post was responding to something to do with Ortega and PBL

You have got to divide 648 by 4 to get 162 because of AUF. So you did the work correctly.

 

[Jaycee]

Ahh, I see. Thanks.

 

[ben1996123]

I was trying to figure what this probability was on my own during my study hall today because the person I've been teaching to solve some puzzles (he's got Pyraminx down so I'm teaching him 2x2) asked me. In my head, it came out to be 1/648. I knew that couldn't be right so I told him I'd tell him tomorrow. Can somebody explain to me why the probability of a LL skip on 2x2 is 1/162? I know it has to do with the possible orientations and permutations of the pieces, I just clearly went about my calculation the wrong way.

Oh and by the way I'm completely disregarding that Daniel's post was responding to something to do with Ortega and PBL

3^4 orientations, 4! permutations /3 for corner twist parity, /4 for AUF
1/(3^4*4!/(3*4)) = 1/162

 

[Antonie faz fan]

Probeltie for no tips scrambled At pyraminx

 

[Username]

Probeltie for no tips scrambled At pyraminx

4 tips, all of them have 3 orientations: 3x3x3x3 = 3^4 = 81

so 1/81

I'm not 100% sure though

 

[ben1996123]

4 tips, all of them have 3 orientations: 3x3x3x3 = 3^4 = 81

so 1/81

I'm not 100% sure though

yeb ittuce 1/81

 

[advincubing]

void cube parity

I thought I had seen this before, but I can't find it on this thread: What is the probability of void cube parity? 1 in 2?

Chris' explanation in this thread of void cube parity was really helpful.

 

[kcl]

I thought I had seen this before, but I can't find it on this thread: What is the probability of void cube parity? 1 in 2?

Chris' explanation in this thread of void cube parity was really helpful.

Almost positive it's 50%.

 

[Lucas Garron]

I thought I had seen this before, but I can't find it on this thread: What is the probability of void cube parity? 1 in 2?

Chris' explanation in this thread of void cube parity was really helpful.

That depends how you solve. Roux solvers can basically avoid it.

However, if you pick an orientation for the centers at random (e.g. by solving cross and F2L without caring about the other pieces), the chance of parity is 1/2 for the usual reasons.

 

[penguinz7]

I don't know what the most rare is, but I find Z Perms fairly rare in my solves.

 

[pipkiksass]

I don't know what the most rare is, but I find Z Perms fairly rare in my solves.

PLLs? Pretty sure it's H perms and N perms at 1/72 and Z, E and maybe others are 1/36. Something about rotational symmetry??

 

[ThomasJE]

PLLs? Pretty sure it's H perms and N perms at 1/72 and Z, E and maybe others are 1/36. Something about rotational symmetry??

I believe you're right.

EDIT: http://www.kungfoomanchu.com/guides/andy-klise-3x3x3-speedcubing-guide-v4.pdf
Second page, on the right

 

[bubbagrub]

Sorry if this has been asked here already, but what are the probabilities of the PBL cases in Ortega? I seem to get the one with two T-perms about 75% of the time (i.e., the one that is described as UF/DF here: http://www.cubewhiz.com/ortegapbl.php)